diff --git a/draft-irtf-cfrg-cpace-13/draft-irtf-cfrg-cpace.html b/draft-irtf-cfrg-cpace-13/draft-irtf-cfrg-cpace.html new file mode 100644 index 0000000..c3323c1 --- /dev/null +++ b/draft-irtf-cfrg-cpace-13/draft-irtf-cfrg-cpace.html @@ -0,0 +1,6421 @@ + + + + + + +CPace, a balanced composable PAKE + + + + + + + + + + + + + + + + + + + + + + + + + +
Internet-DraftCPaceOctober 2024
Abdalla, et al.Expires 18 April 2025[Page]
+
+
+
+
Workgroup:
+
CFRG
+
Internet-Draft:
+
draft-irtf-cfrg-cpace-latest
+
Published:
+
+ +
+
Intended Status:
+
Informational
+
Expires:
+
+
Authors:
+
+
+
M. Abdalla
+
Nexus - San Francisco
+
+
+
B. Haase
+
Endress + Hauser Liquid Analysis - Gerlingen
+
+
+
J. Hesse
+
IBM Research Europe - Zurich
+
+
+
+
+

CPace, a balanced composable PAKE

+
+

Abstract

+

This document describes CPace which is a protocol that allows two +parties that share a low-entropy secret (password) to derive a strong shared key without +disclosing the secret to offline dictionary attacks. +The CPace protocol was tailored for constrained devices and +can be used on groups of prime- and non-prime order.

+
+
+

+Discussion Venues +

+

This note is to be removed before publishing as an RFC.

+

Discussion of this document takes place on the + Crypto Forum Research Group mailing list (cfrg@ietf.org), + which is archived at https://mailarchive.ietf.org/arch/search/?email_list=cfrg.

+

Source for this draft and an issue tracker can be found at + https://github.com/cfrg/draft-irtf-cfrg-cpace.

+
+
+
+

+Status of This Memo +

+

+ This Internet-Draft is submitted in full conformance with the + provisions of BCP 78 and BCP 79.

+

+ Internet-Drafts are working documents of the Internet Engineering Task + Force (IETF). Note that other groups may also distribute working + documents as Internet-Drafts. The list of current Internet-Drafts is + at https://datatracker.ietf.org/drafts/current/.

+

+ Internet-Drafts are draft documents valid for a maximum of six months + and may be updated, replaced, or obsoleted by other documents at any + time. It is inappropriate to use Internet-Drafts as reference + material or to cite them other than as "work in progress."

+

+ This Internet-Draft will expire on 18 April 2025.

+
+
+ +
+
+ ▲

+Table of Contents +

+ +
+
+
+
+

+1. Introduction +

+

This document describes CPace which is a balanced Password-Authenticated-Key-Establishment (PAKE) +protocol for two parties where both parties derive a cryptographic key +of high entropy from a shared secret of low-entropy. +CPace protects the passwords against offline dictionary attacks by requiring +adversaries to actively interact with a protocol party and by allowing +for at most one single password guess per active interaction.

+

The CPace design was tailored considering the following main objectives:

+ +
+
+

+1.1. Outline of this document +

+
    +
  • +

    Section 3 describes the expected properties of an application using CPace, and discusses in particular which application-level aspects are relevant for CPace's security.

    +
    • +
  • +

    Section 4 gives an overview of the recommended +cipher suites for CPace which were optimized for different types of cryptographic +library ecosystems.

    +
    • +
  • +

    Section 5 introduces the notation used throughout this document.

    +
    • +
  • +

    Section 6 specifies the CPace protocol.

    +
    • +
  • +

    The appendix provides code and test vectors of all of the +functions defined for CPace.

    +
    • +
+

As this document is primarily written for implementers and application designers, we would like to refer the theory-inclined reader to the scientific paper [AHH21] which covers the detailed security analysis of the different CPace instantiations as defined in this document via the cipher suites.

+
+
+
+
+
+
+

+2. Requirements Notation +

+

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL +NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", +"MAY", and "OPTIONAL" in this document are to be interpreted as +described in BCP 14 [RFC2119] [RFC8174] when, and only when, they +appear in all capitals, as shown here.

+
+
+
+
+

+3. High-level application perspective +

+

CPace enables balanced password-authenticated key establishment. I.e. with CPace the parties start the protocol with a shared secret octet string, namely the password-related string (PRS). +PRS can be a low-entropy secret itself, for instance a clear-text password encoded according to [RFC8265], or any string derived from a common secret, for instance by use of a key derivation function.

+

Applications with clients and servers where the server side is storing account and password information in its persistent memory are recommended to use augmented +PAKE protocols such as OPAQUE [I-D.irtf-cfrg-opaque].

+

In the course of the CPace protocol, A sends one message to B and B sends one message to A. CPace does not mandate any ordering of these two messages. We use the term "initiator-responder" for CPace where A always speaks first, and the term "symmetric" setting where anyone can speak first.

+

CPace's output is an intermediate session key (ISK), but any party might abort in case of an invalid received message. A and B will produce the same ISK value if and only if both sides did initiate the protocol using the same protocol inputs, specifically the same PRS and the same value for the optional input parameters CI, ADa, ADb and sid that will be specified in section Section 3.1.

+

The naming of ISK as "intermediate" session key highlights the fact that it is RECOMMENDED that applications process ISK by use of a suitable strong key derivation function KDF (such as defined in [RFC5869]) before using the key in a higher-level protocol.

+
+
+

+3.1. Optional CPace inputs +

+

For accommodating different application settings, CPace offers the following OPTIONAL inputs, i.e. inputs which MAY also be the empty string:

+
    +
  • +

    Party identity strings (A,B). +In CPace each party can be given a party identity string which +might be a device name a user name or an URL. +CPace offers two alternative options for authenticating the party identifiers in the course of the protocol run. +The RECOMMENDED option is to integrate both, A and B, into the channel identifier string CI. This option is to be +preferred as A and B will be kept +confidential and as this provides security advantages (see Section 9.11 and Section 9.1). +Integrating A,B into CI, however, requires that both parties know the party identity string of the communication partner +before starting the protocol. If this requirement is not fulfilled in an application setting then CPace offers the alternative of +integrating A as part of the optional input ADa and B as part of the optional input ADb. If the key exchange is successful, parties are guaranteed to learn each other's identity string.

    +
    • +
  • +

    Channel identifier (CI). +CI can be used to bind a session key exchanged with CPace to a specific networking channel which interconnects the protocol parties. +CI could for instance include networking addresses of both parties or party identity strings. +Both parties are required to have the same view of CI. CI will not be publicly sent on the wire and may also include confidential +information. Both parties will only establish a common session key if they initiated the protocol with the same view of CI.

    +
    • +
  • +

    Associated data fields (ADa and ADb). +These fields can be used for authenticating associated data alongside the CPace protocol. +The ADa and ADb will be sent in clear text as part of the protocol messages. +ADa and ADb will become authenticated in a CPace protocol run as +both parties will only agree on a common key if they have had the same view on ADa and ADb.

    +

    +If an application cannot integrate the party identities (A,B) as part of CI, A SHOULD BE included in ADa and B SHOULD BE included in ADb instead +(see Section 9.1).

    +

    +In a setting with clear initiator and responder roles, identity information in ADa +sent by the initiator can be used by the responder for choosing the appropriate PRS (respectively password) for this identity. +ADa and ADb could also include application protocol version information (e.g. to avoid downgrade attacks).

    +
    • +
  • +

    Session identifier (sid). +If both parties have access to the same unique public octet string sid being specific for a communication session before starting the protocol, +it is RECOMMENDED to use this sid value as an additional input for the protocol as this provides security advantages +and will bind the CPace run to this communication session (see Section 9).

    +
    • +
+
+
+
+
+

+3.2. Optional CPace outputs +

+

If a session identifier is not available as input at protocol start CPace can optionally produce a unique public session identifier sid_output +as output that might be helpful for the application for actions subsequent to the CPace protocol step (see Section 9.6, [BGHJ24]).

+
+
+
+
+

+3.3. Responsibilities of the application layer +

+

The following tasks are out of the scope of this document and left to the application layer

+
    +
  • +

    Setup phase: +The application layer is responsible for the handshake that makes parties agree on a common CPace cipher suite.

    +
    • +
  • +

    This document does not specify which encodings applications use for the mandatory PRS input and the optional inputs +CI, sid, ADa and ADb. If PRS is a clear-text password or an octet string derived from a clear-text password, +e.g. by use of a key-derivation function, the clear-text password SHOULD BE encoded according to [RFC8265].

    +
    • +
  • +

    The application needs to settle whether CPace is used in the initiator-responder or the symmetric setting, as in the symmetric +setting transcripts ordered string concatenation must be used for generating protocol transcripts and when integrating +the identity strings A and B into the channel identifier CI. +In this document we will provide test vectors for both, initiator-responder and symmetric settings.

    +
    • +
+
+
+
+
+
+
+

+4. CPace cipher suites +

+

In the setup phase of CPace, both communication partners need to agree on a common cipher suite. +Cipher suites consist of a combination of a hash function H and an elliptic curve environment G.

+

For naming cipher suites we use the convention "CPACE-G-H". We RECOMMEND the following cipher suites:

+ +

The following RECOMMENDED cipher suites provide higher security margins.

+ +

CPace can also securely be implemented using the cipher suites CPACE-RISTR255-SHA512 and CPACE-DECAF448-SHAKE256 defined in +Section 7.3. Section 9 gives guidance on how to implement CPace on further elliptic curves.

+
+
+
+
+

+5. Definitions and notation +

+
+
+

+5.1. Hash function H +

+

Common choices for H are SHA-512 [RFC6234] or SHAKE-256 [FIPS202]. (I.e., the hash function +outputs octet strings, and not group elements.) +For considering both variable-output-length hashes and fixed-output-length hashes, we use the following convention.

+

We use the following notation for referring to the specific properties of a hash function H:

+
    +
  • +

    H.hash(m,l) is a function that operates on an input octet string m and returns the first l octets of the hash of m.

    +
    • +
  • +

    H.b_in_bytes denotes the minimum output size in bytes for collision resistance for the +security level target of the hash function. E.g. H.b_in_bytes = 64 for SHA-512 and SHAKE-256 and H.b_in_bytes = 32 for +SHA-256 and SHAKE-128. We use the notation H.hash(m) = H.hash(m, H.b_in_bytes) and let the hash operation +output the default length if no explicit length parameter is given.

    +
    • +
  • +

    H.bmax_in_bytes denotes the maximum output size in octets supported by the hash function. In case of fixed-size +hashes such as SHA-256, this is the same as H.b_in_bytes, while there is no such limit for hash functions such as SHAKE-256.

    +
    • +
  • +

    H.s_in_bytes denotes the input block size used by H. This number denotes the maximum number of bytes that can be processed +in a single block before applying the compression function or permutation becomes necessary. (See also [RFC2104] for the corresponding block size concepts). +For instance, for SHA-512 the input block size s_in_bytes is 128 as the compression function can process up to 128 bytes, +while for SHAKE-256 the input block size amounts to 136 bytes before the permutation of the sponge state needs to be applied.

    +
    • +
+
+
+
+
+

+5.2. Group environment G +

+

The group environment G specifies an elliptic curve group (also denoted G for convenience) and associated constants +and functions as detailed below. In this document we use additive notation for the group operation.

+
    +
  • +

    G.calculate_generator(H,PRS,CI,sid) denotes a function that outputs a representation of a generator (referred to as "generator" from now on) of the group +which is derived from input octet strings PRS, CI, and sid and with the help of a hash function H.

    +
    • +
  • +

    G.sample_scalar() is a function returning a representation of an integer (referred to as "scalar" from now on) appropriate as a +private Diffie-Hellman key for the group.

    +
    • +
  • +

    G.scalar_mult(y,g) is a function operating on a scalar +y and a group element g. It returns an octet string representation of the group element Y = y*g.

    +
    • +
  • +

    G.I denotes a unique octet string representation of the neutral element of the group. G.I is used for detecting and signaling certain error conditions.

    +
    • +
  • +

    G.scalar_mult_vfy(y,g) is a function operating on +a scalar y and a group element g. It returns an octet string +representation of the group element y*g. Additionally, scalar_mult_vfy specifies validity conditions for y,g and y*g and outputs G.I in case they are not met.

    +
    • +
  • +

    G.DSI denotes a domain-separation identifier octet string which SHALL be uniquely identifying the group environment G.

    +
    • +
+
+
+
+
+

+5.3. Notation for string operations +

+
    +
  • +

    bytes1 || bytes2 denotes concatenation of octet strings.

    +
    • +
  • +

    len(S) denotes the number of octets in an octet string S.

    +
    • +
  • +

    This document uses quotation marks "" both for general language (e.g. for citation of notation used in other documents) and +as syntax for specifying octet strings as in b"CPace25519".

    +

    +We use a preceding lowercase letter b"" in front of the quotation marks if a character sequence is representing an octet string sequence. +I.e., we use the notation convention for byte string representations with single-byte ASCII character encodings from the python programming language. +b"" denotes the empty string of length 0.

    +
    • +
  • +

    LEB128 denotes an algorithm that converts an integer to a variable sized string. The algorithm encodes 7 bits per byte starting with the least significant bits in bits #0 to #6. +As long as significant bits remain, bit #7 will be set. This will result in a single-byte encoding for values below 128. +Test vectors and reference code for LEB128 encoding are available in the appendix.

    +
    • +
  • +

    prepend_len(octet_string) denotes the octet sequence that is obtained from prepending +the length of the octet string to the string itself. The length is encoded using LEB128. +Test vectors and code for prepend_len are available in the appendix.

    +
    • +
  • +

    lv_cat(a0,a1, ...) is the "length-value" encoding function which returns the concatenation of the input strings with an encoding of +their respective length prepended. E.g., lv_cat(a0,a1) returns +prepend_len(a0) || prepend_len(a1). The detailed specification of lv_cat and reference code is available in the appendix.

    +
    • +
  • +

    sample_random_bytes(n) denotes a function that returns n octets, each of which is to be independently sampled from a uniform distribution between 0 and 255.

    +
    • +
  • +

    zero_bytes(n) denotes a function that returns n octets with value 0.

    +
    • +
  • +

    o_cat(bytes1,bytes2) denotes a function for ordered concatenation of octet strings. It places the lexicographically larger octet +string first and prepends the two bytes from the octet string b"oc" to the result. Reference code for this function is available in the appendix.

    +
    • +
  • +

    transcript(Ya,ADa,Yb,ADb) denotes a function outputting an octet string for the protocol transcript. +In applications where CPace is used without clear initiator and responder roles, i.e. where the ordering of messages is +not enforced by the protocol flow, transcript_oc(Ya,Yb,ADa,ADb) = o_cat(lv_cat(Ya,ADa),lv_cat(Yb, ADb)) SHALL be used. +In the initiator-responder setting the implementation transcript_ir(Ya,Yb,ADa,ADb) = lv_cat(Ya,ADa) || lv_cat(Yb, ADb) SHALL be used.

    +
    • +
+
+
+
+
+

+5.4. Notation for group operations +

+

We use additive notation for the group, i.e., 2*X denotes the element that is obtained by computing X+X, for group element X and group operation +.

+
+
+
+
+
+
+

+6. The CPace protocol +

+

CPace is a one round protocol between two parties, A and B. At invocation, A and B are provisioned with PRS,G and H. +Parties will also be provisioned with OPTIONAL CI,sid,ADa (for A) and CI,sid,ADb (for B) which will default to the empty +string b"" if not used. +A sends the public share Ya and optional associated data ADa to B. +Likewise, B sends the public share Yb and optional associated data ADb to A. +Both A and B use the received messages for deriving a shared intermediate session key, ISK.

+
+
+

+6.1. Protocol flow +

+

Optional parameters and messages are denoted with [].

+
+
+                        public: G, H
+
+  A: PRS,[ADa],[CI],[sid]         B: PRS,[ADb],[CI],[sid]
+    ---------------------------------------
+ compute Ya    |     Ya,[ADa]     |  compute Yb
+               |----------------->|
+               |     Yb,[ADb]     |
+ verify inputs |<-----------------|  verify inputs
+ derive ISK    |                  |  derive ISK
+    ---------------------------------------
+ output ISK                          output ISK
+
+
+
+
+
+
+
+

+6.2. CPace protocol instructions +

+

A computes a generator g = G.calculate_generator(H,PRS,CI,sid), scalar ya = G.sample_scalar() and group element Ya = G.scalar_mult (ya,g). A then transmits Ya and +optional associated data ADa to B.

+

B computes a generator g = G.calculate_generator(H,PRS,CI,sid), scalar yb = G.sample_scalar() and group element Yb = G.scalar_mult(yb,g). B sends Yb and optional associated data ADb to A.

+

B then computes K = G.scalar_mult_vfy(yb,Ya). B MUST abort if K=G.I. +Otherwise B calculates +ISK = H.hash(lv_cat(G.DSI || b"_ISK", sid, K)||transcript(Ya,ADa,Yb,ADb)). B returns ISK and terminates.

+

Likewise upon reception of the message from B, A computes K = G.scalar_mult_vfy(ya,Yb). A MUST abort if K=G.I.

+

Otherwise A calculates +ISK = H.hash(lv_cat(G.DSI || b"_ISK", sid, K) || transcript(Ya,ADa,Yb,ADb)). A returns ISK and terminates.

+

The session key ISK returned by A and B is identical if and only if the supplied input parameters PRS, CI and sid match on both sides and the transcript views of both parties match.

+
+
+
+
+ +
+
+

+8. Implementation verification +

+

Any CPace implementation MUST be tested against invalid or weak point attacks. +Implementation MUST be verified to abort upon conditions where G.scalar_mult_vfy functions outputs G.I. +For testing an implementation it is RECOMMENDED to include weak or invalid point encodings within the messages of party A and B and introduce this +in a protocol run. It SHALL be verified that the abort condition is properly handled.

+

Corresponding test vectors are given in the appendix for all recommended cipher suites.

+
+
+
+
+

+9. Security Considerations +

+

A security proof of CPace is found in [AHH21]. This proof covers all recommended cipher suites included in this document. +The security analysis in [BGHJ24] extends the analysis from [AHH21] by covering the case that +no pre-agreed session identifier is available. [BGHJ24] also shows how a unique session id sid_output can be generated along with the protocol +for applications that do not have a session identifier input available.

+
+
+

+9.1. Party identifiers and relay attacks +

+

If unique strings identifying the protocol partners are included either as part of the channel identifier CI or the associated data +fields ADa, ADb, then ISK will provide implicit authentication also regarding the party identities.

+

Incorporating party identifier strings is important for fending off relay attacks. +Such attacks become relevant in a setting where several parties, say, A, B and C, share the same password PRS. +An adversary might relay messages from an honest user A, who aims at interacting with user B, to a party C instead. +If no party identifier strings are used and B and C share the same PRS value then A might be using CPace for +establishing a common ISK key with C while assuming to interact with party B. +Including and checking party identifiers can fend off such relay attacks.

+

The following guidance SHOULD be followed regarding party identifiers.

+
    +
  • +

    If an application layer has party identifiers available, it SHOULD integrate party identifiers in the CPace protocol run, either within CI or ADa/ADb.

    +
    • +
  • +

    The application SHOULD give preference to the option of integrating party identifiers in CI. This avoids the need of an explicit check for the identity strings.

    +
    • +
  • +

    Otherwise A SHOULD integrate its party identifiers in ADa and ADb, such that A integrates its identifier in ADa and B integrates its party identifier as part of ADb. +In this case the application layer will have to add an explicit check for the identity string of the actual communication partner for fending off relay attacks.

    +
    • +
+
+
+
+
+

+9.2. Hashing protocol transcripts +

+

CPace prepends the length of all variable-size input strings before hashing data. +Prepending the length of +all variable-size input strings results in a so-called prefix-free encoding of transcript strings, using terminology introduced in [CDMP05]. This property allows for disregarding length-extension imperfections that come with the commonly used Merkle-Damgard hash function constructions such as SHA256 and SHA512 [CDMP05].

+
+
+
+
+

+9.3. Key derivation +

+

A CPace implementation SHALL output ISK but MUST NOT expose K, because a leaked K +may enable offline dictionary attack +on the password, and a matching value for K does not provide authentication of ADa and ADb.

+

As noted already in Section 6 it is RECOMMENDED to process ISK +by use of a suitable strong key derivation function KDF (such as defined in [RFC5869]) first, +before using the key in a higher-level protocol.

+
+
+
+
+

+9.4. Key confirmation +

+

In many applications it is advisable to add an explicit key confirmation round after the CPace protocol flow. However, as some applications +might only require implicit authentication and as explicit authentication messages are already a built-in feature in many higher-level protocols (e.g. TLS 1.3), the CPace protocol described here does not mandate +key confirmation.

+

Already without explicit key confirmation, CPace enjoys weak forward security under the sCDH and sSDH assumptions [AHH21]. +With added explicit confirmation, CPace enjoys perfect forward security also under the strong sCDH and sSDH assumptions [AHH21].

+

Note that in [ABKLX21] it was shown that an idealized variant of CPace +also enjoys perfect forward security without explicit key confirmation. However this proof does not explicitly cover +the recommended cipher suites +in this document and requires the stronger assumption of an algebraic adversary model. For this reason, we recommend adding +explicit key confirmation if perfect forward security is required.

+

When implementing explicit key confirmation, it is recommended to use an appropriate message-authentication code (MAC) +such as HMAC [RFC2104] or +CMAC [RFC4493] using a key mac_key derived from ISK.

+

One suitable option that works also in the parallel setting without message ordering is to proceed as follows.

+
    +
  • +

    First calculate mac_key as mac_key = H.hash(b"CPaceMac" || sid || ISK).

    +
    • +
  • +

    Then let each party send an authenticator tag calculated over the protocol message that it has sent previously. I.e. +let party A calculate its authentication tag Ta as Ta = MAC(mac_key, lv_cat(Ya,ADa)) and let party B calculate its +authentication tag Tb as Tb = MAC(mac_key, lv_cat(Yb,ADb)).

    +
    • +
  • +

    Let the receiving party check the remote authentication tag for the correct value and abort in case that it's incorrect.

    +
    • +
+
+
+
+
+

+9.5. Integrating CPace in higher-level protocols such as TLS1.3 +

+

When integrating CPace into a higher-level protocol such as TLS1.3 [RFC8446] it is recommended to use ISK +as shared secret (which might otherwise be generated as part of a Diffie-Hellman key exchange output for other cipher suites).

+

Note that unlike the shared secret of a Diffie-Hellman protocol run, ISK will also provide mutual implicit authentication of the protocol partners. +For providing explicit authentication, it is recommended to add a key confirmation round along the lines in Section 9.4, +such as e.g. done in the "Finished" messages in TLS1.3 [RFC8446].

+

If an embedding protocol uses more than two messages (e.g. four message TLS1.3 [RFC8446] flows involving +a hello-retry message and a repeated client-hello message) it is suggested +that the CPace layer only considers the two messages used for the CPace run. I.e., it is suggested that +authenticating the full message sequence involving also the additional messages that might precede the two CPace messages +is done under the responsibility of the embedding application protocol. +This could be done by integrating the full protocol transcript as part of a final explicit key confirmation round (as commonly done by TLS 1.3 as part of the "Finished" messages). +Alternatively, information on communication rounds preceding the CPace flows can also be integrated as part of the CI field, as this will authenticate +the information and will not require both communication partners to keep state information regarding preceding messages in memory until after the CPace run.

+

In case of TLS 1.3 [RFC8446] it is suggested to integrate Ya into the client-hello message and Yb into the server-hello message. Also party identifiers +might best be added to the client-hello and server-hello messages as part of extension fields. +It is recommended to use the full octet stream encoding of the +client-hello message as parameter ADa. Likewise it is recommended to use the encoding of the server-hello message for the parameter ADb. +This approach has the drawback that the public points Ya and Yb might show up redundantly duplicated in the hashing operation for +CPace's transcript strings but has the advantage of simplicity and the advantage that all meta-information in the extension fields within the +client- and server hello fields will always become authenticated as part of the ISK.

+
+
+
+
+

+9.6. Calculating a session identifier alongside with the CPace run +

+

If CPace was run with an empty string sid available as input, both parties can produce a public session identifier string +sid_output = H.hash(b"CPaceSidOutput" || transcript(Ya,ADa,Yb,ADb)) which will be unique for honest parties [BGHJ24].

+
+
+
+
+

+9.7. Sampling of scalars +

+

For curves over fields F_q where q is a prime close to a power of two, we recommend sampling scalars as a uniform bit string of length field_size_bits. We do so in order to reduce both, complexity of the implementation and the attack surface +with respect to side-channels for embedded systems in hostile environments. +[AHH21] demonstrated that non-uniform sampling did not negatively impact security for the case of Curve25519 and Curve448. +This analysis however does not transfer to most curves in Short-Weierstrass form.

+

As a result, we recommend rejection sampling if G is as in Section 7.4. Alternatively an algorithm designed along the lines of the hash_to_field() function from [RFC9380] can also be +used. There, oversampling to an integer significantly larger than the curve order is followed by a modular reduction to the group order.

+
+
+
+
+

+9.8. Preconditions for using the simplified CPace specification from Section 7.2 +

+

The security of the algorithms used for the recommended cipher suites for the Montgomery curves Curve25519 and Curve448 in Section 7.2 rely on the following properties [AHH21]:

+
    +
  • +

    The curve has order (p * c) with p prime and c a small cofactor. Also the curve's quadratic twist must be of order (p' * c') with p' prime and c' a cofactor.

    +
    • +
  • +

    The cofactor c of the curve MUST BE equal to or an integer multiple of the cofactor c' of the curve's quadratic twist. Also, importantly, the +implementation of the scalar_mult and scalar_mult_vfy +functions must ensure that all scalars actually used for the group operation are integer multiples of +c (e.g. such as asserted by the specification of the decodeScalar functions in [RFC7748]).

    +
    • +
  • +

    Both field order q and group order p MUST BE close to a power of two along the lines of [AHH21], Appendix E. Otherwise the simplified scalar sampling specified in Section 7.2 +needs to be changed.

    +
    • +
  • +

    The representation of the neutral element G.I MUST BE the same for both, the curve and its twist.

    +
    • +
  • +

    The implementation of G.scalar_mult_vfy(y,X) MUST map all c low-order points on the curve and all c' low-order points on the twist to G.I.

    +
    • +
+

Algorithms for curves other than the ones recommended here can be based on the principles from Section 7.2 given that the above properties hold.

+
+
+
+
+

+9.9. Nonce values +

+

Secret scalars ya and yb MUST NOT be reused. Values for sid SHOULD NOT be reused since the composability +guarantees established by the simulation-based proof rely on the uniqueness of session ids [AHH21].

+

If the higher-level protocol that integrates CPace is able to establish a unique sid identifier for the communication session, +it is RECOMMENDED that this is passed to CPace as sid parameter. +One suitable option for generating sid is concatenation of ephemeral random strings contributed by both parties.

+
+
+
+
+

+9.10. Side channel attacks +

+

All state-of-the art methods for realizing constant-time execution SHOULD be used. +Special care is RECOMMENDED specifically for elliptic curves in Short-Weierstrass form +as important standard documents including [IEEE1363] describe curve operations with +non-constant-time algorithms.

+

In case that side channel attacks are to be considered practical for a given application, it is RECOMMENDED to pay special +attention on computing the secret generator G.calculate_generator(PRS,CI,sid). +The most critical substep to consider might be the processing of the first block of the hash that includes +the PRS string. +The zero-padding introduced when hashing the sensitive PRS string can be expected to make +the task for a side-channel attack somewhat more complex. Still this feature alone is not sufficient for ruling out power analysis attacks.

+

Even though the calculate_generator operation might be considered to form the primary target for side-channel attacks as information on long-term secrets might be exposed, +also the subsequent operations on ephemeral values, such as scalar +sampling and scalar multiplication should be protected from side-channels.

+
+
+
+
+

+9.11. Quantum computers +

+

CPace is proven secure under the hardness of the strong computational Simultaneous Diffie-Hellmann (sSDH) and strong computational Diffie-Hellmann (sCDH) +assumptions in the group G (as defined in [AHH21]). +These assumptions are not expected to hold any longer when large-scale quantum computers (LSQC) are available. +Still, even in case that LSQC emerge, it is reasonable to assume that discrete-logarithm computations will remain costly. CPace with ephemeral pre-established session id values +sid forces the adversary to solve one computational Diffie-Hellman problem per password guess [ES21]. +If party identifiers are included as part of CI then the adversary is forced to solve one computational Diffie-Hellman problem per password +guess and party identifier pair. +For this reason it is RECOMMENDED to use the optional inputs sid if available in an application setting. +For the same reason it is RECOMMENDED to integrate party identity strings A,B into CI.

+

In this sense, using the wording suggested by Steve Thomas on the CFRG mailing list, CPace is "quantum-annoying".

+
+
+
+
+
+
+

+10. IANA Considerations +

+

No IANA action is required.

+
+
+
+
+

+11. Reference implementation and test vector generation +

+

The reference implementation that was used for deriving test vectors is available at [REFIMP]. +The embedded base64-encoded test vectors will decode to JSON files having the test vector's octet strings encoded as base16 (i.e. hexadecimal) strings.

+
+
+
+
+

+12. Acknowledgements +

+

We would like to thank the participants on the CFRG list for comments and advice. Any comment and advice is appreciated.

+
+
+
+
+

+13. References +

+
+
+

+13.1. Normative References +

+
+
[I-D.draft-irtf-cfrg-ristretto255-decaf448]
+
+de Valence, H., Grigg, J., Hamburg, M., Lovecruft, I., Tankersley, G., and F. Valsorda, "The ristretto255 and decaf448 Groups", Work in Progress, Internet-Draft, draft-irtf-cfrg-ristretto255-decaf448-08, , <https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448-08>.
+
+
[IEEE1363]
+
+"Standard Specifications for Public Key Cryptography, IEEE 1363", .
+
+
[RFC2119]
+
+Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/rfc/rfc2119>.
+
+
[RFC7748]
+
+Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, , <https://www.rfc-editor.org/rfc/rfc7748>.
+
+
[RFC8174]
+
+Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, , <https://www.rfc-editor.org/rfc/rfc8174>.
+
+
[SEC1]
+
+Standards for Efficient Cryptography Group (SECG), "SEC 1: Elliptic Curve Cryptography", , <http://www.secg.org/sec1-v2.pdf>.
+
+
+
+
+
+
+

+13.2. Informative References +

+
+
[ABKLX21]
+
+Abdalla, M., Barbosa, M., Katz, J., Loss, J., and J. Xu, "Algebraic Adversaries in the Universal Composability Framework.", n.d., <https://eprint.iacr.org/2021/1218>.
+
+
[AHH21]
+
+Abdalla, M., Haase, B., and J. Hesse, "Security analysis of CPace", n.d., <https://eprint.iacr.org/2021/114>.
+
+
[BGHJ24]
+
+Barbosa, M., Gellert, K., Hesse, J., and S. Jarecki, "Bare PAKE: Universally Composable Key Exchange from Just Passwords", n.d., <link.springer.com/chapter/10.1007/978-3-031-68379-4_6>.
+
+
[CDMP05]
+
+Coron, J.-S., Dodis, Y., Malinaud, C., and P. Puniya, "Merkle-Damgaard Revisited: How to Construct a Hash Function", In Advances in Cryptology - CRYPTO 2005, pages 430-448, DOI 10.1007/11535218_26, , <https://doi.org/10.1007/11535218_26>.
+
+
[ES21]
+
+Eaton, E. and D. Stebila, "The 'quantum annoying' property of password-authenticated key exchange protocols.", n.d., <https://eprint.iacr.org/2021/696>.
+
+
[FIPS202]
+
+National Institute of Standards and Technology (NIST), "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf>.
+
+
[I-D.irtf-cfrg-opaque]
+
+Bourdrez, D., Krawczyk, H., Lewi, K., and C. A. Wood, "The OPAQUE Augmented PAKE Protocol", Work in Progress, Internet-Draft, draft-irtf-cfrg-opaque-17, , <https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-opaque-17>.
+
+
[REFIMP]
+
+"CPace reference implementation (sage)", , <https://github.com/cfrg/draft-irtf-cfrg-cpace/tree/master/poc>.
+
+
[RFC2104]
+
+Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-Hashing for Message Authentication", RFC 2104, DOI 10.17487/RFC2104, , <https://www.rfc-editor.org/rfc/rfc2104>.
+
+
[RFC4493]
+
+Song, JH., Poovendran, R., Lee, J., and T. Iwata, "The AES-CMAC Algorithm", RFC 4493, DOI 10.17487/RFC4493, , <https://www.rfc-editor.org/rfc/rfc4493>.
+
+
[RFC5246]
+
+Dierks, T. and E. Rescorla, "The Transport Layer Security (TLS) Protocol Version 1.2", RFC 5246, DOI 10.17487/RFC5246, , <https://www.rfc-editor.org/rfc/rfc5246>.
+
+
[RFC5639]
+
+Lochter, M. and J. Merkle, "Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation", RFC 5639, DOI 10.17487/RFC5639, , <https://www.rfc-editor.org/rfc/rfc5639>.
+
+
[RFC5869]
+
+Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand Key Derivation Function (HKDF)", RFC 5869, DOI 10.17487/RFC5869, , <https://www.rfc-editor.org/rfc/rfc5869>.
+
+
[RFC6234]
+
+Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, DOI 10.17487/RFC6234, , <https://www.rfc-editor.org/rfc/rfc6234>.
+
+
[RFC8265]
+
+Saint-Andre, P. and A. Melnikov, "Preparation, Enforcement, and Comparison of Internationalized Strings Representing Usernames and Passwords", RFC 8265, DOI 10.17487/RFC8265, , <https://www.rfc-editor.org/rfc/rfc8265>.
+
+
[RFC8446]
+
+Rescorla, E., "The Transport Layer Security (TLS) Protocol Version 1.3", RFC 8446, DOI 10.17487/RFC8446, , <https://www.rfc-editor.org/rfc/rfc8446>.
+
+
[RFC9380]
+
+Faz-Hernandez, A., Scott, S., Sullivan, N., Wahby, R. S., and C. A. Wood, "Hashing to Elliptic Curves", RFC 9380, DOI 10.17487/RFC9380, , <https://www.rfc-editor.org/rfc/rfc9380>.
+
+
[SEC2]
+
+Standards for Efficient Cryptography Group (SECG), "SEC 2: Recommended Elliptic Curve Domain Parameters", , <http://www.secg.org/sec2-v2.pdf>.
+
+
+
+
+
+
+
+
+

+Appendix A. CPace function definitions +

+
+
+

+A.1. Definition and test vectors for string utility functions +

+
+
+

+A.1.1. prepend_len function +

+
+
+def prepend_len(data):
+    "prepend LEB128 encoding of length"
+    length = len(data)
+    length_encoded = b""
+    while True:
+        if length < 128:
+            length_encoded += bytes([length])
+        else:
+            length_encoded += bytes([(length & 0x7f) + 0x80])
+        length = int(length >> 7)
+        if length == 0:
+            break;
+    return length_encoded + data
+
+
+
+
+
+
+

+A.1.2. prepend_len test vectors +

+
+
+  prepend_len(b""): (length: 1 bytes)
+    00
+  prepend_len(b"1234"): (length: 5 bytes)
+    0431323334
+  prepend_len(bytes(range(127))): (length: 128 bytes)
+    7f000102030405060708090a0b0c0d0e0f101112131415161718191a1b
+    1c1d1e1f202122232425262728292a2b2c2d2e2f303132333435363738
+    393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f505152535455
+    565758595a5b5c5d5e5f606162636465666768696a6b6c6d6e6f707172
+    737475767778797a7b7c7d7e
+  prepend_len(bytes(range(128))): (length: 130 bytes)
+    8001000102030405060708090a0b0c0d0e0f101112131415161718191a
+    1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334353637
+    38393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f5051525354
+    55565758595a5b5c5d5e5f606162636465666768696a6b6c6d6e6f7071
+    72737475767778797a7b7c7d7e7f
+
+
+
+
+
+A.1.2.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJwcmVwZW5kX2xlbihiJycpIjogIjAwIiwgImInMTIzNCciOiAiMzEzMjMzMzQiLC
+ #AicHJlcGVuZF9sZW4oYicxMjM0JykiOiAiMDQzMTMyMzMzNCIsICJwcmVwZW5kX2xl
+ #bihieXRlcyhyYW5nZSgxMjcpKSkiOiAiN0YwMDAxMDIwMzA0MDUwNjA3MDgwOTBBME
+ #IwQzBEMEUwRjEwMTExMjEzMTQxNTE2MTcxODE5MUExQjFDMUQxRTFGMjAyMTIyMjMy
+ #NDI1MjYyNzI4MjkyQTJCMkMyRDJFMkYzMDMxMzIzMzM0MzUzNjM3MzgzOTNBM0IzQz
+ #NEM0UzRjQwNDE0MjQzNDQ0NTQ2NDc0ODQ5NEE0QjRDNEQ0RTRGNTA1MTUyNTM1NDU1
+ #NTY1NzU4NTk1QTVCNUM1RDVFNUY2MDYxNjI2MzY0NjU2NjY3Njg2OTZBNkI2QzZENk
+ #U2RjcwNzE3MjczNzQ3NTc2Nzc3ODc5N0E3QjdDN0Q3RSIsICJwcmVwZW5kX2xlbihi
+ #eXRlcyhyYW5nZSgxMjgpKSkiOiAiODAwMTAwMDEwMjAzMDQwNTA2MDcwODA5MEEwQj
+ #BDMEQwRTBGMTAxMTEyMTMxNDE1MTYxNzE4MTkxQTFCMUMxRDFFMUYyMDIxMjIyMzI0
+ #MjUyNjI3MjgyOTJBMkIyQzJEMkUyRjMwMzEzMjMzMzQzNTM2MzczODM5M0EzQjNDM0
+ #QzRTNGNDA0MTQyNDM0NDQ1NDY0NzQ4NDk0QTRCNEM0RDRFNEY1MDUxNTI1MzU0NTU1
+ #NjU3NTg1OTVBNUI1QzVENUU1RjYwNjE2MjYzNjQ2NTY2Njc2ODY5NkE2QjZDNkQ2RT
+ #ZGNzA3MTcyNzM3NDc1NzY3Nzc4Nzk3QTdCN0M3RDdFN0YifQ==
+
+
+
+
+
+
+
+
+

+A.1.3. lv_cat function +

+
+
+  def lv_cat(*args):
+      result = b""
+      for arg in args:
+          result += prepend_len(arg)
+      return result
+
+
+
+
+
+
+

+A.1.4. Testvector for lv_cat() +

+
+
+  lv_cat(b"1234",b"5",b"",b"678"): (length: 12 bytes)
+    043132333401350003363738
+
+
+
+
+
+A.1.4.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJiJzEyMzQnIjogIjMxMzIzMzM0IiwgImInNSciOiAiMzUiLCAiYic2NzgnIjogIj
+ #M2MzczOCIsICJsdl9jYXQoYicxMjM0JyxiJzUnLGInJyxiJzY3OCcpIjogIjA0MzEz
+ #MjMzMzQwMTM1MDAwMzM2MzczOCJ9
+
+
+
+
+
+
+
+
+
+
+

+A.2. Definition of generator_string function. +

+
+
+def generator_string(DSI,PRS,CI,sid,s_in_bytes):
+    # Concat all input fields with prepended length information.
+    # Add zero padding in the first hash block after DSI and PRS.
+    len_zpad = max(0,s_in_bytes - 1 - len(prepend_len(PRS))
+                     - len(prepend_len(DSI)))
+    return lv_cat(DSI, PRS, zero_bytes(len_zpad),
+                           CI, sid)
+
+
+
+
+
+
+

+A.3. Definitions and test vector ordered concatenation +

+
+
+

+A.3.1. Definitions for lexiographical ordering +

+

For ordered concatenation lexiographical ordering of byte sequences is used:

+
+
+   def lexiographically_larger(bytes1,bytes2):
+      "Returns True if bytes1>bytes2 using lexiographical ordering."
+      min_len = min (len(bytes1), len(bytes2))
+      for m in range(min_len):
+          if bytes1[m] > bytes2[m]:
+              return True;
+          elif bytes1[m] < bytes2[m]:
+              return False;
+      return len(bytes1) > len(bytes2)
+
+
+
+
+
+
+

+A.3.2. Definitions for ordered concatenation +

+

With the above definition of lexiographical ordering ordered concatenation is specified as follows.

+
+
+  def o_cat(bytes1,bytes2):
+      if lexiographically_larger(bytes1,bytes2):
+          return b"oc" + bytes1 + bytes2
+      else:
+          return b"oc" + bytes2 + bytes1
+
+
+
+
+
+
+

+A.3.3. Test vectors ordered concatenation +

+
+
+  string comparison for o_cat:
+    lexiographically_larger(b"\0", b"\0\0") == False
+    lexiographically_larger(b"\1", b"\0\0") == True
+    lexiographically_larger(b"\0\0", b"\0") == True
+    lexiographically_larger(b"\0\0", b"\1") == False
+    lexiographically_larger(b"\0\1", b"\1") == False
+    lexiographically_larger(b"ABCD", b"BCD") == False
+
+  o_cat(b"ABCD",b"BCD"): (length: 9 bytes)
+    6f6342434441424344
+  o_cat(b"BCD",b"ABCDE"): (length: 10 bytes)
+    6f634243444142434445
+
+
+
+
+
+A.3.3.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJiJ0FCQ0QnIjogIjQxNDI0MzQ0IiwgImInQkNEJyI6ICI0MjQzNDQiLCAiYidBQk
+ #NERSciOiAiNDE0MjQzNDQ0NSIsICJvX2NhdChiJ0FCQ0QnLGInQkNEJykiOiAiNkY2
+ #MzQyNDM0NDQxNDI0MzQ0IiwgIm9fY2F0KGInQkNEJyxiJ0FCQ0RFJykiOiAiNkY2Mz
+ #QyNDM0NDQxNDI0MzQ0NDUifQ==
+
+
+
+
+
+
+
+
+

+A.3.4. Definitions for transcript_ir function +

+
+
+def transcript_ir(Ya,ADa,Yb,ADb):
+    result = lv_cat(Ya,ADa) + lv_cat(Yb,ADb)
+    return result
+
+
+
+
+
+
+

+A.3.5. Test vectors transcript_ir function +

+
+
+  transcript_ir(b"123", b"PartyA", b"234",b"PartyB"):
+  (length: 22 bytes)
+    03313233065061727479410332333406506172747942
+  transcript_ir(b"3456",b"PartyA",b"2345",b"PartyB"):
+  (length: 24 bytes)
+    043334353606506172747941043233343506506172747942
+
+
+
+
+
+A.3.5.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJiJzEyMyciOiAiMzEzMjMzIiwgImInMjM0JyI6ICIzMjMzMzQiLCAiYidQYXJ0eU
+ #EnIjogIjUwNjE3Mjc0Nzk0MSIsICJiJ1BhcnR5QiciOiAiNTA2MTcyNzQ3OTQyIiwg
+ #ImInMzQ1NiciOiAiMzMzNDM1MzYiLCAiYicyMzQ1JyI6ICIzMjMzMzQzNSIsICJ0cm
+ #Fuc2NyaXB0X2lyKGInMTIzJyxiJ1BhcnR5QScsYicyMzQnLGInUGFydHlCJykiOiAi
+ #MDMzMTMyMzMwNjUwNjE3Mjc0Nzk0MTAzMzIzMzM0MDY1MDYxNzI3NDc5NDIiLCAidH
+ #JhbnNjcmlwdF9pcihiJzM0NTYnLGInUGFydHlBJyxiJzIzNDUnLGInUGFydHlCJyki
+ #OiAiMDQzMzM0MzUzNjA2NTA2MTcyNzQ3OTQxMDQzMjMzMzQzNTA2NTA2MTcyNzQ3OT
+ #QyIn0=
+
+
+
+
+
+
+
+
+

+A.3.6. Definitions for transcript_oc function +

+
+
+def transcript_oc(Ya,ADa,Yb,ADb):
+    result = o_cat(lv_cat(Ya,ADa),lv_cat(Yb,ADb))
+    return result
+
+
+
+
+
+
+

+A.3.7. Test vectors for transcript_oc function +

+
+
+  transcript_oc(b"123", b"PartyA", b"234",b"PartyB"):
+  (length: 24 bytes)
+    6f6303323334065061727479420331323306506172747941
+  transcript_oc(b"3456",b"PartyA",b"2345",b"PartyB"):
+  (length: 26 bytes)
+    6f63043334353606506172747941043233343506506172747942
+
+
+
+
+
+A.3.7.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJiJzEyMyciOiAiMzEzMjMzIiwgImInMjM0JyI6ICIzMjMzMzQiLCAiYidQYXJ0eU
+ #EnIjogIjUwNjE3Mjc0Nzk0MSIsICJiJ1BhcnR5QiciOiAiNTA2MTcyNzQ3OTQyIiwg
+ #ImInMzQ1NiciOiAiMzMzNDM1MzYiLCAiYicyMzQ1JyI6ICIzMjMzMzQzNSIsICJ0cm
+ #Fuc2NyaXB0X29jKGInMTIzJyxiJ1BhcnR5QScsYicyMzQnLGInUGFydHlCJykiOiAi
+ #NkY2MzAzMzIzMzM0MDY1MDYxNzI3NDc5NDIwMzMxMzIzMzA2NTA2MTcyNzQ3OTQxIi
+ #wgInRyYW5zY3JpcHRfb2MoYiczNDU2JyxiJ1BhcnR5QScsYicyMzQ1JyxiJ1BhcnR5
+ #QicpIjogIjZGNjMwNDMzMzQzNTM2MDY1MDYxNzI3NDc5NDEwNDMyMzMzNDM1MDY1MD
+ #YxNzI3NDc5NDIifQ==
+
+
+
+
+
+
+
+
+
+
+

+A.4. Decoding and Encoding functions according to RFC7748 +

+
+
+   def decodeLittleEndian(b, bits):
+       return sum([b[i] << 8*i for i in range((bits+7)/8)])
+
+   def decodeUCoordinate(u, bits):
+       u_list = [ord(b) for b in u]
+       # Ignore any unused bits.
+       if bits % 8:
+           u_list[-1] &= (1<<(bits%8))-1
+       return decodeLittleEndian(u_list, bits)
+
+   def encodeUCoordinate(u, bits):
+       return ''.join([chr((u >> 8*i) & 0xff)
+                       for i in range((bits+7)/8)])
+
+
+
+
+
+
+

+A.5. Elligator 2 reference implementation +

+

The Elligator 2 map requires a non-square field element Z which shall be calculated +as follows.

+
+
+    def find_z_ell2(F):
+        # Find nonsquare for Elligator2
+        # Argument: F, a field object, e.g., F = GF(2^255 - 19)
+        ctr = F.gen()
+        while True:
+            for Z_cand in (F(ctr), F(-ctr)):
+                # Z must be a non-square in F.
+                if is_square(Z_cand):
+                    continue
+                return Z_cand
+            ctr += 1
+
+
+

The values of the non-square Z only depend on the curve. The algorithm above +results in a value of Z = 2 for Curve25519 and Z=-1 for Ed448.

+

The following code maps a field element r to an encoded field element which +is a valid u-coordinate of a Montgomery curve with curve parameter A.

+
+
+    def elligator2(r, q, A, field_size_bits):
+        # Inputs: field element r, field order q,
+        #         curve parameter A and field size in bits
+        Fq = GF(q); A = Fq(A); B = Fq(1);
+
+        # get non-square z as specified in the hash2curve draft.
+        z = Fq(find_z_ell2(Fq))
+        powerForLegendreSymbol = floor((q-1)/2)
+
+        v = - A / (1 + z * r^2)
+        epsilon = (v^3 + A * v^2 + B * v)^powerForLegendreSymbol
+        x = epsilon * v - (1 - epsilon) * A/2
+        return encodeUCoordinate(Integer(x), field_size_bits)
+
+
+
+
+
+
+
+
+

+Appendix B. Test vectors +

+
+
+

+B.1. Test vector for CPace using group X25519 and hash SHA-512 +

+
+
+

+B.1.1. Test vectors for calculate_generator with group X25519 +

+
+
+  Inputs
+    H   = SHA-512 with input block size 128 bytes.
+    PRS = b'Password' ; ZPAD length: 109 ; DSI = b'CPace255'
+    CI = b'oc\x0bB_responder\x0bA_initiator'
+    CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72
+    sid = 7e4b4791d6a8ef019b936c79fb7f2c57
+  Outputs
+    generator_string(G.DSI,PRS,CI,sid,H.s_in_bytes):
+    (length: 172 bytes)
+      0843506163653235350850617373776f72646d000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      000000000000000000000000000000001a6f630b425f726573706f6e
+      6465720b415f696e69746961746f72107e4b4791d6a8ef019b936c79
+      fb7f2c57
+    hash generator string: (length: 32 bytes)
+      92806dc608984dbf4e4aae478c6ec453ae979cc01ecc1a2a7cf49f5c
+      ee56551b
+    decoded field element of 255 bits: (length: 32 bytes)
+      92806dc608984dbf4e4aae478c6ec453ae979cc01ecc1a2a7cf49f5c
+      ee56551b
+    generator g: (length: 32 bytes)
+      64e8099e3ea682cfdc5cb665c057ebb514d06bf23ebc9f743b51b822
+      42327074
+
+
+
+
+
+B.1.1.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJIIjogIlNIQS01MTIiLCAiSC5zX2luX2J5dGVzIjogMTI4LCAiUFJTIjogIjUwNj
+ #E3MzczNzc2RjcyNjQiLCAiWlBBRCBsZW5ndGgiOiAxMDksICJEU0kiOiAiNDM1MDYx
+ #NjM2NTMyMzUzNSIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NTczNzA2RjZFNjQ2NTcyME
+ #I0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI3RTRCNDc5MUQ2QThFRjAx
+ #OUI5MzZDNzlGQjdGMkM1NyIsICJnZW5lcmF0b3Jfc3RyaW5nKEcuRFNJLFBSUyxDSS
+ #xzaWQsSC5zX2luX2J5dGVzKSI6ICIwODQzNTA2MTYzNjUzMjM1MzUwODUwNjE3Mzcz
+ #Nzc2RjcyNjQ2RDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMUE2RjYzMEI0MjVGNzI2NTczNz
+ #A2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyMTA3RTRCNDc5MUQ2QThF
+ #RjAxOUI5MzZDNzlGQjdGMkM1NyIsICJoYXNoIGdlbmVyYXRvciBzdHJpbmciOiAiOT
+ #I4MDZEQzYwODk4NERCRjRFNEFBRTQ3OEM2RUM0NTNBRTk3OUNDMDFFQ0MxQTJBN0NG
+ #NDlGNUNFRTU2NTUxQiIsICJkZWNvZGVkIGZpZWxkIGVsZW1lbnQgb2YgMjU1IGJpdH
+ #MiOiAiOTI4MDZEQzYwODk4NERCRjRFNEFBRTQ3OEM2RUM0NTNBRTk3OUNDMDFFQ0Mx
+ #QTJBN0NGNDlGNUNFRTU2NTUxQiIsICJnZW5lcmF0b3IgZyI6ICI2NEU4MDk5RTNFQT
+ #Y4MkNGREM1Q0I2NjVDMDU3RUJCNTE0RDA2QkYyM0VCQzlGNzQzQjUxQjgyMjQyMzI3
+ #MDc0In0=
+
+
+
+
+
+
+
+
+

+B.1.2. Test vector for message from A +

+
+
+  Inputs
+    ADa = b'ADa'
+    ya (little endian): (length: 32 bytes)
+      21b4f4bd9e64ed355c3eb676a28ebedaf6d8f17bdc365995b3190971
+      53044080
+  Outputs
+    Ya: (length: 32 bytes)
+      1b02dad6dbd29a07b6d28c9e04cb2f184f0734350e32bb7e62ff9dbc
+      fdb63d15
+
+
+
+
+
+
+

+B.1.3. Test vector for message from B +

+
+
+  Inputs
+    ADb = b'ADb'
+    yb (little endian): (length: 32 bytes)
+      848b0779ff415f0af4ea14df9dd1d3c29ac41d836c7808896c4eba19
+      c51ac40a
+  Outputs
+    Yb: (length: 32 bytes)
+      20cda5955f82c4931545bcbf40758ce1010d7db4db2a907013d79c7a
+      8fcf957f
+
+
+
+
+
+
+

+B.1.4. Test vector for secret points K +

+
+
+    scalar_mult_vfy(ya,Yb): (length: 32 bytes)
+      f97fdfcfff1c983ed6283856a401de3191ca919902b323c5f950c970
+      3df7297a
+    scalar_mult_vfy(yb,Ya): (length: 32 bytes)
+      f97fdfcfff1c983ed6283856a401de3191ca919902b323c5f950c970
+      3df7297a
+
+
+
+
+
+
+

+B.1.5. Test vector for ISK calculation initiator/responder +

+
+
+    transcript_ir(Ya,ADa,Yb,ADb): (length: 74 bytes)
+      201b02dad6dbd29a07b6d28c9e04cb2f184f0734350e32bb7e62ff9d
+      bcfdb63d15034144612020cda5955f82c4931545bcbf40758ce1010d
+      7db4db2a907013d79c7a8fcf957f03414462
+    DSI = G.DSI_ISK, b'CPace255_ISK': (length: 12 bytes)
+      43506163653235355f49534b
+    lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb):
+    (length: 137 bytes)
+      0c43506163653235355f49534b107e4b4791d6a8ef019b936c79fb7f
+      2c5720f97fdfcfff1c983ed6283856a401de3191ca919902b323c5f9
+      50c9703df7297a201b02dad6dbd29a07b6d28c9e04cb2f184f073435
+      0e32bb7e62ff9dbcfdb63d15034144612020cda5955f82c4931545bc
+      bf40758ce1010d7db4db2a907013d79c7a8fcf957f03414462
+    ISK result: (length: 64 bytes)
+      a051ee5ee2499d16da3f69f430218b8ea94a18a45b67f9e86495b382
+      c33d14a5c38cecc0cc834f960e39e0d1bf7d76b9ef5d54eecc5e0f38
+      6c97ad12da8c3d5f
+
+
+
+
+
+
+

+B.1.6. Test vector for ISK calculation parallel execution +

+
+
+    transcript_oc(Ya,ADa,Yb,ADb): (length: 76 bytes)
+      6f632020cda5955f82c4931545bcbf40758ce1010d7db4db2a907013
+      d79c7a8fcf957f03414462201b02dad6dbd29a07b6d28c9e04cb2f18
+      4f0734350e32bb7e62ff9dbcfdb63d1503414461
+    DSI = G.DSI_ISK, b'CPace255_ISK': (length: 12 bytes)
+      43506163653235355f49534b
+    lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb):
+    (length: 139 bytes)
+      0c43506163653235355f49534b107e4b4791d6a8ef019b936c79fb7f
+      2c5720f97fdfcfff1c983ed6283856a401de3191ca919902b323c5f9
+      50c9703df7297a6f632020cda5955f82c4931545bcbf40758ce1010d
+      7db4db2a907013d79c7a8fcf957f03414462201b02dad6dbd29a07b6
+      d28c9e04cb2f184f0734350e32bb7e62ff9dbcfdb63d1503414461
+    ISK result: (length: 64 bytes)
+      5cc27e49679423f81a37d7521d9fb1327c840d2ea4a1543652e7de5c
+      abb89ebad27d24761b3288a3fd5764b441ecb78d30abc26161ff45ea
+      297bb311dde04727
+
+
+
+
+
+
+

+B.1.7. Test vector for optional output of session id +

+
+
+    H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      f7ae11ac3ee85c3c42d8bd51ba823fbe17158f43d34a1296f1cb2567
+      bcc71dc8b201a134b566b468aad8fd04f02f96e3caf9d5601f7ed760
+      a0a951a5a861b5e7
+    H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      a38389e34fa492788c1df43b06b427710491174e53c33b01362a490d
+      116fe1b7e870aa6e2a7fc018725e3b7f969f7508042e44cd3863f39a
+      a75026a190d1902b
+
+
+
+
+
+
+

+B.1.8. Corresponding C programming language initializers +

+
+
+const unsigned char tc_PRS[] = {
+ 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64,
+};
+const unsigned char tc_CI[] = {
+ 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64,
+ 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74,
+ 0x6f,0x72,
+};
+const unsigned char tc_sid[] = {
+ 0x7e,0x4b,0x47,0x91,0xd6,0xa8,0xef,0x01,0x9b,0x93,0x6c,0x79,
+ 0xfb,0x7f,0x2c,0x57,
+};
+const unsigned char tc_g[] = {
+ 0x64,0xe8,0x09,0x9e,0x3e,0xa6,0x82,0xcf,0xdc,0x5c,0xb6,0x65,
+ 0xc0,0x57,0xeb,0xb5,0x14,0xd0,0x6b,0xf2,0x3e,0xbc,0x9f,0x74,
+ 0x3b,0x51,0xb8,0x22,0x42,0x32,0x70,0x74,
+};
+const unsigned char tc_ya[] = {
+ 0x21,0xb4,0xf4,0xbd,0x9e,0x64,0xed,0x35,0x5c,0x3e,0xb6,0x76,
+ 0xa2,0x8e,0xbe,0xda,0xf6,0xd8,0xf1,0x7b,0xdc,0x36,0x59,0x95,
+ 0xb3,0x19,0x09,0x71,0x53,0x04,0x40,0x80,
+};
+const unsigned char tc_ADa[] = {
+ 0x41,0x44,0x61,
+};
+const unsigned char tc_Ya[] = {
+ 0x1b,0x02,0xda,0xd6,0xdb,0xd2,0x9a,0x07,0xb6,0xd2,0x8c,0x9e,
+ 0x04,0xcb,0x2f,0x18,0x4f,0x07,0x34,0x35,0x0e,0x32,0xbb,0x7e,
+ 0x62,0xff,0x9d,0xbc,0xfd,0xb6,0x3d,0x15,
+};
+const unsigned char tc_yb[] = {
+ 0x84,0x8b,0x07,0x79,0xff,0x41,0x5f,0x0a,0xf4,0xea,0x14,0xdf,
+ 0x9d,0xd1,0xd3,0xc2,0x9a,0xc4,0x1d,0x83,0x6c,0x78,0x08,0x89,
+ 0x6c,0x4e,0xba,0x19,0xc5,0x1a,0xc4,0x0a,
+};
+const unsigned char tc_ADb[] = {
+ 0x41,0x44,0x62,
+};
+const unsigned char tc_Yb[] = {
+ 0x20,0xcd,0xa5,0x95,0x5f,0x82,0xc4,0x93,0x15,0x45,0xbc,0xbf,
+ 0x40,0x75,0x8c,0xe1,0x01,0x0d,0x7d,0xb4,0xdb,0x2a,0x90,0x70,
+ 0x13,0xd7,0x9c,0x7a,0x8f,0xcf,0x95,0x7f,
+};
+const unsigned char tc_K[] = {
+ 0xf9,0x7f,0xdf,0xcf,0xff,0x1c,0x98,0x3e,0xd6,0x28,0x38,0x56,
+ 0xa4,0x01,0xde,0x31,0x91,0xca,0x91,0x99,0x02,0xb3,0x23,0xc5,
+ 0xf9,0x50,0xc9,0x70,0x3d,0xf7,0x29,0x7a,
+};
+const unsigned char tc_ISK_IR[] = {
+ 0xa0,0x51,0xee,0x5e,0xe2,0x49,0x9d,0x16,0xda,0x3f,0x69,0xf4,
+ 0x30,0x21,0x8b,0x8e,0xa9,0x4a,0x18,0xa4,0x5b,0x67,0xf9,0xe8,
+ 0x64,0x95,0xb3,0x82,0xc3,0x3d,0x14,0xa5,0xc3,0x8c,0xec,0xc0,
+ 0xcc,0x83,0x4f,0x96,0x0e,0x39,0xe0,0xd1,0xbf,0x7d,0x76,0xb9,
+ 0xef,0x5d,0x54,0xee,0xcc,0x5e,0x0f,0x38,0x6c,0x97,0xad,0x12,
+ 0xda,0x8c,0x3d,0x5f,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x5c,0xc2,0x7e,0x49,0x67,0x94,0x23,0xf8,0x1a,0x37,0xd7,0x52,
+ 0x1d,0x9f,0xb1,0x32,0x7c,0x84,0x0d,0x2e,0xa4,0xa1,0x54,0x36,
+ 0x52,0xe7,0xde,0x5c,0xab,0xb8,0x9e,0xba,0xd2,0x7d,0x24,0x76,
+ 0x1b,0x32,0x88,0xa3,0xfd,0x57,0x64,0xb4,0x41,0xec,0xb7,0x8d,
+ 0x30,0xab,0xc2,0x61,0x61,0xff,0x45,0xea,0x29,0x7b,0xb3,0x11,
+ 0xdd,0xe0,0x47,0x27,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x5c,0xc2,0x7e,0x49,0x67,0x94,0x23,0xf8,0x1a,0x37,0xd7,0x52,
+ 0x1d,0x9f,0xb1,0x32,0x7c,0x84,0x0d,0x2e,0xa4,0xa1,0x54,0x36,
+ 0x52,0xe7,0xde,0x5c,0xab,0xb8,0x9e,0xba,0xd2,0x7d,0x24,0x76,
+ 0x1b,0x32,0x88,0xa3,0xfd,0x57,0x64,0xb4,0x41,0xec,0xb7,0x8d,
+ 0x30,0xab,0xc2,0x61,0x61,0xff,0x45,0xea,0x29,0x7b,0xb3,0x11,
+ 0xdd,0xe0,0x47,0x27,
+};
+const unsigned char tc_sid_out_ir[] = {
+ 0xf7,0xae,0x11,0xac,0x3e,0xe8,0x5c,0x3c,0x42,0xd8,0xbd,0x51,
+ 0xba,0x82,0x3f,0xbe,0x17,0x15,0x8f,0x43,0xd3,0x4a,0x12,0x96,
+ 0xf1,0xcb,0x25,0x67,0xbc,0xc7,0x1d,0xc8,0xb2,0x01,0xa1,0x34,
+ 0xb5,0x66,0xb4,0x68,0xaa,0xd8,0xfd,0x04,0xf0,0x2f,0x96,0xe3,
+ 0xca,0xf9,0xd5,0x60,0x1f,0x7e,0xd7,0x60,0xa0,0xa9,0x51,0xa5,
+ 0xa8,0x61,0xb5,0xe7,
+};
+const unsigned char tc_sid_out_oc[] = {
+ 0xa3,0x83,0x89,0xe3,0x4f,0xa4,0x92,0x78,0x8c,0x1d,0xf4,0x3b,
+ 0x06,0xb4,0x27,0x71,0x04,0x91,0x17,0x4e,0x53,0xc3,0x3b,0x01,
+ 0x36,0x2a,0x49,0x0d,0x11,0x6f,0xe1,0xb7,0xe8,0x70,0xaa,0x6e,
+ 0x2a,0x7f,0xc0,0x18,0x72,0x5e,0x3b,0x7f,0x96,0x9f,0x75,0x08,
+ 0x04,0x2e,0x44,0xcd,0x38,0x63,0xf3,0x9a,0xa7,0x50,0x26,0xa1,
+ 0x90,0xd1,0x90,0x2b,
+};
+
+
+
+
+
+
+

+B.1.9. Testvectors as JSON file encoded as BASE64 +

+
+
+ #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT
+ #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI3
+ #RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJnIjogIjY0RTgwOTlFM0
+ #VBNjgyQ0ZEQzVDQjY2NUMwNTdFQkI1MTREMDZCRjIzRUJDOUY3NDNCNTFCODIyNDIz
+ #MjcwNzQiLCAieWEiOiAiMjFCNEY0QkQ5RTY0RUQzNTVDM0VCNjc2QTI4RUJFREFGNk
+ #Q4RjE3QkRDMzY1OTk1QjMxOTA5NzE1MzA0NDA4MCIsICJBRGEiOiAiNDE0NDYxIiwg
+ #IllhIjogIjFCMDJEQUQ2REJEMjlBMDdCNkQyOEM5RTA0Q0IyRjE4NEYwNzM0MzUwRT
+ #MyQkI3RTYyRkY5REJDRkRCNjNEMTUiLCAieWIiOiAiODQ4QjA3NzlGRjQxNUYwQUY0
+ #RUExNERGOUREMUQzQzI5QUM0MUQ4MzZDNzgwODg5NkM0RUJBMTlDNTFBQzQwQSIsIC
+ #JBRGIiOiAiNDE0NDYyIiwgIlliIjogIjIwQ0RBNTk1NUY4MkM0OTMxNTQ1QkNCRjQw
+ #NzU4Q0UxMDEwRDdEQjREQjJBOTA3MDEzRDc5QzdBOEZDRjk1N0YiLCAiSyI6ICJGOT
+ #dGREZDRkZGMUM5ODNFRDYyODM4NTZBNDAxREUzMTkxQ0E5MTk5MDJCMzIzQzVGOTUw
+ #Qzk3MDNERjcyOTdBIiwgIklTS19JUiI6ICJBMDUxRUU1RUUyNDk5RDE2REEzRjY5Rj
+ #QzMDIxOEI4RUE5NEExOEE0NUI2N0Y5RTg2NDk1QjM4MkMzM0QxNEE1QzM4Q0VDQzBD
+ #QzgzNEY5NjBFMzlFMEQxQkY3RDc2QjlFRjVENTRFRUNDNUUwRjM4NkM5N0FEMTJEQT
+ #hDM0Q1RiIsICJJU0tfU1kiOiAiNUNDMjdFNDk2Nzk0MjNGODFBMzdENzUyMUQ5RkIx
+ #MzI3Qzg0MEQyRUE0QTE1NDM2NTJFN0RFNUNBQkI4OUVCQUQyN0QyNDc2MUIzMjg4QT
+ #NGRDU3NjRCNDQxRUNCNzhEMzBBQkMyNjE2MUZGNDVFQTI5N0JCMzExRERFMDQ3Mjci
+ #LCAic2lkX291dHB1dF9pciI6ICJGN0FFMTFBQzNFRTg1QzNDNDJEOEJENTFCQTgyM0
+ #ZCRTE3MTU4RjQzRDM0QTEyOTZGMUNCMjU2N0JDQzcxREM4QjIwMUExMzRCNTY2QjQ2
+ #OEFBRDhGRDA0RjAyRjk2RTNDQUY5RDU2MDFGN0VENzYwQTBBOTUxQTVBODYxQjVFNy
+ #IsICJzaWRfb3V0cHV0X29jIjogIkEzODM4OUUzNEZBNDkyNzg4QzFERjQzQjA2QjQy
+ #NzcxMDQ5MTE3NEU1M0MzM0IwMTM2MkE0OTBEMTE2RkUxQjdFODcwQUE2RTJBN0ZDMD
+ #E4NzI1RTNCN0Y5NjlGNzUwODA0MkU0NENEMzg2M0YzOUFBNzUwMjZBMTkwRDE5MDJC
+ #In0=
+
+
+
+
+
+
+

+B.1.10. Test vectors for G_X25519.scalar_mult_vfy: low order points +

+

Test vectors for which G_X25519.scalar_mult_vfy(s_in,ux) must return the neutral +element or would return the neutral element if bit #255 of field element +representation was not correctly cleared. (The decodeUCoordinate function from RFC7748 mandates clearing bit #255 for field element representations for use in the X25519 function.).

+
+
+u0: 0000000000000000000000000000000000000000000000000000000000000000
+u1: 0100000000000000000000000000000000000000000000000000000000000000
+u2: ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
+u3: e0eb7a7c3b41b8ae1656e3faf19fc46ada098deb9c32b1fd866205165f49b800
+u4: 5f9c95bca3508c24b1d0b1559c83ef5b04445cc4581c8e86d8224eddd09f1157
+u5: edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
+u6: daffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
+u7: eeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
+u8: dbffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
+u9: d9ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
+ua: cdeb7a7c3b41b8ae1656e3faf19fc46ada098deb9c32b1fd866205165f49b880
+ub: 4c9c95bca3508c24b1d0b1559c83ef5b04445cc4581c8e86d8224eddd09f11d7
+
+u0 ... ub MUST be verified to produce the correct results q0 ... qb:
+
+Additionally, u0,u1,u2,u3,u4,u5 and u7 MUST trigger the abort case
+when included in message from A or B.
+
+s = af46e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449aff
+qN = G_X25519.scalar_mult_vfy(s, uX)
+q0: 0000000000000000000000000000000000000000000000000000000000000000
+q1: 0000000000000000000000000000000000000000000000000000000000000000
+q2: 0000000000000000000000000000000000000000000000000000000000000000
+q3: 0000000000000000000000000000000000000000000000000000000000000000
+q4: 0000000000000000000000000000000000000000000000000000000000000000
+q5: 0000000000000000000000000000000000000000000000000000000000000000
+q6: d8e2c776bbacd510d09fd9278b7edcd25fc5ae9adfba3b6e040e8d3b71b21806
+q7: 0000000000000000000000000000000000000000000000000000000000000000
+q8: c85c655ebe8be44ba9c0ffde69f2fe10194458d137f09bbff725ce58803cdb38
+q9: db64dafa9b8fdd136914e61461935fe92aa372cb056314e1231bc4ec12417456
+qa: e062dcd5376d58297be2618c7498f55baa07d7e03184e8aada20bca28888bf7a
+qb: 993c6ad11c4c29da9a56f7691fd0ff8d732e49de6250b6c2e80003ff4629a175
+
+
+
+
+
+B.1.10.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJJbnZhbGlkIFkwIjogIjAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAiLCAiSW52YWxpZCBZMSI6ICIw
+ #MTAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwIiwgIkludmFsaWQgWTIiOiAiRUNGRkZGRkZGRkZGRkZGRkZG
+ #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkY3RiIsIC
+ #JJbnZhbGlkIFkzIjogIkUwRUI3QTdDM0I0MUI4QUUxNjU2RTNGQUYxOUZDNDZBREEw
+ #OThERUI5QzMyQjFGRDg2NjIwNTE2NUY0OUI4MDAiLCAiSW52YWxpZCBZNCI6ICI1Rj
+ #lDOTVCQ0EzNTA4QzI0QjFEMEIxNTU5QzgzRUY1QjA0NDQ1Q0M0NTgxQzhFODZEODIy
+ #NEVEREQwOUYxMTU3IiwgIkludmFsaWQgWTUiOiAiRURGRkZGRkZGRkZGRkZGRkZGRk
+ #ZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkY3RiIsICJJ
+ #bnZhbGlkIFk2IjogIkRBRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRk
+ #ZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkYiLCAiSW52YWxpZCBZNyI6ICJFRUZG
+ #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRk
+ #ZGRkZGRkZGRjdGIiwgIkludmFsaWQgWTgiOiAiREJGRkZGRkZGRkZGRkZGRkZGRkZG
+ #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRiIsICJJbn
+ #ZhbGlkIFk5IjogIkQ5RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZG
+ #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkYiLCAiSW52YWxpZCBZMTAiOiAiQ0RFQj
+ #dBN0MzQjQxQjhBRTE2NTZFM0ZBRjE5RkM0NkFEQTA5OERFQjlDMzJCMUZEODY2MjA1
+ #MTY1RjQ5Qjg4MCIsICJJbnZhbGlkIFkxMSI6ICI0QzlDOTVCQ0EzNTA4QzI0QjFEME
+ #IxNTU5QzgzRUY1QjA0NDQ1Q0M0NTgxQzhFODZEODIyNEVEREQwOUYxMUQ3In0=
+
+
+
+
+
+
+
+
+
+
+

+B.2. Test vector for CPace using group X448 and hash SHAKE-256 +

+
+
+

+B.2.1. Test vectors for calculate_generator with group X448 +

+
+
+  Inputs
+    H   = SHAKE-256 with input block size 136 bytes.
+    PRS = b'Password' ; ZPAD length: 117 ; DSI = b'CPace448'
+    CI = b'oc\x0bB_responder\x0bA_initiator'
+    CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72
+    sid = 5223e0cdc45d6575668d64c552004124
+  Outputs
+    generator_string(G.DSI,PRS,CI,sid,H.s_in_bytes):
+    (length: 180 bytes)
+      0843506163653434380850617373776f726475000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      0000000000000000000000000000000000000000000000001a6f630b
+      425f726573706f6e6465720b415f696e69746961746f72105223e0cd
+      c45d6575668d64c552004124
+    hash generator string: (length: 56 bytes)
+      98b713f84529194d719a7d86cb0f504b8afeb05354d68747e18b2e7c
+      c8b6da526085e4263bd8bea7d69e479ebad09e30ae062e5d089da7f3
+    decoded field element of 448 bits: (length: 56 bytes)
+      98b713f84529194d719a7d86cb0f504b8afeb05354d68747e18b2e7c
+      c8b6da526085e4263bd8bea7d69e479ebad09e30ae062e5d089da7f3
+    generator g: (length: 56 bytes)
+      e293b7ccf61ca7eb928a26391cf38b660f874a001fdf0bf3a91fd182
+      f2b6d83e61a9377ede127eba7e0d4c08592eaff33d4aa705d6ce54bb
+
+
+
+
+
+B.2.1.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJIIjogIlNIQUtFLTI1NiIsICJILnNfaW5fYnl0ZXMiOiAxMzYsICJQUlMiOiAiNT
+ #A2MTczNzM3NzZGNzI2NCIsICJaUEFEIGxlbmd0aCI6IDExNywgIkRTSSI6ICI0MzUw
+ #NjE2MzY1MzQzNDM4IiwgIkNJIjogIjZGNjMwQjQyNUY3MjY1NzM3MDZGNkU2NDY1Nz
+ #IwQjQxNUY2OTZFNjk3NDY5NjE3NDZGNzIiLCAic2lkIjogIjUyMjNFMENEQzQ1RDY1
+ #NzU2NjhENjRDNTUyMDA0MTI0IiwgImdlbmVyYXRvcl9zdHJpbmcoRy5EU0ksUFJTLE
+ #NJLHNpZCxILnNfaW5fYnl0ZXMpIjogIjA4NDM1MDYxNjM2NTM0MzQzODA4NTA2MTcz
+ #NzM3NzZGNzI2NDc1MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMU
+ #E2RjYzMEI0MjVGNzI2NTczNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2
+ #RjcyMTA1MjIzRTBDREM0NUQ2NTc1NjY4RDY0QzU1MjAwNDEyNCIsICJoYXNoIGdlbm
+ #VyYXRvciBzdHJpbmciOiAiOThCNzEzRjg0NTI5MTk0RDcxOUE3RDg2Q0IwRjUwNEI4
+ #QUZFQjA1MzU0RDY4NzQ3RTE4QjJFN0NDOEI2REE1MjYwODVFNDI2M0JEOEJFQTdENj
+ #lFNDc5RUJBRDA5RTMwQUUwNjJFNUQwODlEQTdGMyIsICJkZWNvZGVkIGZpZWxkIGVs
+ #ZW1lbnQgb2YgNDQ4IGJpdHMiOiAiOThCNzEzRjg0NTI5MTk0RDcxOUE3RDg2Q0IwRj
+ #UwNEI4QUZFQjA1MzU0RDY4NzQ3RTE4QjJFN0NDOEI2REE1MjYwODVFNDI2M0JEOEJF
+ #QTdENjlFNDc5RUJBRDA5RTMwQUUwNjJFNUQwODlEQTdGMyIsICJnZW5lcmF0b3IgZy
+ #I6ICJFMjkzQjdDQ0Y2MUNBN0VCOTI4QTI2MzkxQ0YzOEI2NjBGODc0QTAwMUZERjBC
+ #RjNBOTFGRDE4MkYyQjZEODNFNjFBOTM3N0VERTEyN0VCQTdFMEQ0QzA4NTkyRUFGRj
+ #MzRDRBQTcwNUQ2Q0U1NEJCIn0=
+
+
+
+
+
+
+
+
+

+B.2.2. Test vector for message from A +

+
+
+  Inputs
+    ADa = b'ADa'
+    ya (little endian): (length: 56 bytes)
+      21b4f4bd9e64ed355c3eb676a28ebedaf6d8f17bdc365995b3190971
+      53044080516bd083bfcce66121a3072646994c8430cc382b8dc543e8
+  Outputs
+    Ya: (length: 56 bytes)
+      7f645772cc209bf9fd9d76dbb10283bea71b12235e3bb21878d5e56a
+      70506e165743a632de98eca9932c5d2efe36500a59b2fdaed0d8a148
+
+
+
+
+
+
+

+B.2.3. Test vector for message from B +

+
+
+  Inputs
+    ADb = b'ADb'
+    yb (little endian): (length: 56 bytes)
+      848b0779ff415f0af4ea14df9dd1d3c29ac41d836c7808896c4eba19
+      c51ac40a439caf5e61ec88c307c7d619195229412eaa73fb2a5ea20d
+  Outputs
+    Yb: (length: 56 bytes)
+      a4690a0750c42b288ddd0ba08e3f4902dfe70bae5c9e2c6ee95844de
+      f2692be77646b20d3b429f8da00d21433ee0891c667658d8d0c48e38
+
+
+
+
+
+
+

+B.2.4. Test vector for secret points K +

+
+
+    scalar_mult_vfy(ya,Yb): (length: 56 bytes)
+      db3fff9da59576715b04d4df8dc8d18db2430e57bbed337dbeee5bb2
+      d6ab6ceddc9c75c5c0b17fad7eb724daa12f8f1903dd6c2cede6135a
+    scalar_mult_vfy(yb,Ya): (length: 56 bytes)
+      db3fff9da59576715b04d4df8dc8d18db2430e57bbed337dbeee5bb2
+      d6ab6ceddc9c75c5c0b17fad7eb724daa12f8f1903dd6c2cede6135a
+
+
+
+
+
+
+

+B.2.5. Test vector for ISK calculation initiator/responder +

+
+
+    transcript_ir(Ya,ADa,Yb,ADb): (length: 122 bytes)
+      387f645772cc209bf9fd9d76dbb10283bea71b12235e3bb21878d5e5
+      6a70506e165743a632de98eca9932c5d2efe36500a59b2fdaed0d8a1
+      480341446138a4690a0750c42b288ddd0ba08e3f4902dfe70bae5c9e
+      2c6ee95844def2692be77646b20d3b429f8da00d21433ee0891c6676
+      58d8d0c48e3803414462
+    DSI = G.DSI_ISK, b'CPace448_ISK': (length: 12 bytes)
+      43506163653434385f49534b
+    lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb):
+    (length: 209 bytes)
+      0c43506163653434385f49534b105223e0cdc45d6575668d64c55200
+      412438db3fff9da59576715b04d4df8dc8d18db2430e57bbed337dbe
+      ee5bb2d6ab6ceddc9c75c5c0b17fad7eb724daa12f8f1903dd6c2ced
+      e6135a387f645772cc209bf9fd9d76dbb10283bea71b12235e3bb218
+      78d5e56a70506e165743a632de98eca9932c5d2efe36500a59b2fdae
+      d0d8a1480341446138a4690a0750c42b288ddd0ba08e3f4902dfe70b
+      ae5c9e2c6ee95844def2692be77646b20d3b429f8da00d21433ee089
+      1c667658d8d0c48e3803414462
+    ISK result: (length: 64 bytes)
+      599892a2078a8c988181625e1e5e5f7a6163f7d72f21b93ebefba0f1
+      7ff7ea3aa0594bd569cf74264157b3c0087bdccf2f59c77156628487
+      f5ca1645b8e9d05b
+
+
+
+
+
+
+

+B.2.6. Test vector for ISK calculation parallel execution +

+
+
+    transcript_oc(Ya,ADa,Yb,ADb): (length: 124 bytes)
+      6f6338a4690a0750c42b288ddd0ba08e3f4902dfe70bae5c9e2c6ee9
+      5844def2692be77646b20d3b429f8da00d21433ee0891c667658d8d0
+      c48e3803414462387f645772cc209bf9fd9d76dbb10283bea71b1223
+      5e3bb21878d5e56a70506e165743a632de98eca9932c5d2efe36500a
+      59b2fdaed0d8a14803414461
+    DSI = G.DSI_ISK, b'CPace448_ISK': (length: 12 bytes)
+      43506163653434385f49534b
+    lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb):
+    (length: 211 bytes)
+      0c43506163653434385f49534b105223e0cdc45d6575668d64c55200
+      412438db3fff9da59576715b04d4df8dc8d18db2430e57bbed337dbe
+      ee5bb2d6ab6ceddc9c75c5c0b17fad7eb724daa12f8f1903dd6c2ced
+      e6135a6f6338a4690a0750c42b288ddd0ba08e3f4902dfe70bae5c9e
+      2c6ee95844def2692be77646b20d3b429f8da00d21433ee0891c6676
+      58d8d0c48e3803414462387f645772cc209bf9fd9d76dbb10283bea7
+      1b12235e3bb21878d5e56a70506e165743a632de98eca9932c5d2efe
+      36500a59b2fdaed0d8a14803414461
+    ISK result: (length: 64 bytes)
+      3ac73f03030296aa591f01326b18afa47e1189129cd06ae8dfb05e6e
+      b1310cde948b59eef0755365c06a339266afe594948c56a538d98a65
+      767113938a9a78d8
+
+
+
+
+
+
+

+B.2.7. Test vector for optional output of session id +

+
+
+    H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      00a2333a79481abe71efd6594d7bbaac55c808482e869c9b65c4b53d
+      7100d3da8f3cabd59fa0c1f22d6d2f9ac0c093962292798fca2c0b93
+      268974cad75d575a
+    H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      a1ce90537a8d53b06d77e79fe719461cc5ed8300d21d1866a59f9638
+      601833f57a8b5e88db9a52abfa1b4e8a651a400bc9205082aad81eb3
+      11c44373b9a19eff
+
+
+
+
+
+
+

+B.2.8. Corresponding C programming language initializers +

+
+
+const unsigned char tc_PRS[] = {
+ 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64,
+};
+const unsigned char tc_CI[] = {
+ 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64,
+ 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74,
+ 0x6f,0x72,
+};
+const unsigned char tc_sid[] = {
+ 0x52,0x23,0xe0,0xcd,0xc4,0x5d,0x65,0x75,0x66,0x8d,0x64,0xc5,
+ 0x52,0x00,0x41,0x24,
+};
+const unsigned char tc_g[] = {
+ 0xe2,0x93,0xb7,0xcc,0xf6,0x1c,0xa7,0xeb,0x92,0x8a,0x26,0x39,
+ 0x1c,0xf3,0x8b,0x66,0x0f,0x87,0x4a,0x00,0x1f,0xdf,0x0b,0xf3,
+ 0xa9,0x1f,0xd1,0x82,0xf2,0xb6,0xd8,0x3e,0x61,0xa9,0x37,0x7e,
+ 0xde,0x12,0x7e,0xba,0x7e,0x0d,0x4c,0x08,0x59,0x2e,0xaf,0xf3,
+ 0x3d,0x4a,0xa7,0x05,0xd6,0xce,0x54,0xbb,
+};
+const unsigned char tc_ya[] = {
+ 0x21,0xb4,0xf4,0xbd,0x9e,0x64,0xed,0x35,0x5c,0x3e,0xb6,0x76,
+ 0xa2,0x8e,0xbe,0xda,0xf6,0xd8,0xf1,0x7b,0xdc,0x36,0x59,0x95,
+ 0xb3,0x19,0x09,0x71,0x53,0x04,0x40,0x80,0x51,0x6b,0xd0,0x83,
+ 0xbf,0xcc,0xe6,0x61,0x21,0xa3,0x07,0x26,0x46,0x99,0x4c,0x84,
+ 0x30,0xcc,0x38,0x2b,0x8d,0xc5,0x43,0xe8,
+};
+const unsigned char tc_ADa[] = {
+ 0x41,0x44,0x61,
+};
+const unsigned char tc_Ya[] = {
+ 0x7f,0x64,0x57,0x72,0xcc,0x20,0x9b,0xf9,0xfd,0x9d,0x76,0xdb,
+ 0xb1,0x02,0x83,0xbe,0xa7,0x1b,0x12,0x23,0x5e,0x3b,0xb2,0x18,
+ 0x78,0xd5,0xe5,0x6a,0x70,0x50,0x6e,0x16,0x57,0x43,0xa6,0x32,
+ 0xde,0x98,0xec,0xa9,0x93,0x2c,0x5d,0x2e,0xfe,0x36,0x50,0x0a,
+ 0x59,0xb2,0xfd,0xae,0xd0,0xd8,0xa1,0x48,
+};
+const unsigned char tc_yb[] = {
+ 0x84,0x8b,0x07,0x79,0xff,0x41,0x5f,0x0a,0xf4,0xea,0x14,0xdf,
+ 0x9d,0xd1,0xd3,0xc2,0x9a,0xc4,0x1d,0x83,0x6c,0x78,0x08,0x89,
+ 0x6c,0x4e,0xba,0x19,0xc5,0x1a,0xc4,0x0a,0x43,0x9c,0xaf,0x5e,
+ 0x61,0xec,0x88,0xc3,0x07,0xc7,0xd6,0x19,0x19,0x52,0x29,0x41,
+ 0x2e,0xaa,0x73,0xfb,0x2a,0x5e,0xa2,0x0d,
+};
+const unsigned char tc_ADb[] = {
+ 0x41,0x44,0x62,
+};
+const unsigned char tc_Yb[] = {
+ 0xa4,0x69,0x0a,0x07,0x50,0xc4,0x2b,0x28,0x8d,0xdd,0x0b,0xa0,
+ 0x8e,0x3f,0x49,0x02,0xdf,0xe7,0x0b,0xae,0x5c,0x9e,0x2c,0x6e,
+ 0xe9,0x58,0x44,0xde,0xf2,0x69,0x2b,0xe7,0x76,0x46,0xb2,0x0d,
+ 0x3b,0x42,0x9f,0x8d,0xa0,0x0d,0x21,0x43,0x3e,0xe0,0x89,0x1c,
+ 0x66,0x76,0x58,0xd8,0xd0,0xc4,0x8e,0x38,
+};
+const unsigned char tc_K[] = {
+ 0xdb,0x3f,0xff,0x9d,0xa5,0x95,0x76,0x71,0x5b,0x04,0xd4,0xdf,
+ 0x8d,0xc8,0xd1,0x8d,0xb2,0x43,0x0e,0x57,0xbb,0xed,0x33,0x7d,
+ 0xbe,0xee,0x5b,0xb2,0xd6,0xab,0x6c,0xed,0xdc,0x9c,0x75,0xc5,
+ 0xc0,0xb1,0x7f,0xad,0x7e,0xb7,0x24,0xda,0xa1,0x2f,0x8f,0x19,
+ 0x03,0xdd,0x6c,0x2c,0xed,0xe6,0x13,0x5a,
+};
+const unsigned char tc_ISK_IR[] = {
+ 0x59,0x98,0x92,0xa2,0x07,0x8a,0x8c,0x98,0x81,0x81,0x62,0x5e,
+ 0x1e,0x5e,0x5f,0x7a,0x61,0x63,0xf7,0xd7,0x2f,0x21,0xb9,0x3e,
+ 0xbe,0xfb,0xa0,0xf1,0x7f,0xf7,0xea,0x3a,0xa0,0x59,0x4b,0xd5,
+ 0x69,0xcf,0x74,0x26,0x41,0x57,0xb3,0xc0,0x08,0x7b,0xdc,0xcf,
+ 0x2f,0x59,0xc7,0x71,0x56,0x62,0x84,0x87,0xf5,0xca,0x16,0x45,
+ 0xb8,0xe9,0xd0,0x5b,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x3a,0xc7,0x3f,0x03,0x03,0x02,0x96,0xaa,0x59,0x1f,0x01,0x32,
+ 0x6b,0x18,0xaf,0xa4,0x7e,0x11,0x89,0x12,0x9c,0xd0,0x6a,0xe8,
+ 0xdf,0xb0,0x5e,0x6e,0xb1,0x31,0x0c,0xde,0x94,0x8b,0x59,0xee,
+ 0xf0,0x75,0x53,0x65,0xc0,0x6a,0x33,0x92,0x66,0xaf,0xe5,0x94,
+ 0x94,0x8c,0x56,0xa5,0x38,0xd9,0x8a,0x65,0x76,0x71,0x13,0x93,
+ 0x8a,0x9a,0x78,0xd8,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x3a,0xc7,0x3f,0x03,0x03,0x02,0x96,0xaa,0x59,0x1f,0x01,0x32,
+ 0x6b,0x18,0xaf,0xa4,0x7e,0x11,0x89,0x12,0x9c,0xd0,0x6a,0xe8,
+ 0xdf,0xb0,0x5e,0x6e,0xb1,0x31,0x0c,0xde,0x94,0x8b,0x59,0xee,
+ 0xf0,0x75,0x53,0x65,0xc0,0x6a,0x33,0x92,0x66,0xaf,0xe5,0x94,
+ 0x94,0x8c,0x56,0xa5,0x38,0xd9,0x8a,0x65,0x76,0x71,0x13,0x93,
+ 0x8a,0x9a,0x78,0xd8,
+};
+const unsigned char tc_sid_out_ir[] = {
+ 0x00,0xa2,0x33,0x3a,0x79,0x48,0x1a,0xbe,0x71,0xef,0xd6,0x59,
+ 0x4d,0x7b,0xba,0xac,0x55,0xc8,0x08,0x48,0x2e,0x86,0x9c,0x9b,
+ 0x65,0xc4,0xb5,0x3d,0x71,0x00,0xd3,0xda,0x8f,0x3c,0xab,0xd5,
+ 0x9f,0xa0,0xc1,0xf2,0x2d,0x6d,0x2f,0x9a,0xc0,0xc0,0x93,0x96,
+ 0x22,0x92,0x79,0x8f,0xca,0x2c,0x0b,0x93,0x26,0x89,0x74,0xca,
+ 0xd7,0x5d,0x57,0x5a,
+};
+const unsigned char tc_sid_out_oc[] = {
+ 0xa1,0xce,0x90,0x53,0x7a,0x8d,0x53,0xb0,0x6d,0x77,0xe7,0x9f,
+ 0xe7,0x19,0x46,0x1c,0xc5,0xed,0x83,0x00,0xd2,0x1d,0x18,0x66,
+ 0xa5,0x9f,0x96,0x38,0x60,0x18,0x33,0xf5,0x7a,0x8b,0x5e,0x88,
+ 0xdb,0x9a,0x52,0xab,0xfa,0x1b,0x4e,0x8a,0x65,0x1a,0x40,0x0b,
+ 0xc9,0x20,0x50,0x82,0xaa,0xd8,0x1e,0xb3,0x11,0xc4,0x43,0x73,
+ 0xb9,0xa1,0x9e,0xff,
+};
+
+
+
+
+
+
+

+B.2.9. Testvectors as JSON file encoded as BASE64 +

+
+
+ #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT
+ #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI1
+ #MjIzRTBDREM0NUQ2NTc1NjY4RDY0QzU1MjAwNDEyNCIsICJnIjogIkUyOTNCN0NDRj
+ #YxQ0E3RUI5MjhBMjYzOTFDRjM4QjY2MEY4NzRBMDAxRkRGMEJGM0E5MUZEMTgyRjJC
+ #NkQ4M0U2MUE5Mzc3RURFMTI3RUJBN0UwRDRDMDg1OTJFQUZGMzNENEFBNzA1RDZDRT
+ #U0QkIiLCAieWEiOiAiMjFCNEY0QkQ5RTY0RUQzNTVDM0VCNjc2QTI4RUJFREFGNkQ4
+ #RjE3QkRDMzY1OTk1QjMxOTA5NzE1MzA0NDA4MDUxNkJEMDgzQkZDQ0U2NjEyMUEzMD
+ #cyNjQ2OTk0Qzg0MzBDQzM4MkI4REM1NDNFOCIsICJBRGEiOiAiNDE0NDYxIiwgIllh
+ #IjogIjdGNjQ1NzcyQ0MyMDlCRjlGRDlENzZEQkIxMDI4M0JFQTcxQjEyMjM1RTNCQj
+ #IxODc4RDVFNTZBNzA1MDZFMTY1NzQzQTYzMkRFOThFQ0E5OTMyQzVEMkVGRTM2NTAw
+ #QTU5QjJGREFFRDBEOEExNDgiLCAieWIiOiAiODQ4QjA3NzlGRjQxNUYwQUY0RUExNE
+ #RGOUREMUQzQzI5QUM0MUQ4MzZDNzgwODg5NkM0RUJBMTlDNTFBQzQwQTQzOUNBRjVF
+ #NjFFQzg4QzMwN0M3RDYxOTE5NTIyOTQxMkVBQTczRkIyQTVFQTIwRCIsICJBRGIiOi
+ #AiNDE0NDYyIiwgIlliIjogIkE0NjkwQTA3NTBDNDJCMjg4REREMEJBMDhFM0Y0OTAy
+ #REZFNzBCQUU1QzlFMkM2RUU5NTg0NERFRjI2OTJCRTc3NjQ2QjIwRDNCNDI5RjhEQT
+ #AwRDIxNDMzRUUwODkxQzY2NzY1OEQ4RDBDNDhFMzgiLCAiSyI6ICJEQjNGRkY5REE1
+ #OTU3NjcxNUIwNEQ0REY4REM4RDE4REIyNDMwRTU3QkJFRDMzN0RCRUVFNUJCMkQ2QU
+ #I2Q0VEREM5Qzc1QzVDMEIxN0ZBRDdFQjcyNERBQTEyRjhGMTkwM0RENkMyQ0VERTYx
+ #MzVBIiwgIklTS19JUiI6ICI1OTk4OTJBMjA3OEE4Qzk4ODE4MTYyNUUxRTVFNUY3QT
+ #YxNjNGN0Q3MkYyMUI5M0VCRUZCQTBGMTdGRjdFQTNBQTA1OTRCRDU2OUNGNzQyNjQx
+ #NTdCM0MwMDg3QkRDQ0YyRjU5Qzc3MTU2NjI4NDg3RjVDQTE2NDVCOEU5RDA1QiIsIC
+ #JJU0tfU1kiOiAiM0FDNzNGMDMwMzAyOTZBQTU5MUYwMTMyNkIxOEFGQTQ3RTExODkx
+ #MjlDRDA2QUU4REZCMDVFNkVCMTMxMENERTk0OEI1OUVFRjA3NTUzNjVDMDZBMzM5Mj
+ #Y2QUZFNTk0OTQ4QzU2QTUzOEQ5OEE2NTc2NzExMzkzOEE5QTc4RDgiLCAic2lkX291
+ #dHB1dF9pciI6ICIwMEEyMzMzQTc5NDgxQUJFNzFFRkQ2NTk0RDdCQkFBQzU1QzgwOD
+ #Q4MkU4NjlDOUI2NUM0QjUzRDcxMDBEM0RBOEYzQ0FCRDU5RkEwQzFGMjJENkQyRjlB
+ #QzBDMDkzOTYyMjkyNzk4RkNBMkMwQjkzMjY4OTc0Q0FENzVENTc1QSIsICJzaWRfb3
+ #V0cHV0X29jIjogIkExQ0U5MDUzN0E4RDUzQjA2RDc3RTc5RkU3MTk0NjFDQzVFRDgz
+ #MDBEMjFEMTg2NkE1OUY5NjM4NjAxODMzRjU3QThCNUU4OERCOUE1MkFCRkExQjRFOE
+ #E2NTFBNDAwQkM5MjA1MDgyQUFEODFFQjMxMUM0NDM3M0I5QTE5RUZGIn0=
+
+
+
+
+
+
+

+B.2.10. Test vectors for G_X448.scalar_mult_vfy: low order points +

+

Test vectors for which G_X448.scalar_mult_vfy(s_in,ux) must return the neutral +element. +This includes points that are non-canonicaly encoded, i.e. have coordinate values +larger +than the field prime.

+

Weak points for X448 smaller than the field prime (canonical)

+
+
+  u0: (length: 56 bytes)
+    0000000000000000000000000000000000000000000000000000000000
+    000000000000000000000000000000000000000000000000000000
+  u1: (length: 56 bytes)
+    0100000000000000000000000000000000000000000000000000000000
+    000000000000000000000000000000000000000000000000000000
+  u2: (length: 56 bytes)
+    fefffffffffffffffffffffffffffffffffffffffffffffffffffffffe
+    ffffffffffffffffffffffffffffffffffffffffffffffffffffff
+
+
+

Weak points for X448 larger or equal to the field prime (non-canonical)

+
+
+  u3: (length: 56 bytes)
+    fffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
+    ffffffffffffffffffffffffffffffffffffffffffffffffffffff
+  u4: (length: 56 bytes)
+    00000000000000000000000000000000000000000000000000000000ff
+    ffffffffffffffffffffffffffffffffffffffffffffffffffffff
+
+All of the above points u0 ... u4 MUST trigger the abort case
+when included in the protocol messages from A or B.
+
+
+

Expected results for X448 resp. G_X448.scalar_mult_vfy

+
+
+  scalar s: (length: 56 bytes)
+    af8a14218bf2a2062926d2ea9b8fe4e8b6817349b6ed2feb1e5d64d7a4
+    523f15fceec70fb111e870dc58d191e66a14d3e9d482d04432cadd
+  G_X448.scalar_mult_vfy(s,u0): (length: 56 bytes)
+    0000000000000000000000000000000000000000000000000000000000
+    000000000000000000000000000000000000000000000000000000
+  G_X448.scalar_mult_vfy(s,u1): (length: 56 bytes)
+    0000000000000000000000000000000000000000000000000000000000
+    000000000000000000000000000000000000000000000000000000
+  G_X448.scalar_mult_vfy(s,u2): (length: 56 bytes)
+    0000000000000000000000000000000000000000000000000000000000
+    000000000000000000000000000000000000000000000000000000
+  G_X448.scalar_mult_vfy(s,u3): (length: 56 bytes)
+    0000000000000000000000000000000000000000000000000000000000
+    000000000000000000000000000000000000000000000000000000
+  G_X448.scalar_mult_vfy(s,u4): (length: 56 bytes)
+    0000000000000000000000000000000000000000000000000000000000
+    000000000000000000000000000000000000000000000000000000
+
+
+

Test vectors for scalar_mult with nonzero outputs

+
+
+  scalar s: (length: 56 bytes)
+    af8a14218bf2a2062926d2ea9b8fe4e8b6817349b6ed2feb1e5d64d7a4
+    523f15fceec70fb111e870dc58d191e66a14d3e9d482d04432cadd
+  point coordinate u_curve on the curve: (length: 56 bytes)
+    ab0c68d772ec2eb9de25c49700e46d6325e66d6aa39d7b65eb84a68c55
+    69d47bd71b41f3e0d210f44e146dec8926b174acb3f940a0b82cab
+  G_X448.scalar_mult_vfy(s,u_curve): (length: 56 bytes)
+    3b0fa9bc40a6fdc78c9e06ff7a54c143c5d52f365607053bf0656f5142
+    0496295f910a101b38edc1acd3bd240fd55dcb7a360553b8a7627e
+
+  point coordinate u_twist on the twist: (length: 56 bytes)
+    c981cd1e1f72d9c35c7d7cf6be426757c0dc8206a2fcfa564a8e7618c0
+    3c0e61f9a2eb1c3e0dd97d6e9b1010f5edd03397a83f5a914cb3ff
+  G_X448.scalar_mult_vfy(s,u_twist): (length: 56 bytes)
+    d0a2bb7e9c5c2c627793d8342f23b759fe7d9e3320a85ca4fd61376331
+    50ffd9a9148a9b75c349fac43d64bec49a6e126cc92cbfbf353961
+
+
+
+
+
+B.2.10.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJJbnZhbGlkIFkxIjogIjAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAiLCAiSW52YWxpZCBZMiI6ICIwMT
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwIiwgIkludmFsaWQgWTMiOiAiRkVGRkZGRkZGRkZGRkZGRkZGRkZG
+ #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRUZGRkZGRkZGRkZGRk
+ #ZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRiIsICJJbnZh
+ #bGlkIFk0IjogIkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRk
+ #ZGRkZGRkZGRkZGRkZGRkZGRkVGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZG
+ #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkYiLCAiSW52YWxpZCBZNSI6ICIwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMEZG
+ #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRk
+ #ZGRkZGIiwgIlZhbGlkIChvbiBjdXJ2ZSkiOiB7InMiOiAiQUY4QTE0MjE4QkYyQTIw
+ #NjI5MjZEMkVBOUI4RkU0RThCNjgxNzM0OUI2RUQyRkVCMUU1RDY0RDdBNDUyM0YxNU
+ #ZDRUVDNzBGQjExMUU4NzBEQzU4RDE5MUU2NkExNEQzRTlENDgyRDA0NDMyQ0FERCIs
+ #ICJ1X2N1cnZlIjogIkFCMEM2OEQ3NzJFQzJFQjlERTI1QzQ5NzAwRTQ2RDYzMjVFNj
+ #ZENkFBMzlEN0I2NUVCODRBNjhDNTU2OUQ0N0JENzFCNDFGM0UwRDIxMEY0NEUxNDZE
+ #RUM4OTI2QjE3NEFDQjNGOTQwQTBCODJDQUIiLCAicmVzX2N1cnZlIjogIjNCMEZBOU
+ #JDNDBBNkZEQzc4QzlFMDZGRjdBNTRDMTQzQzVENTJGMzY1NjA3MDUzQkYwNjU2RjUx
+ #NDIwNDk2Mjk1RjkxMEExMDFCMzhFREMxQUNEM0JEMjQwRkQ1NURDQjdBMzYwNTUzQj
+ #hBNzYyN0UifSwgIlZhbGlkIChvbiB0d2lzdCkiOiB7InMiOiAiQUY4QTE0MjE4QkYy
+ #QTIwNjI5MjZEMkVBOUI4RkU0RThCNjgxNzM0OUI2RUQyRkVCMUU1RDY0RDdBNDUyM0
+ #YxNUZDRUVDNzBGQjExMUU4NzBEQzU4RDE5MUU2NkExNEQzRTlENDgyRDA0NDMyQ0FE
+ #RCIsICJ1X3R3aXN0IjogIkM5ODFDRDFFMUY3MkQ5QzM1QzdEN0NGNkJFNDI2NzU3Qz
+ #BEQzgyMDZBMkZDRkE1NjRBOEU3NjE4QzAzQzBFNjFGOUEyRUIxQzNFMEREOTdENkU5
+ #QjEwMTBGNUVERDAzMzk3QTgzRjVBOTE0Q0IzRkYiLCAicmVzX3R3aXN0IjogIkQwQT
+ #JCQjdFOUM1QzJDNjI3NzkzRDgzNDJGMjNCNzU5RkU3RDlFMzMyMEE4NUNBNEZENjEz
+ #NzYzMzE1MEZGRDlBOTE0OEE5Qjc1QzM0OUZBQzQzRDY0QkVDNDlBNkUxMjZDQzkyQ0
+ #JGQkYzNTM5NjEifX0=
+
+
+
+
+
+
+
+
+
+
+

+B.3. Test vector for CPace using group ristretto255 and hash SHA-512 +

+
+
+

+B.3.1. Test vectors for calculate_generator with group ristretto255 +

+
+
+  Inputs
+    H   = SHA-512 with input block size 128 bytes.
+    PRS = b'Password' ; ZPAD length: 100 ;
+    DSI = b'CPaceRistretto255'
+    CI = b'oc\x0bB_responder\x0bA_initiator'
+    CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72
+    sid = 7e4b4791d6a8ef019b936c79fb7f2c57
+  Outputs
+    generator_string(G.DSI,PRS,CI,sid,H.s_in_bytes):
+    (length: 172 bytes)
+      11435061636552697374726574746f3235350850617373776f726464
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      000000000000000000000000000000001a6f630b425f726573706f6e
+      6465720b415f696e69746961746f72107e4b4791d6a8ef019b936c79
+      fb7f2c57
+    hash result: (length: 64 bytes)
+      c63a5750e2439c17ccd8213be14fde2f87e1bc637001a97f5929c77b
+      30ea0e08afbc75ace5d3d73b2842a79d01488c5fd7ea30d475ee6095
+      45af1bfd1ff77c8e
+    encoded generator g: (length: 32 bytes)
+      a6fc82c3b8968fbb2e06fee81ca858586dea50d248f0c7ca6a18b090
+      2a30b36b
+
+
+
+
+
+B.3.1.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJIIjogIlNIQS01MTIiLCAiSC5zX2luX2J5dGVzIjogMTI4LCAiUFJTIjogIjUwNj
+ #E3MzczNzc2RjcyNjQiLCAiWlBBRCBsZW5ndGgiOiAxMDAsICJEU0kiOiAiNDM1MDYx
+ #NjM2NTUyNjk3Mzc0NzI2NTc0NzQ2RjMyMzUzNSIsICJDSSI6ICI2RjYzMEI0MjVGNz
+ #I2NTczNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6
+ #ICI3RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJnZW5lcmF0b3Jfc3
+ #RyaW5nKEcuRFNJLFBSUyxDSSxzaWQsSC5zX2luX2J5dGVzKSI6ICIxMTQzNTA2MTYz
+ #NjU1MjY5NzM3NDcyNjU3NDc0NkYzMjM1MzUwODUwNjE3MzczNzc2RjcyNjQ2NDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMU
+ #E2RjYzMEI0MjVGNzI2NTczNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2
+ #RjcyMTA3RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJoYXNoIHJlc3
+ #VsdCI6ICJDNjNBNTc1MEUyNDM5QzE3Q0NEODIxM0JFMTRGREUyRjg3RTFCQzYzNzAw
+ #MUE5N0Y1OTI5Qzc3QjMwRUEwRTA4QUZCQzc1QUNFNUQzRDczQjI4NDJBNzlEMDE0OD
+ #hDNUZEN0VBMzBENDc1RUU2MDk1NDVBRjFCRkQxRkY3N0M4RSIsICJlbmNvZGVkIGdl
+ #bmVyYXRvciBnIjogIkE2RkM4MkMzQjg5NjhGQkIyRTA2RkVFODFDQTg1ODU4NkRFQT
+ #UwRDI0OEYwQzdDQTZBMThCMDkwMkEzMEIzNkIifQ==
+
+
+
+
+
+
+
+
+

+B.3.2. Test vector for message from A +

+
+
+  Inputs
+    ADa = b'ADa'
+    ya (little endian): (length: 32 bytes)
+      da3d23700a9e5699258aef94dc060dfda5ebb61f02a5ea77fad53f4f
+      f0976d08
+  Outputs
+    Ya: (length: 32 bytes)
+      d40fb265a7abeaee7939d91a585fe59f7053f982c296ec413c624c66
+      9308f87a
+
+
+
+
+
+
+

+B.3.3. Test vector for message from B +

+
+
+  Inputs
+    ADb = b'ADb'
+    yb (little endian): (length: 32 bytes)
+      d2316b454718c35362d83d69df6320f38578ed5984651435e2949762
+      d900b80d
+  Outputs
+    Yb: (length: 32 bytes)
+      08bcf6e9777a9c313a3db6daa510f2d398403319c2341bd506a92e67
+      2eb7e307
+
+
+
+
+
+
+

+B.3.4. Test vector for secret points K +

+
+
+    scalar_mult_vfy(ya,Yb): (length: 32 bytes)
+      e22b1ef7788f661478f3cddd4c600774fc0f41e6b711569190ff88fa
+      0e607e09
+    scalar_mult_vfy(yb,Ya): (length: 32 bytes)
+      e22b1ef7788f661478f3cddd4c600774fc0f41e6b711569190ff88fa
+      0e607e09
+
+
+
+
+
+
+

+B.3.5. Test vector for ISK calculation initiator/responder +

+
+
+    transcript_ir(Ya,ADa,Yb,ADb): (length: 74 bytes)
+      20d40fb265a7abeaee7939d91a585fe59f7053f982c296ec413c624c
+      669308f87a034144612008bcf6e9777a9c313a3db6daa510f2d39840
+      3319c2341bd506a92e672eb7e30703414462
+    DSI = G.DSI_ISK, b'CPaceRistretto255_ISK':
+    (length: 21 bytes)
+      435061636552697374726574746f3235355f49534b
+    lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb):
+    (length: 146 bytes)
+      15435061636552697374726574746f3235355f49534b107e4b4791d6
+      a8ef019b936c79fb7f2c5720e22b1ef7788f661478f3cddd4c600774
+      fc0f41e6b711569190ff88fa0e607e0920d40fb265a7abeaee7939d9
+      1a585fe59f7053f982c296ec413c624c669308f87a034144612008bc
+      f6e9777a9c313a3db6daa510f2d398403319c2341bd506a92e672eb7
+      e30703414462
+    ISK result: (length: 64 bytes)
+      4c5469a16b2364c4b944ebc1a79e51d1674ad47db26e8718154f59fa
+      ebfaa52d8346f30aa58377117eb20d527f2cbc5c76381f7fd372e89d
+      f8239f87f2e02ed1
+
+
+
+
+
+
+

+B.3.6. Test vector for ISK calculation parallel execution +

+
+
+    transcript_oc(Ya,ADa,Yb,ADb): (length: 76 bytes)
+      6f6320d40fb265a7abeaee7939d91a585fe59f7053f982c296ec413c
+      624c669308f87a034144612008bcf6e9777a9c313a3db6daa510f2d3
+      98403319c2341bd506a92e672eb7e30703414462
+    DSI = G.DSI_ISK, b'CPaceRistretto255_ISK':
+    (length: 21 bytes)
+      435061636552697374726574746f3235355f49534b
+    lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb):
+    (length: 148 bytes)
+      15435061636552697374726574746f3235355f49534b107e4b4791d6
+      a8ef019b936c79fb7f2c5720e22b1ef7788f661478f3cddd4c600774
+      fc0f41e6b711569190ff88fa0e607e096f6320d40fb265a7abeaee79
+      39d91a585fe59f7053f982c296ec413c624c669308f87a0341446120
+      08bcf6e9777a9c313a3db6daa510f2d398403319c2341bd506a92e67
+      2eb7e30703414462
+    ISK result: (length: 64 bytes)
+      980dcc5a1c52ceea031e75f38ed266586616488c5c5780285fcbcf79
+      087c7bcdbd993502eee606b718ba31e840a000a7b7befe15ea427c5c
+      fe88344fa1237f35
+
+
+
+
+
+
+

+B.3.7. Test vector for optional output of session id +

+
+
+    H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      2a76d3bbc499dfdc4dcacc9ff042f4e1a54e3843258e100ccd7c60f0
+      a541f9d3ebf025e68a460dde218bd39f0711bc6fa11409c9d7b69d8c
+      cf6b32fc51ddb699
+    H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      ca4b50700c46203ccd10bc0e9f31095e508189cb59857537be561048
+      d34b9ed9a9697af11c998f484c3d783b0b531434caa6835d4c32344f
+      cd17160c9c348fc7
+
+
+
+
+
+
+

+B.3.8. Corresponding C programming language initializers +

+
+
+const unsigned char tc_PRS[] = {
+ 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64,
+};
+const unsigned char tc_CI[] = {
+ 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64,
+ 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74,
+ 0x6f,0x72,
+};
+const unsigned char tc_sid[] = {
+ 0x7e,0x4b,0x47,0x91,0xd6,0xa8,0xef,0x01,0x9b,0x93,0x6c,0x79,
+ 0xfb,0x7f,0x2c,0x57,
+};
+const unsigned char tc_g[] = {
+ 0xa6,0xfc,0x82,0xc3,0xb8,0x96,0x8f,0xbb,0x2e,0x06,0xfe,0xe8,
+ 0x1c,0xa8,0x58,0x58,0x6d,0xea,0x50,0xd2,0x48,0xf0,0xc7,0xca,
+ 0x6a,0x18,0xb0,0x90,0x2a,0x30,0xb3,0x6b,
+};
+const unsigned char tc_ya[] = {
+ 0xda,0x3d,0x23,0x70,0x0a,0x9e,0x56,0x99,0x25,0x8a,0xef,0x94,
+ 0xdc,0x06,0x0d,0xfd,0xa5,0xeb,0xb6,0x1f,0x02,0xa5,0xea,0x77,
+ 0xfa,0xd5,0x3f,0x4f,0xf0,0x97,0x6d,0x08,
+};
+const unsigned char tc_ADa[] = {
+ 0x41,0x44,0x61,
+};
+const unsigned char tc_Ya[] = {
+ 0xd4,0x0f,0xb2,0x65,0xa7,0xab,0xea,0xee,0x79,0x39,0xd9,0x1a,
+ 0x58,0x5f,0xe5,0x9f,0x70,0x53,0xf9,0x82,0xc2,0x96,0xec,0x41,
+ 0x3c,0x62,0x4c,0x66,0x93,0x08,0xf8,0x7a,
+};
+const unsigned char tc_yb[] = {
+ 0xd2,0x31,0x6b,0x45,0x47,0x18,0xc3,0x53,0x62,0xd8,0x3d,0x69,
+ 0xdf,0x63,0x20,0xf3,0x85,0x78,0xed,0x59,0x84,0x65,0x14,0x35,
+ 0xe2,0x94,0x97,0x62,0xd9,0x00,0xb8,0x0d,
+};
+const unsigned char tc_ADb[] = {
+ 0x41,0x44,0x62,
+};
+const unsigned char tc_Yb[] = {
+ 0x08,0xbc,0xf6,0xe9,0x77,0x7a,0x9c,0x31,0x3a,0x3d,0xb6,0xda,
+ 0xa5,0x10,0xf2,0xd3,0x98,0x40,0x33,0x19,0xc2,0x34,0x1b,0xd5,
+ 0x06,0xa9,0x2e,0x67,0x2e,0xb7,0xe3,0x07,
+};
+const unsigned char tc_K[] = {
+ 0xe2,0x2b,0x1e,0xf7,0x78,0x8f,0x66,0x14,0x78,0xf3,0xcd,0xdd,
+ 0x4c,0x60,0x07,0x74,0xfc,0x0f,0x41,0xe6,0xb7,0x11,0x56,0x91,
+ 0x90,0xff,0x88,0xfa,0x0e,0x60,0x7e,0x09,
+};
+const unsigned char tc_ISK_IR[] = {
+ 0x4c,0x54,0x69,0xa1,0x6b,0x23,0x64,0xc4,0xb9,0x44,0xeb,0xc1,
+ 0xa7,0x9e,0x51,0xd1,0x67,0x4a,0xd4,0x7d,0xb2,0x6e,0x87,0x18,
+ 0x15,0x4f,0x59,0xfa,0xeb,0xfa,0xa5,0x2d,0x83,0x46,0xf3,0x0a,
+ 0xa5,0x83,0x77,0x11,0x7e,0xb2,0x0d,0x52,0x7f,0x2c,0xbc,0x5c,
+ 0x76,0x38,0x1f,0x7f,0xd3,0x72,0xe8,0x9d,0xf8,0x23,0x9f,0x87,
+ 0xf2,0xe0,0x2e,0xd1,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x98,0x0d,0xcc,0x5a,0x1c,0x52,0xce,0xea,0x03,0x1e,0x75,0xf3,
+ 0x8e,0xd2,0x66,0x58,0x66,0x16,0x48,0x8c,0x5c,0x57,0x80,0x28,
+ 0x5f,0xcb,0xcf,0x79,0x08,0x7c,0x7b,0xcd,0xbd,0x99,0x35,0x02,
+ 0xee,0xe6,0x06,0xb7,0x18,0xba,0x31,0xe8,0x40,0xa0,0x00,0xa7,
+ 0xb7,0xbe,0xfe,0x15,0xea,0x42,0x7c,0x5c,0xfe,0x88,0x34,0x4f,
+ 0xa1,0x23,0x7f,0x35,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x98,0x0d,0xcc,0x5a,0x1c,0x52,0xce,0xea,0x03,0x1e,0x75,0xf3,
+ 0x8e,0xd2,0x66,0x58,0x66,0x16,0x48,0x8c,0x5c,0x57,0x80,0x28,
+ 0x5f,0xcb,0xcf,0x79,0x08,0x7c,0x7b,0xcd,0xbd,0x99,0x35,0x02,
+ 0xee,0xe6,0x06,0xb7,0x18,0xba,0x31,0xe8,0x40,0xa0,0x00,0xa7,
+ 0xb7,0xbe,0xfe,0x15,0xea,0x42,0x7c,0x5c,0xfe,0x88,0x34,0x4f,
+ 0xa1,0x23,0x7f,0x35,
+};
+const unsigned char tc_sid_out_ir[] = {
+ 0x2a,0x76,0xd3,0xbb,0xc4,0x99,0xdf,0xdc,0x4d,0xca,0xcc,0x9f,
+ 0xf0,0x42,0xf4,0xe1,0xa5,0x4e,0x38,0x43,0x25,0x8e,0x10,0x0c,
+ 0xcd,0x7c,0x60,0xf0,0xa5,0x41,0xf9,0xd3,0xeb,0xf0,0x25,0xe6,
+ 0x8a,0x46,0x0d,0xde,0x21,0x8b,0xd3,0x9f,0x07,0x11,0xbc,0x6f,
+ 0xa1,0x14,0x09,0xc9,0xd7,0xb6,0x9d,0x8c,0xcf,0x6b,0x32,0xfc,
+ 0x51,0xdd,0xb6,0x99,
+};
+const unsigned char tc_sid_out_oc[] = {
+ 0xca,0x4b,0x50,0x70,0x0c,0x46,0x20,0x3c,0xcd,0x10,0xbc,0x0e,
+ 0x9f,0x31,0x09,0x5e,0x50,0x81,0x89,0xcb,0x59,0x85,0x75,0x37,
+ 0xbe,0x56,0x10,0x48,0xd3,0x4b,0x9e,0xd9,0xa9,0x69,0x7a,0xf1,
+ 0x1c,0x99,0x8f,0x48,0x4c,0x3d,0x78,0x3b,0x0b,0x53,0x14,0x34,
+ 0xca,0xa6,0x83,0x5d,0x4c,0x32,0x34,0x4f,0xcd,0x17,0x16,0x0c,
+ 0x9c,0x34,0x8f,0xc7,
+};
+
+
+
+
+
+
+

+B.3.9. Testvectors as JSON file encoded as BASE64 +

+
+
+ #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT
+ #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI3
+ #RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJnIjogIkE2RkM4MkMzQj
+ #g5NjhGQkIyRTA2RkVFODFDQTg1ODU4NkRFQTUwRDI0OEYwQzdDQTZBMThCMDkwMkEz
+ #MEIzNkIiLCAieWEiOiAiREEzRDIzNzAwQTlFNTY5OTI1OEFFRjk0REMwNjBERkRBNU
+ #VCQjYxRjAyQTVFQTc3RkFENTNGNEZGMDk3NkQwOCIsICJBRGEiOiAiNDE0NDYxIiwg
+ #IllhIjogIkQ0MEZCMjY1QTdBQkVBRUU3OTM5RDkxQTU4NUZFNTlGNzA1M0Y5ODJDMj
+ #k2RUM0MTNDNjI0QzY2OTMwOEY4N0EiLCAieWIiOiAiRDIzMTZCNDU0NzE4QzM1MzYy
+ #RDgzRDY5REY2MzIwRjM4NTc4RUQ1OTg0NjUxNDM1RTI5NDk3NjJEOTAwQjgwRCIsIC
+ #JBRGIiOiAiNDE0NDYyIiwgIlliIjogIjA4QkNGNkU5Nzc3QTlDMzEzQTNEQjZEQUE1
+ #MTBGMkQzOTg0MDMzMTlDMjM0MUJENTA2QTkyRTY3MkVCN0UzMDciLCAiSyI6ICJFMj
+ #JCMUVGNzc4OEY2NjE0NzhGM0NEREQ0QzYwMDc3NEZDMEY0MUU2QjcxMTU2OTE5MEZG
+ #ODhGQTBFNjA3RTA5IiwgIklTS19JUiI6ICI0QzU0NjlBMTZCMjM2NEM0Qjk0NEVCQz
+ #FBNzlFNTFEMTY3NEFENDdEQjI2RTg3MTgxNTRGNTlGQUVCRkFBNTJEODM0NkYzMEFB
+ #NTgzNzcxMTdFQjIwRDUyN0YyQ0JDNUM3NjM4MUY3RkQzNzJFODlERjgyMzlGODdGMk
+ #UwMkVEMSIsICJJU0tfU1kiOiAiOTgwRENDNUExQzUyQ0VFQTAzMUU3NUYzOEVEMjY2
+ #NTg2NjE2NDg4QzVDNTc4MDI4NUZDQkNGNzkwODdDN0JDREJEOTkzNTAyRUVFNjA2Qj
+ #cxOEJBMzFFODQwQTAwMEE3QjdCRUZFMTVFQTQyN0M1Q0ZFODgzNDRGQTEyMzdGMzUi
+ #LCAic2lkX291dHB1dF9pciI6ICIyQTc2RDNCQkM0OTlERkRDNERDQUNDOUZGMDQyRj
+ #RFMUE1NEUzODQzMjU4RTEwMENDRDdDNjBGMEE1NDFGOUQzRUJGMDI1RTY4QTQ2MERE
+ #RTIxOEJEMzlGMDcxMUJDNkZBMTE0MDlDOUQ3QjY5RDhDQ0Y2QjMyRkM1MUREQjY5OS
+ #IsICJzaWRfb3V0cHV0X29jIjogIkNBNEI1MDcwMEM0NjIwM0NDRDEwQkMwRTlGMzEw
+ #OTVFNTA4MTg5Q0I1OTg1NzUzN0JFNTYxMDQ4RDM0QjlFRDlBOTY5N0FGMTFDOTk4Rj
+ #Q4NEMzRDc4M0IwQjUzMTQzNENBQTY4MzVENEMzMjM0NEZDRDE3MTYwQzlDMzQ4RkM3
+ #In0=
+
+
+
+
+
+
+

+B.3.10. Test case for scalar_mult with valid inputs +

+
+
+    s: (length: 32 bytes)
+      7cd0e075fa7955ba52c02759a6c90dbbfc10e6d40aea8d283e407d88
+      cf538a05
+    X: (length: 32 bytes)
+      2c3c6b8c4f3800e7aef6864025b4ed79bd599117e427c41bd47d93d6
+      54b4a51c
+    G.scalar_mult(s,decode(X)): (length: 32 bytes)
+      7c13645fe790a468f62c39beb7388e541d8405d1ade69d1778c5fe3e
+      7f6b600e
+    G.scalar_mult_vfy(s,X): (length: 32 bytes)
+      7c13645fe790a468f62c39beb7388e541d8405d1ade69d1778c5fe3e
+      7f6b600e
+
+
+
+
+
+
+

+B.3.11. Invalid inputs for scalar_mult_vfy +

+

For these test cases scalar_mult_vfy(y,.) MUST return the representation of the neutral element G.I. When points Y_i1 or Y_i2 are included in message of A or B the protocol MUST abort.

+
+
+    s: (length: 32 bytes)
+      7cd0e075fa7955ba52c02759a6c90dbbfc10e6d40aea8d283e407d88
+      cf538a05
+    Y_i1: (length: 32 bytes)
+      2b3c6b8c4f3800e7aef6864025b4ed79bd599117e427c41bd47d93d6
+      54b4a51c
+    Y_i2 == G.I: (length: 32 bytes)
+      00000000000000000000000000000000000000000000000000000000
+      00000000
+    G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I
+
+
+
+
+
+B.3.11.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJWYWxpZCI6IHsicyI6ICI3Q0QwRTA3NUZBNzk1NUJBNTJDMDI3NTlBNkM5MERCQk
+ #ZDMTBFNkQ0MEFFQThEMjgzRTQwN0Q4OENGNTM4QTA1IiwgIlgiOiAiMkMzQzZCOEM0
+ #RjM4MDBFN0FFRjY4NjQwMjVCNEVENzlCRDU5OTExN0U0MjdDNDFCRDQ3RDkzRDY1NE
+ #I0QTUxQyIsICJHLnNjYWxhcl9tdWx0KHMsZGVjb2RlKFgpKSI6ICI3QzEzNjQ1RkU3
+ #OTBBNDY4RjYyQzM5QkVCNzM4OEU1NDFEODQwNUQxQURFNjlEMTc3OEM1RkUzRTdGNk
+ #I2MDBFIiwgIkcuc2NhbGFyX211bHRfdmZ5KHMsWCkiOiAiN0MxMzY0NUZFNzkwQTQ2
+ #OEY2MkMzOUJFQjczODhFNTQxRDg0MDVEMUFERTY5RDE3NzhDNUZFM0U3RjZCNjAwRS
+ #J9LCAiSW52YWxpZCBZMSI6ICIyQjNDNkI4QzRGMzgwMEU3QUVGNjg2NDAyNUI0RUQ3
+ #OUJENTk5MTE3RTQyN0M0MUJENDdEOTNENjU0QjRBNTFDIiwgIkludmFsaWQgWTIiOi
+ #AiMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMCJ9
+
+
+
+
+
+
+
+
+
+
+

+B.4. Test vector for CPace using group decaf448 and hash SHAKE-256 +

+
+
+

+B.4.1. Test vectors for calculate_generator with group decaf448 +

+
+
+  Inputs
+    H   = SHAKE-256 with input block size 136 bytes.
+    PRS = b'Password' ; ZPAD length: 112 ;
+    DSI = b'CPaceDecaf448'
+    CI = b'oc\x0bB_responder\x0bA_initiator'
+    CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72
+    sid = 5223e0cdc45d6575668d64c552004124
+  Outputs
+    generator_string(G.DSI,PRS,CI,sid,H.s_in_bytes):
+    (length: 180 bytes)
+      0d435061636544656361663434380850617373776f72647000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      0000000000000000000000000000000000000000000000001a6f630b
+      425f726573706f6e6465720b415f696e69746961746f72105223e0cd
+      c45d6575668d64c552004124
+    hash result: (length: 112 bytes)
+      7148f4d60587aaafa64d2fd6bcfe45ee71e8b971d1d5ff3bbf8c1451
+      797c62a1af22ab25638749f97f9b15fedcf4aeee87282cf667594ab0
+      92b6023c8f8d3a61c38b0af791c9271137df01b57d63b79734bbce69
+      91e3e2e10fdc805abc9e6e6f3daeff6fd34093d26de240b326764252
+    encoded generator g: (length: 56 bytes)
+      9a700ecc378eb98e57387df456d5b4b4f1dceebbb1371527eeb7e1bf
+      bab64ecc9c9303396145ba04f5b5aea5baedfa61f31f00fbc5fd5606
+
+
+
+
+
+B.4.1.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJIIjogIlNIQUtFLTI1NiIsICJILnNfaW5fYnl0ZXMiOiAxMzYsICJQUlMiOiAiNT
+ #A2MTczNzM3NzZGNzI2NCIsICJaUEFEIGxlbmd0aCI6IDExMiwgIkRTSSI6ICI0MzUw
+ #NjE2MzY1NDQ2NTYzNjE2NjM0MzQzOCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NTczNz
+ #A2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI1MjIz
+ #RTBDREM0NUQ2NTc1NjY4RDY0QzU1MjAwNDEyNCIsICJnZW5lcmF0b3Jfc3RyaW5nKE
+ #cuRFNJLFBSUyxDSSxzaWQsSC5zX2luX2J5dGVzKSI6ICIwRDQzNTA2MTYzNjU0NDY1
+ #NjM2MTY2MzQzNDM4MDg1MDYxNzM3Mzc3NkY3MjY0NzAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDFBNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0NjU3MjBCNDE1RjY5NkU2
+ #OTc0Njk2MTc0NkY3MjEwNTIyM0UwQ0RDNDVENjU3NTY2OEQ2NEM1NTIwMDQxMjQiLC
+ #AiaGFzaCByZXN1bHQiOiAiNzE0OEY0RDYwNTg3QUFBRkE2NEQyRkQ2QkNGRTQ1RUU3
+ #MUU4Qjk3MUQxRDVGRjNCQkY4QzE0NTE3OTdDNjJBMUFGMjJBQjI1NjM4NzQ5Rjk3Rj
+ #lCMTVGRURDRjRBRUVFODcyODJDRjY2NzU5NEFCMDkyQjYwMjNDOEY4RDNBNjFDMzhC
+ #MEFGNzkxQzkyNzExMzdERjAxQjU3RDYzQjc5NzM0QkJDRTY5OTFFM0UyRTEwRkRDOD
+ #A1QUJDOUU2RTZGM0RBRUZGNkZEMzQwOTNEMjZERTI0MEIzMjY3NjQyNTIiLCAiZW5j
+ #b2RlZCBnZW5lcmF0b3IgZyI6ICI5QTcwMEVDQzM3OEVCOThFNTczODdERjQ1NkQ1Qj
+ #RCNEYxRENFRUJCQjEzNzE1MjdFRUI3RTFCRkJBQjY0RUNDOUM5MzAzMzk2MTQ1QkEw
+ #NEY1QjVBRUE1QkFFREZBNjFGMzFGMDBGQkM1RkQ1NjA2In0=
+
+
+
+
+
+
+
+
+

+B.4.2. Test vector for message from A +

+
+
+  Inputs
+    ADa = b'ADa'
+    ya (little endian): (length: 56 bytes)
+      33d561f13cfc0dca279c30e8cde895175dc25483892819eba132d58c
+      13c0462a8eb0d73fda941950594bef5191d8394691f86edffcad6c1e
+  Outputs
+    Ya: (length: 56 bytes)
+      627f8bb2ae945e2a518967df9b00aff19253d3086398f2ec18be846c
+      c0d1f286c2ce3caf1da639859ccd2a6a01a9372a17e66bb7006e571b
+
+
+
+
+
+
+

+B.4.3. Test vector for message from B +

+
+
+  Inputs
+    ADb = b'ADb'
+    yb (little endian): (length: 56 bytes)
+      2523c969f68fa2b2aea294c2539ef36eb1e0558abd14712a7828f16a
+      85ed2c7e77e2bdd418994405fb1b57b6bbaadd66849892aac9d81402
+  Outputs
+    Yb: (length: 56 bytes)
+      8e9811e4402fac098743ca7b2b509b91b38c8cf1360cc6cab3011871
+      7019782b7f58a591c63d9c9247b774e6b0e0b826ff4f8399f94772db
+
+
+
+
+
+
+

+B.4.4. Test vector for secret points K +

+
+
+    scalar_mult_vfy(ya,Yb): (length: 56 bytes)
+      94f4ae494f4e8b07ade3354726eee49c5518b363cda544f5b4541b97
+      32830be37ea0e63fc83f54be280dea0747a043c76d473e01689af77f
+    scalar_mult_vfy(yb,Ya): (length: 56 bytes)
+      94f4ae494f4e8b07ade3354726eee49c5518b363cda544f5b4541b97
+      32830be37ea0e63fc83f54be280dea0747a043c76d473e01689af77f
+
+
+
+
+
+
+

+B.4.5. Test vector for ISK calculation initiator/responder +

+
+
+    transcript_ir(Ya,ADa,Yb,ADb): (length: 122 bytes)
+      38627f8bb2ae945e2a518967df9b00aff19253d3086398f2ec18be84
+      6cc0d1f286c2ce3caf1da639859ccd2a6a01a9372a17e66bb7006e57
+      1b03414461388e9811e4402fac098743ca7b2b509b91b38c8cf1360c
+      c6cab30118717019782b7f58a591c63d9c9247b774e6b0e0b826ff4f
+      8399f94772db03414462
+    DSI = G.DSI_ISK, b'CPaceDecaf448_ISK': (length: 17 bytes)
+      435061636544656361663434385f49534b
+    lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb):
+    (length: 214 bytes)
+      11435061636544656361663434385f49534b105223e0cdc45d657566
+      8d64c5520041243894f4ae494f4e8b07ade3354726eee49c5518b363
+      cda544f5b4541b9732830be37ea0e63fc83f54be280dea0747a043c7
+      6d473e01689af77f38627f8bb2ae945e2a518967df9b00aff19253d3
+      086398f2ec18be846cc0d1f286c2ce3caf1da639859ccd2a6a01a937
+      2a17e66bb7006e571b03414461388e9811e4402fac098743ca7b2b50
+      9b91b38c8cf1360cc6cab30118717019782b7f58a591c63d9c9247b7
+      74e6b0e0b826ff4f8399f94772db03414462
+    ISK result: (length: 64 bytes)
+      9c2726a6cda1179349cbc38f31765eab646a2a5f176f3019fab4a0aa
+      bd9d17c2ba895998cff698d801761a003512c1cf67d144b21e1cb6d6
+      b82da71d0da76cad
+
+
+
+
+
+
+

+B.4.6. Test vector for ISK calculation parallel execution +

+
+
+    transcript_oc(Ya,ADa,Yb,ADb): (length: 124 bytes)
+      6f63388e9811e4402fac098743ca7b2b509b91b38c8cf1360cc6cab3
+      0118717019782b7f58a591c63d9c9247b774e6b0e0b826ff4f8399f9
+      4772db0341446238627f8bb2ae945e2a518967df9b00aff19253d308
+      6398f2ec18be846cc0d1f286c2ce3caf1da639859ccd2a6a01a9372a
+      17e66bb7006e571b03414461
+    DSI = G.DSI_ISK, b'CPaceDecaf448_ISK': (length: 17 bytes)
+      435061636544656361663434385f49534b
+    lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb):
+    (length: 216 bytes)
+      11435061636544656361663434385f49534b105223e0cdc45d657566
+      8d64c5520041243894f4ae494f4e8b07ade3354726eee49c5518b363
+      cda544f5b4541b9732830be37ea0e63fc83f54be280dea0747a043c7
+      6d473e01689af77f6f63388e9811e4402fac098743ca7b2b509b91b3
+      8c8cf1360cc6cab30118717019782b7f58a591c63d9c9247b774e6b0
+      e0b826ff4f8399f94772db0341446238627f8bb2ae945e2a518967df
+      9b00aff19253d3086398f2ec18be846cc0d1f286c2ce3caf1da63985
+      9ccd2a6a01a9372a17e66bb7006e571b03414461
+    ISK result: (length: 64 bytes)
+      6d2178ed3048703025b9007ec84c4d969e8d8135df455e608c16aa15
+      2e1219c86cea563254428a9d969903ae3649d1050da1e6e0c1c060e1
+      ebf7316a7e993389
+
+
+
+
+
+
+

+B.4.7. Test vector for optional output of session id +

+
+
+    H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      65bffde17b7acf07cfd437bdb973a8f7340bf911d393a61498c0a50e
+      f0d68bca103fbdb0f5b799505562e59811df1bc5d9b4f5f0f7c57c22
+      cd7ed6db4d153e3a
+    H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      7ce27043d1b1d0d0e02e16979637e2a00547ed6e15ea988f7d3c9b3c
+      2159b26ab3834bff7ff86240323e25216ba2ee6ea6e1582502017f8e
+      6d65f8c4a5e65543
+
+
+
+
+
+
+

+B.4.8. Corresponding C programming language initializers +

+
+
+const unsigned char tc_PRS[] = {
+ 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64,
+};
+const unsigned char tc_CI[] = {
+ 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64,
+ 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74,
+ 0x6f,0x72,
+};
+const unsigned char tc_sid[] = {
+ 0x52,0x23,0xe0,0xcd,0xc4,0x5d,0x65,0x75,0x66,0x8d,0x64,0xc5,
+ 0x52,0x00,0x41,0x24,
+};
+const unsigned char tc_g[] = {
+ 0x9a,0x70,0x0e,0xcc,0x37,0x8e,0xb9,0x8e,0x57,0x38,0x7d,0xf4,
+ 0x56,0xd5,0xb4,0xb4,0xf1,0xdc,0xee,0xbb,0xb1,0x37,0x15,0x27,
+ 0xee,0xb7,0xe1,0xbf,0xba,0xb6,0x4e,0xcc,0x9c,0x93,0x03,0x39,
+ 0x61,0x45,0xba,0x04,0xf5,0xb5,0xae,0xa5,0xba,0xed,0xfa,0x61,
+ 0xf3,0x1f,0x00,0xfb,0xc5,0xfd,0x56,0x06,
+};
+const unsigned char tc_ya[] = {
+ 0x33,0xd5,0x61,0xf1,0x3c,0xfc,0x0d,0xca,0x27,0x9c,0x30,0xe8,
+ 0xcd,0xe8,0x95,0x17,0x5d,0xc2,0x54,0x83,0x89,0x28,0x19,0xeb,
+ 0xa1,0x32,0xd5,0x8c,0x13,0xc0,0x46,0x2a,0x8e,0xb0,0xd7,0x3f,
+ 0xda,0x94,0x19,0x50,0x59,0x4b,0xef,0x51,0x91,0xd8,0x39,0x46,
+ 0x91,0xf8,0x6e,0xdf,0xfc,0xad,0x6c,0x1e,
+};
+const unsigned char tc_ADa[] = {
+ 0x41,0x44,0x61,
+};
+const unsigned char tc_Ya[] = {
+ 0x62,0x7f,0x8b,0xb2,0xae,0x94,0x5e,0x2a,0x51,0x89,0x67,0xdf,
+ 0x9b,0x00,0xaf,0xf1,0x92,0x53,0xd3,0x08,0x63,0x98,0xf2,0xec,
+ 0x18,0xbe,0x84,0x6c,0xc0,0xd1,0xf2,0x86,0xc2,0xce,0x3c,0xaf,
+ 0x1d,0xa6,0x39,0x85,0x9c,0xcd,0x2a,0x6a,0x01,0xa9,0x37,0x2a,
+ 0x17,0xe6,0x6b,0xb7,0x00,0x6e,0x57,0x1b,
+};
+const unsigned char tc_yb[] = {
+ 0x25,0x23,0xc9,0x69,0xf6,0x8f,0xa2,0xb2,0xae,0xa2,0x94,0xc2,
+ 0x53,0x9e,0xf3,0x6e,0xb1,0xe0,0x55,0x8a,0xbd,0x14,0x71,0x2a,
+ 0x78,0x28,0xf1,0x6a,0x85,0xed,0x2c,0x7e,0x77,0xe2,0xbd,0xd4,
+ 0x18,0x99,0x44,0x05,0xfb,0x1b,0x57,0xb6,0xbb,0xaa,0xdd,0x66,
+ 0x84,0x98,0x92,0xaa,0xc9,0xd8,0x14,0x02,
+};
+const unsigned char tc_ADb[] = {
+ 0x41,0x44,0x62,
+};
+const unsigned char tc_Yb[] = {
+ 0x8e,0x98,0x11,0xe4,0x40,0x2f,0xac,0x09,0x87,0x43,0xca,0x7b,
+ 0x2b,0x50,0x9b,0x91,0xb3,0x8c,0x8c,0xf1,0x36,0x0c,0xc6,0xca,
+ 0xb3,0x01,0x18,0x71,0x70,0x19,0x78,0x2b,0x7f,0x58,0xa5,0x91,
+ 0xc6,0x3d,0x9c,0x92,0x47,0xb7,0x74,0xe6,0xb0,0xe0,0xb8,0x26,
+ 0xff,0x4f,0x83,0x99,0xf9,0x47,0x72,0xdb,
+};
+const unsigned char tc_K[] = {
+ 0x94,0xf4,0xae,0x49,0x4f,0x4e,0x8b,0x07,0xad,0xe3,0x35,0x47,
+ 0x26,0xee,0xe4,0x9c,0x55,0x18,0xb3,0x63,0xcd,0xa5,0x44,0xf5,
+ 0xb4,0x54,0x1b,0x97,0x32,0x83,0x0b,0xe3,0x7e,0xa0,0xe6,0x3f,
+ 0xc8,0x3f,0x54,0xbe,0x28,0x0d,0xea,0x07,0x47,0xa0,0x43,0xc7,
+ 0x6d,0x47,0x3e,0x01,0x68,0x9a,0xf7,0x7f,
+};
+const unsigned char tc_ISK_IR[] = {
+ 0x9c,0x27,0x26,0xa6,0xcd,0xa1,0x17,0x93,0x49,0xcb,0xc3,0x8f,
+ 0x31,0x76,0x5e,0xab,0x64,0x6a,0x2a,0x5f,0x17,0x6f,0x30,0x19,
+ 0xfa,0xb4,0xa0,0xaa,0xbd,0x9d,0x17,0xc2,0xba,0x89,0x59,0x98,
+ 0xcf,0xf6,0x98,0xd8,0x01,0x76,0x1a,0x00,0x35,0x12,0xc1,0xcf,
+ 0x67,0xd1,0x44,0xb2,0x1e,0x1c,0xb6,0xd6,0xb8,0x2d,0xa7,0x1d,
+ 0x0d,0xa7,0x6c,0xad,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x6d,0x21,0x78,0xed,0x30,0x48,0x70,0x30,0x25,0xb9,0x00,0x7e,
+ 0xc8,0x4c,0x4d,0x96,0x9e,0x8d,0x81,0x35,0xdf,0x45,0x5e,0x60,
+ 0x8c,0x16,0xaa,0x15,0x2e,0x12,0x19,0xc8,0x6c,0xea,0x56,0x32,
+ 0x54,0x42,0x8a,0x9d,0x96,0x99,0x03,0xae,0x36,0x49,0xd1,0x05,
+ 0x0d,0xa1,0xe6,0xe0,0xc1,0xc0,0x60,0xe1,0xeb,0xf7,0x31,0x6a,
+ 0x7e,0x99,0x33,0x89,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x6d,0x21,0x78,0xed,0x30,0x48,0x70,0x30,0x25,0xb9,0x00,0x7e,
+ 0xc8,0x4c,0x4d,0x96,0x9e,0x8d,0x81,0x35,0xdf,0x45,0x5e,0x60,
+ 0x8c,0x16,0xaa,0x15,0x2e,0x12,0x19,0xc8,0x6c,0xea,0x56,0x32,
+ 0x54,0x42,0x8a,0x9d,0x96,0x99,0x03,0xae,0x36,0x49,0xd1,0x05,
+ 0x0d,0xa1,0xe6,0xe0,0xc1,0xc0,0x60,0xe1,0xeb,0xf7,0x31,0x6a,
+ 0x7e,0x99,0x33,0x89,
+};
+const unsigned char tc_sid_out_ir[] = {
+ 0x65,0xbf,0xfd,0xe1,0x7b,0x7a,0xcf,0x07,0xcf,0xd4,0x37,0xbd,
+ 0xb9,0x73,0xa8,0xf7,0x34,0x0b,0xf9,0x11,0xd3,0x93,0xa6,0x14,
+ 0x98,0xc0,0xa5,0x0e,0xf0,0xd6,0x8b,0xca,0x10,0x3f,0xbd,0xb0,
+ 0xf5,0xb7,0x99,0x50,0x55,0x62,0xe5,0x98,0x11,0xdf,0x1b,0xc5,
+ 0xd9,0xb4,0xf5,0xf0,0xf7,0xc5,0x7c,0x22,0xcd,0x7e,0xd6,0xdb,
+ 0x4d,0x15,0x3e,0x3a,
+};
+const unsigned char tc_sid_out_oc[] = {
+ 0x7c,0xe2,0x70,0x43,0xd1,0xb1,0xd0,0xd0,0xe0,0x2e,0x16,0x97,
+ 0x96,0x37,0xe2,0xa0,0x05,0x47,0xed,0x6e,0x15,0xea,0x98,0x8f,
+ 0x7d,0x3c,0x9b,0x3c,0x21,0x59,0xb2,0x6a,0xb3,0x83,0x4b,0xff,
+ 0x7f,0xf8,0x62,0x40,0x32,0x3e,0x25,0x21,0x6b,0xa2,0xee,0x6e,
+ 0xa6,0xe1,0x58,0x25,0x02,0x01,0x7f,0x8e,0x6d,0x65,0xf8,0xc4,
+ 0xa5,0xe6,0x55,0x43,
+};
+
+
+
+
+
+
+

+B.4.9. Testvectors as JSON file encoded as BASE64 +

+
+
+ #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT
+ #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI1
+ #MjIzRTBDREM0NUQ2NTc1NjY4RDY0QzU1MjAwNDEyNCIsICJnIjogIjlBNzAwRUNDMz
+ #c4RUI5OEU1NzM4N0RGNDU2RDVCNEI0RjFEQ0VFQkJCMTM3MTUyN0VFQjdFMUJGQkFC
+ #NjRFQ0M5QzkzMDMzOTYxNDVCQTA0RjVCNUFFQTVCQUVERkE2MUYzMUYwMEZCQzVGRD
+ #U2MDYiLCAieWEiOiAiMzNENTYxRjEzQ0ZDMERDQTI3OUMzMEU4Q0RFODk1MTc1REMy
+ #NTQ4Mzg5MjgxOUVCQTEzMkQ1OEMxM0MwNDYyQThFQjBENzNGREE5NDE5NTA1OTRCRU
+ #Y1MTkxRDgzOTQ2OTFGODZFREZGQ0FENkMxRSIsICJBRGEiOiAiNDE0NDYxIiwgIllh
+ #IjogIjYyN0Y4QkIyQUU5NDVFMkE1MTg5NjdERjlCMDBBRkYxOTI1M0QzMDg2Mzk4Rj
+ #JFQzE4QkU4NDZDQzBEMUYyODZDMkNFM0NBRjFEQTYzOTg1OUNDRDJBNkEwMUE5Mzcy
+ #QTE3RTY2QkI3MDA2RTU3MUIiLCAieWIiOiAiMjUyM0M5NjlGNjhGQTJCMkFFQTI5NE
+ #MyNTM5RUYzNkVCMUUwNTU4QUJEMTQ3MTJBNzgyOEYxNkE4NUVEMkM3RTc3RTJCREQ0
+ #MTg5OTQ0MDVGQjFCNTdCNkJCQUFERDY2ODQ5ODkyQUFDOUQ4MTQwMiIsICJBRGIiOi
+ #AiNDE0NDYyIiwgIlliIjogIjhFOTgxMUU0NDAyRkFDMDk4NzQzQ0E3QjJCNTA5Qjkx
+ #QjM4QzhDRjEzNjBDQzZDQUIzMDExODcxNzAxOTc4MkI3RjU4QTU5MUM2M0Q5QzkyND
+ #dCNzc0RTZCMEUwQjgyNkZGNEY4Mzk5Rjk0NzcyREIiLCAiSyI6ICI5NEY0QUU0OTRG
+ #NEU4QjA3QURFMzM1NDcyNkVFRTQ5QzU1MThCMzYzQ0RBNTQ0RjVCNDU0MUI5NzMyOD
+ #MwQkUzN0VBMEU2M0ZDODNGNTRCRTI4MERFQTA3NDdBMDQzQzc2RDQ3M0UwMTY4OUFG
+ #NzdGIiwgIklTS19JUiI6ICI5QzI3MjZBNkNEQTExNzkzNDlDQkMzOEYzMTc2NUVBQj
+ #Y0NkEyQTVGMTc2RjMwMTlGQUI0QTBBQUJEOUQxN0MyQkE4OTU5OThDRkY2OThEODAx
+ #NzYxQTAwMzUxMkMxQ0Y2N0QxNDRCMjFFMUNCNkQ2QjgyREE3MUQwREE3NkNBRCIsIC
+ #JJU0tfU1kiOiAiNkQyMTc4RUQzMDQ4NzAzMDI1QjkwMDdFQzg0QzREOTY5RThEODEz
+ #NURGNDU1RTYwOEMxNkFBMTUyRTEyMTlDODZDRUE1NjMyNTQ0MjhBOUQ5Njk5MDNBRT
+ #M2NDlEMTA1MERBMUU2RTBDMUMwNjBFMUVCRjczMTZBN0U5OTMzODkiLCAic2lkX291
+ #dHB1dF9pciI6ICI2NUJGRkRFMTdCN0FDRjA3Q0ZENDM3QkRCOTczQThGNzM0MEJGOT
+ #ExRDM5M0E2MTQ5OEMwQTUwRUYwRDY4QkNBMTAzRkJEQjBGNUI3OTk1MDU1NjJFNTk4
+ #MTFERjFCQzVEOUI0RjVGMEY3QzU3QzIyQ0Q3RUQ2REI0RDE1M0UzQSIsICJzaWRfb3
+ #V0cHV0X29jIjogIjdDRTI3MDQzRDFCMUQwRDBFMDJFMTY5Nzk2MzdFMkEwMDU0N0VE
+ #NkUxNUVBOTg4RjdEM0M5QjNDMjE1OUIyNkFCMzgzNEJGRjdGRjg2MjQwMzIzRTI1Mj
+ #E2QkEyRUU2RUE2RTE1ODI1MDIwMTdGOEU2RDY1RjhDNEE1RTY1NTQzIn0=
+
+
+
+
+
+
+

+B.4.10. Test case for scalar_mult with valid inputs +

+
+
+    s: (length: 56 bytes)
+      dd1bc7015daabb7672129cc35a3ba815486b139deff9bdeca7a4fc61
+      34323d34658761e90ff079972a7ca8aa5606498f4f4f0ebc0933a819
+    X: (length: 56 bytes)
+      601431d5e51f43d422a92d3fb2373bde28217aab42524c341aa404ea
+      ba5aa5541f7042dbb3253ce4c90f772b038a413dcb3a0f6bf3ae9e21
+    G.scalar_mult(s,decode(X)): (length: 56 bytes)
+      388b35c60eb41b66085a2118316218681d78979d667702de105fdc1f
+      21ffe884a577d795f45691781390a229a3bd7b527e831380f2f585a4
+    G.scalar_mult_vfy(s,X): (length: 56 bytes)
+      388b35c60eb41b66085a2118316218681d78979d667702de105fdc1f
+      21ffe884a577d795f45691781390a229a3bd7b527e831380f2f585a4
+
+
+
+
+
+
+

+B.4.11. Invalid inputs for scalar_mult_vfy +

+

For these test cases scalar_mult_vfy(y,.) MUST return the representation of the neutral element G.I. When points Y_i1 or Y_i2 are included in message of A or B the protocol MUST abort.

+
+
+    s: (length: 56 bytes)
+      dd1bc7015daabb7672129cc35a3ba815486b139deff9bdeca7a4fc61
+      34323d34658761e90ff079972a7ca8aa5606498f4f4f0ebc0933a819
+    Y_i1: (length: 56 bytes)
+      5f1431d5e51f43d422a92d3fb2373bde28217aab42524c341aa404ea
+      ba5aa5541f7042dbb3253ce4c90f772b038a413dcb3a0f6bf3ae9e21
+    Y_i2 == G.I: (length: 56 bytes)
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+    G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I
+
+
+
+
+
+B.4.11.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJWYWxpZCI6IHsicyI6ICJERDFCQzcwMTVEQUFCQjc2NzIxMjlDQzM1QTNCQTgxNT
+ #Q4NkIxMzlERUZGOUJERUNBN0E0RkM2MTM0MzIzRDM0NjU4NzYxRTkwRkYwNzk5NzJB
+ #N0NBOEFBNTYwNjQ5OEY0RjRGMEVCQzA5MzNBODE5IiwgIlgiOiAiNjAxNDMxRDVFNT
+ #FGNDNENDIyQTkyRDNGQjIzNzNCREUyODIxN0FBQjQyNTI0QzM0MUFBNDA0RUFCQTVB
+ #QTU1NDFGNzA0MkRCQjMyNTNDRTRDOTBGNzcyQjAzOEE0MTNEQ0IzQTBGNkJGM0FFOU
+ #UyMSIsICJHLnNjYWxhcl9tdWx0KHMsZGVjb2RlKFgpKSI6ICIzODhCMzVDNjBFQjQx
+ #QjY2MDg1QTIxMTgzMTYyMTg2ODFENzg5NzlENjY3NzAyREUxMDVGREMxRjIxRkZFOD
+ #g0QTU3N0Q3OTVGNDU2OTE3ODEzOTBBMjI5QTNCRDdCNTI3RTgzMTM4MEYyRjU4NUE0
+ #IiwgIkcuc2NhbGFyX211bHRfdmZ5KHMsWCkiOiAiMzg4QjM1QzYwRUI0MUI2NjA4NU
+ #EyMTE4MzE2MjE4NjgxRDc4OTc5RDY2NzcwMkRFMTA1RkRDMUYyMUZGRTg4NEE1NzdE
+ #Nzk1RjQ1NjkxNzgxMzkwQTIyOUEzQkQ3QjUyN0U4MzEzODBGMkY1ODVBNCJ9LCAiSW
+ #52YWxpZCBZMSI6ICI1RjE0MzFENUU1MUY0M0Q0MjJBOTJEM0ZCMjM3M0JERTI4MjE3
+ #QUFCNDI1MjRDMzQxQUE0MDRFQUJBNUFBNTU0MUY3MDQyREJCMzI1M0NFNEM5MEY3Nz
+ #JCMDM4QTQxM0RDQjNBMEY2QkYzQUU5RTIxIiwgIkludmFsaWQgWTIiOiAiMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMCJ9
+
+
+
+
+
+
+
+
+
+
+

+B.5. Test vector for CPace using group NIST P-256 and hash SHA-256 +

+
+
+

+B.5.1. Test vectors for calculate_generator with group NIST P-256 +

+
+
+  Inputs
+    H   = SHA-256 with input block size 64 bytes.
+    PRS = b'Password' ; ZPAD length: 23 ;
+    DSI = b'CPaceP256_XMD:SHA-256_SSWU_NU_'
+    DST = b'CPaceP256_XMD:SHA-256_SSWU_NU__DST'
+    CI = b'oc\x0bB_responder\x0bA_initiator'
+    CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72
+    sid = 34b36454cab2e7842c389f7d88ecb7df
+  Outputs
+    generator_string(PRS,G.DSI,CI,sid,H.s_in_bytes):
+    (length: 108 bytes)
+      1e4350616365503235365f584d443a5348412d3235365f535357555f
+      4e555f0850617373776f726417000000000000000000000000000000
+      00000000000000001a6f630b425f726573706f6e6465720b415f696e
+      69746961746f721034b36454cab2e7842c389f7d88ecb7df
+    generator g: (length: 65 bytes)
+      04eee577320b1c241a79419fcde5718c2b63f81ef8717d56a57d2fb2
+      6b65a8beb63573b52605efb32ff4cf31aaef9a92df84e4e8408cc6c7
+      cf27a535aad2b38a56
+
+
+
+
+
+B.5.1.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJIIjogIlNIQS0yNTYiLCAiSC5zX2luX2J5dGVzIjogNjQsICJQUlMiOiAiNTA2MT
+ #czNzM3NzZGNzI2NCIsICJaUEFEIGxlbmd0aCI6IDIzLCAiRFNJIjogIjQzNTA2MTYz
+ #NjU1MDMyMzUzNjVGNTg0RDQ0M0E1MzQ4NDEyRDMyMzUzNjVGNTM1MzU3NTU1RjRFNT
+ #U1RiIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NTczNzA2RjZFNjQ2NTcyMEI0MTVGNjk2
+ #RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICIzNEIzNjQ1NENBQjJFNzg0MkMzODlGN0
+ #Q4OEVDQjdERiIsICJnZW5lcmF0b3Jfc3RyaW5nKEcuRFNJLFBSUyxDSSxzaWQsSC5z
+ #X2luX2J5dGVzKSI6ICIxRTQzNTA2MTYzNjU1MDMyMzUzNjVGNTg0RDQ0M0E1MzQ4ND
+ #EyRDMyMzUzNjVGNTM1MzU3NTU1RjRFNTU1RjA4NTA2MTczNzM3NzZGNzI2NDE3MDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDFBNkY2Mz
+ #BCNDI1RjcyNjU3MzcwNkY2RTY0NjU3MjBCNDE1RjY5NkU2OTc0Njk2MTc0NkY3MjEw
+ #MzRCMzY0NTRDQUIyRTc4NDJDMzg5RjdEODhFQ0I3REYiLCAiZ2VuZXJhdG9yIGciOi
+ #AiMDRFRUU1NzczMjBCMUMyNDFBNzk0MTlGQ0RFNTcxOEMyQjYzRjgxRUY4NzE3RDU2
+ #QTU3RDJGQjI2QjY1QThCRUI2MzU3M0I1MjYwNUVGQjMyRkY0Q0YzMUFBRUY5QTkyRE
+ #Y4NEU0RTg0MDhDQzZDN0NGMjdBNTM1QUFEMkIzOEE1NiJ9
+
+
+
+
+
+
+
+
+

+B.5.2. Test vector for message from A +

+
+
+  Inputs
+    ADa = b'ADa'
+    ya (big endian): (length: 32 bytes)
+      37574cfbf1b95ff6a8e2d7be462d4d01e6dde2618f34f4de9df869b2
+      4f532c5d
+  Outputs
+    Ya: (length: 65 bytes)
+      041f12ad5fc65010a24fc04c86197109a36df0e9ce85a7479e1e1364
+      692fdace17ea5a634e19c207a5d52ead6c6817a163cf2f2fe3406c5d
+      fdfc2ecdf8e42c5e16
+    Alternative correct value for Ya: (-ya)*g:
+    (length: 65 bytes)
+      041f12ad5fc65010a24fc04c86197109a36df0e9ce85a7479e1e1364
+      692fdace1715a59cb0e63df85b2ad1529397e85e9c30d0d01dbf93a2
+      0203d132071bd3a1e9
+
+
+
+
+
+
+

+B.5.3. Test vector for message from B +

+
+
+  Inputs
+    ADb = b'ADb'
+    yb (big endian): (length: 32 bytes)
+      e5672fc9eb4e721f41d80181ec4c9fd9886668acc48024d33c82bb10
+      2aecba52
+  Outputs
+    Yb: (length: 65 bytes)
+      046a51180b6ebabaf5ed0af8cd786886d93342bcae4c158ce1617a0a
+      cc8ec354486f9ed2e9210913206d1e3f5e463d2d320c4f1f5ce8b677
+      a7e38a26f752bf8f84
+    Alternative correct value for Yb: (-yb)*g:
+    (length: 65 bytes)
+      046a51180b6ebabaf5ed0af8cd786886d93342bcae4c158ce1617a0a
+      cc8ec3544890612d15def6ece092e1c0a1b9c2d2cdf3b0e0a4174988
+      581c75d908ad40707b
+
+
+
+
+
+
+

+B.5.4. Test vector for secret points K +

+
+
+    scalar_mult_vfy(ya,Yb): (length: 32 bytes)
+      3e0e2f8976fb8d0deee30aef4b5cd3631eed249af32f53d0dd009b5d
+      7b8f6b6c
+    scalar_mult_vfy(yb,Ya): (length: 32 bytes)
+      3e0e2f8976fb8d0deee30aef4b5cd3631eed249af32f53d0dd009b5d
+      7b8f6b6c
+
+
+
+
+
+
+

+B.5.5. Test vector for ISK calculation initiator/responder +

+
+
+    transcript_ir(Ya,ADa,Yb,ADb): (length: 140 bytes)
+      41041f12ad5fc65010a24fc04c86197109a36df0e9ce85a7479e1e13
+      64692fdace17ea5a634e19c207a5d52ead6c6817a163cf2f2fe3406c
+      5dfdfc2ecdf8e42c5e160341446141046a51180b6ebabaf5ed0af8cd
+      786886d93342bcae4c158ce1617a0acc8ec354486f9ed2e921091320
+      6d1e3f5e463d2d320c4f1f5ce8b677a7e38a26f752bf8f8403414462
+    DSI = G.DSI_ISK, b'CPaceP256_XMD:SHA-256_SSWU_NU__ISK':
+    (length: 34 bytes)
+      4350616365503235365f584d443a5348412d3235365f535357555f4e
+      555f5f49534b
+    lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb):
+    (length: 225 bytes)
+      224350616365503235365f584d443a5348412d3235365f535357555f
+      4e555f5f49534b1034b36454cab2e7842c389f7d88ecb7df203e0e2f
+      8976fb8d0deee30aef4b5cd3631eed249af32f53d0dd009b5d7b8f6b
+      6c41041f12ad5fc65010a24fc04c86197109a36df0e9ce85a7479e1e
+      1364692fdace17ea5a634e19c207a5d52ead6c6817a163cf2f2fe340
+      6c5dfdfc2ecdf8e42c5e160341446141046a51180b6ebabaf5ed0af8
+      cd786886d93342bcae4c158ce1617a0acc8ec354486f9ed2e9210913
+      206d1e3f5e463d2d320c4f1f5ce8b677a7e38a26f752bf8f84034144
+      62
+    ISK result: (length: 32 bytes)
+      9565ed286b6e3cf1f943fd31746f9a22935537025a1328d4980005ba
+      984f0c39
+
+
+
+
+
+
+

+B.5.6. Test vector for ISK calculation parallel execution +

+
+
+    transcript_oc(Ya,ADa,Yb,ADb): (length: 142 bytes)
+      6f6341046a51180b6ebabaf5ed0af8cd786886d93342bcae4c158ce1
+      617a0acc8ec354486f9ed2e9210913206d1e3f5e463d2d320c4f1f5c
+      e8b677a7e38a26f752bf8f840341446241041f12ad5fc65010a24fc0
+      4c86197109a36df0e9ce85a7479e1e1364692fdace17ea5a634e19c2
+      07a5d52ead6c6817a163cf2f2fe3406c5dfdfc2ecdf8e42c5e160341
+      4461
+    DSI = G.DSI_ISK, b'CPaceP256_XMD:SHA-256_SSWU_NU__ISK':
+    (length: 34 bytes)
+      4350616365503235365f584d443a5348412d3235365f535357555f4e
+      555f5f49534b
+    lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb):
+    (length: 227 bytes)
+      224350616365503235365f584d443a5348412d3235365f535357555f
+      4e555f5f49534b1034b36454cab2e7842c389f7d88ecb7df203e0e2f
+      8976fb8d0deee30aef4b5cd3631eed249af32f53d0dd009b5d7b8f6b
+      6c6f6341046a51180b6ebabaf5ed0af8cd786886d93342bcae4c158c
+      e1617a0acc8ec354486f9ed2e9210913206d1e3f5e463d2d320c4f1f
+      5ce8b677a7e38a26f752bf8f840341446241041f12ad5fc65010a24f
+      c04c86197109a36df0e9ce85a7479e1e1364692fdace17ea5a634e19
+      c207a5d52ead6c6817a163cf2f2fe3406c5dfdfc2ecdf8e42c5e1603
+      414461
+    ISK result: (length: 32 bytes)
+      62a445a4daa3546dd031c66ead2e4e015abbcc83bde31c90f841149f
+      d441c58a
+
+
+
+
+
+
+

+B.5.7. Test vector for optional output of session id +

+
+
+    H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)):
+    (length: 32 bytes)
+      a7386d1c2eb06e8056d7fecbcf691e08d189d96236020ef31b414069
+      8a4b99f9
+    H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)):
+    (length: 32 bytes)
+      d337dbc0dd797b4e6f2f14ea4925c58e5d5523871e8cb43a3c1b0f2b
+      1a1ffde3
+
+
+
+
+
+
+

+B.5.8. Corresponding C programming language initializers +

+
+
+const unsigned char tc_PRS[] = {
+ 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64,
+};
+const unsigned char tc_CI[] = {
+ 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64,
+ 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74,
+ 0x6f,0x72,
+};
+const unsigned char tc_sid[] = {
+ 0x34,0xb3,0x64,0x54,0xca,0xb2,0xe7,0x84,0x2c,0x38,0x9f,0x7d,
+ 0x88,0xec,0xb7,0xdf,
+};
+const unsigned char tc_g[] = {
+ 0x04,0xee,0xe5,0x77,0x32,0x0b,0x1c,0x24,0x1a,0x79,0x41,0x9f,
+ 0xcd,0xe5,0x71,0x8c,0x2b,0x63,0xf8,0x1e,0xf8,0x71,0x7d,0x56,
+ 0xa5,0x7d,0x2f,0xb2,0x6b,0x65,0xa8,0xbe,0xb6,0x35,0x73,0xb5,
+ 0x26,0x05,0xef,0xb3,0x2f,0xf4,0xcf,0x31,0xaa,0xef,0x9a,0x92,
+ 0xdf,0x84,0xe4,0xe8,0x40,0x8c,0xc6,0xc7,0xcf,0x27,0xa5,0x35,
+ 0xaa,0xd2,0xb3,0x8a,0x56,
+};
+const unsigned char tc_ya[] = {
+ 0x37,0x57,0x4c,0xfb,0xf1,0xb9,0x5f,0xf6,0xa8,0xe2,0xd7,0xbe,
+ 0x46,0x2d,0x4d,0x01,0xe6,0xdd,0xe2,0x61,0x8f,0x34,0xf4,0xde,
+ 0x9d,0xf8,0x69,0xb2,0x4f,0x53,0x2c,0x5d,
+};
+const unsigned char tc_ADa[] = {
+ 0x41,0x44,0x61,
+};
+const unsigned char tc_Ya[] = {
+ 0x04,0x1f,0x12,0xad,0x5f,0xc6,0x50,0x10,0xa2,0x4f,0xc0,0x4c,
+ 0x86,0x19,0x71,0x09,0xa3,0x6d,0xf0,0xe9,0xce,0x85,0xa7,0x47,
+ 0x9e,0x1e,0x13,0x64,0x69,0x2f,0xda,0xce,0x17,0xea,0x5a,0x63,
+ 0x4e,0x19,0xc2,0x07,0xa5,0xd5,0x2e,0xad,0x6c,0x68,0x17,0xa1,
+ 0x63,0xcf,0x2f,0x2f,0xe3,0x40,0x6c,0x5d,0xfd,0xfc,0x2e,0xcd,
+ 0xf8,0xe4,0x2c,0x5e,0x16,
+};
+const unsigned char tc_yb[] = {
+ 0xe5,0x67,0x2f,0xc9,0xeb,0x4e,0x72,0x1f,0x41,0xd8,0x01,0x81,
+ 0xec,0x4c,0x9f,0xd9,0x88,0x66,0x68,0xac,0xc4,0x80,0x24,0xd3,
+ 0x3c,0x82,0xbb,0x10,0x2a,0xec,0xba,0x52,
+};
+const unsigned char tc_ADb[] = {
+ 0x41,0x44,0x62,
+};
+const unsigned char tc_Yb[] = {
+ 0x04,0x6a,0x51,0x18,0x0b,0x6e,0xba,0xba,0xf5,0xed,0x0a,0xf8,
+ 0xcd,0x78,0x68,0x86,0xd9,0x33,0x42,0xbc,0xae,0x4c,0x15,0x8c,
+ 0xe1,0x61,0x7a,0x0a,0xcc,0x8e,0xc3,0x54,0x48,0x6f,0x9e,0xd2,
+ 0xe9,0x21,0x09,0x13,0x20,0x6d,0x1e,0x3f,0x5e,0x46,0x3d,0x2d,
+ 0x32,0x0c,0x4f,0x1f,0x5c,0xe8,0xb6,0x77,0xa7,0xe3,0x8a,0x26,
+ 0xf7,0x52,0xbf,0x8f,0x84,
+};
+const unsigned char tc_K[] = {
+ 0x3e,0x0e,0x2f,0x89,0x76,0xfb,0x8d,0x0d,0xee,0xe3,0x0a,0xef,
+ 0x4b,0x5c,0xd3,0x63,0x1e,0xed,0x24,0x9a,0xf3,0x2f,0x53,0xd0,
+ 0xdd,0x00,0x9b,0x5d,0x7b,0x8f,0x6b,0x6c,
+};
+const unsigned char tc_ISK_IR[] = {
+ 0x95,0x65,0xed,0x28,0x6b,0x6e,0x3c,0xf1,0xf9,0x43,0xfd,0x31,
+ 0x74,0x6f,0x9a,0x22,0x93,0x55,0x37,0x02,0x5a,0x13,0x28,0xd4,
+ 0x98,0x00,0x05,0xba,0x98,0x4f,0x0c,0x39,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x62,0xa4,0x45,0xa4,0xda,0xa3,0x54,0x6d,0xd0,0x31,0xc6,0x6e,
+ 0xad,0x2e,0x4e,0x01,0x5a,0xbb,0xcc,0x83,0xbd,0xe3,0x1c,0x90,
+ 0xf8,0x41,0x14,0x9f,0xd4,0x41,0xc5,0x8a,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0x62,0xa4,0x45,0xa4,0xda,0xa3,0x54,0x6d,0xd0,0x31,0xc6,0x6e,
+ 0xad,0x2e,0x4e,0x01,0x5a,0xbb,0xcc,0x83,0xbd,0xe3,0x1c,0x90,
+ 0xf8,0x41,0x14,0x9f,0xd4,0x41,0xc5,0x8a,
+};
+const unsigned char tc_sid_out_ir[] = {
+ 0xa7,0x38,0x6d,0x1c,0x2e,0xb0,0x6e,0x80,0x56,0xd7,0xfe,0xcb,
+ 0xcf,0x69,0x1e,0x08,0xd1,0x89,0xd9,0x62,0x36,0x02,0x0e,0xf3,
+ 0x1b,0x41,0x40,0x69,0x8a,0x4b,0x99,0xf9,
+};
+const unsigned char tc_sid_out_oc[] = {
+ 0xd3,0x37,0xdb,0xc0,0xdd,0x79,0x7b,0x4e,0x6f,0x2f,0x14,0xea,
+ 0x49,0x25,0xc5,0x8e,0x5d,0x55,0x23,0x87,0x1e,0x8c,0xb4,0x3a,
+ 0x3c,0x1b,0x0f,0x2b,0x1a,0x1f,0xfd,0xe3,
+};
+
+
+
+
+
+
+

+B.5.9. Testvectors as JSON file encoded as BASE64 +

+
+
+ #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT
+ #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICIz
+ #NEIzNjQ1NENBQjJFNzg0MkMzODlGN0Q4OEVDQjdERiIsICJnIjogIjA0RUVFNTc3Mz
+ #IwQjFDMjQxQTc5NDE5RkNERTU3MThDMkI2M0Y4MUVGODcxN0Q1NkE1N0QyRkIyNkI2
+ #NUE4QkVCNjM1NzNCNTI2MDVFRkIzMkZGNENGMzFBQUVGOUE5MkRGODRFNEU4NDA4Q0
+ #M2QzdDRjI3QTUzNUFBRDJCMzhBNTYiLCAieWEiOiAiMzc1NzRDRkJGMUI5NUZGNkE4
+ #RTJEN0JFNDYyRDREMDFFNkRERTI2MThGMzRGNERFOURGODY5QjI0RjUzMkM1RCIsIC
+ #JBRGEiOiAiNDE0NDYxIiwgIllhIjogIjA0MUYxMkFENUZDNjUwMTBBMjRGQzA0Qzg2
+ #MTk3MTA5QTM2REYwRTlDRTg1QTc0NzlFMUUxMzY0NjkyRkRBQ0UxN0VBNUE2MzRFMT
+ #lDMjA3QTVENTJFQUQ2QzY4MTdBMTYzQ0YyRjJGRTM0MDZDNURGREZDMkVDREY4RTQy
+ #QzVFMTYiLCAieWIiOiAiRTU2NzJGQzlFQjRFNzIxRjQxRDgwMTgxRUM0QzlGRDk4OD
+ #Y2NjhBQ0M0ODAyNEQzM0M4MkJCMTAyQUVDQkE1MiIsICJBRGIiOiAiNDE0NDYyIiwg
+ #IlliIjogIjA0NkE1MTE4MEI2RUJBQkFGNUVEMEFGOENENzg2ODg2RDkzMzQyQkNBRT
+ #RDMTU4Q0UxNjE3QTBBQ0M4RUMzNTQ0ODZGOUVEMkU5MjEwOTEzMjA2RDFFM0Y1RTQ2
+ #M0QyRDMyMEM0RjFGNUNFOEI2NzdBN0UzOEEyNkY3NTJCRjhGODQiLCAiSyI6ICIzRT
+ #BFMkY4OTc2RkI4RDBERUVFMzBBRUY0QjVDRDM2MzFFRUQyNDlBRjMyRjUzRDBERDAw
+ #OUI1RDdCOEY2QjZDIiwgIklTS19JUiI6ICI5NTY1RUQyODZCNkUzQ0YxRjk0M0ZEMz
+ #E3NDZGOUEyMjkzNTUzNzAyNUExMzI4RDQ5ODAwMDVCQTk4NEYwQzM5IiwgIklTS19T
+ #WSI6ICI2MkE0NDVBNERBQTM1NDZERDAzMUM2NkVBRDJFNEUwMTVBQkJDQzgzQkRFMz
+ #FDOTBGODQxMTQ5RkQ0NDFDNThBIiwgInNpZF9vdXRwdXRfaXIiOiAiQTczODZEMUMy
+ #RUIwNkU4MDU2RDdGRUNCQ0Y2OTFFMDhEMTg5RDk2MjM2MDIwRUYzMUI0MTQwNjk4QT
+ #RCOTlGOSIsICJzaWRfb3V0cHV0X29jIjogIkQzMzdEQkMwREQ3OTdCNEU2RjJGMTRF
+ #QTQ5MjVDNThFNUQ1NTIzODcxRThDQjQzQTNDMUIwRjJCMUExRkZERTMifQ==
+
+
+
+
+
+
+

+B.5.10. Test case for scalar_mult_vfy with correct inputs +

+
+
+    s: (length: 32 bytes)
+      f012501c091ff9b99a123fffe571d8bc01e8077ee581362e1bd21399
+      0835643b
+    X: (length: 65 bytes)
+      0424648eb986c2be0af636455cef0550671d6bcd8aa26e0d72ffa1b1
+      fd12ba4e0f78da2b6d2184f31af39e566aef127014b6936c9a37346d
+      10a4ab2514faef5831
+    G.scalar_mult(s,X) (full coordinates): (length: 65 bytes)
+      04f5a191f078c87c36633b78c701751159d56c59f3fe9105b5720673
+      470f303ab925b6a7fd1cdd8f649a21cf36b68d9e9c4a11919a951892
+      519786104b27033757
+    G.scalar_mult_vfy(s,X) (only X-coordinate):
+    (length: 32 bytes)
+      f5a191f078c87c36633b78c701751159d56c59f3fe9105b572067347
+      0f303ab9
+
+
+
+
+
+
+

+B.5.11. Invalid inputs for scalar_mult_vfy +

+

For these test cases scalar_mult_vfy(y,.) MUST return the representation of the neutral element G.I. When including Y_i1 or Y_i2 in messages of A or B the protocol MUST abort.

+
+
+    s: (length: 32 bytes)
+      f012501c091ff9b99a123fffe571d8bc01e8077ee581362e1bd21399
+      0835643b
+    Y_i1: (length: 65 bytes)
+      0424648eb986c2be0af636455cef0550671d6bcd8aa26e0d72ffa1b1
+      fd12ba4e0f78da2b6d2184f31af39e566aef127014b6936c9a37346d
+      10a4ab2514faef5857
+    Y_i2: (length: 1 bytes)
+      00
+    G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I
+
+
+
+
+
+B.5.11.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJWYWxpZCI6IHsicyI6ICJGMDEyNTAxQzA5MUZGOUI5OUExMjNGRkZFNTcxRDhCQz
+ #AxRTgwNzdFRTU4MTM2MkUxQkQyMTM5OTA4MzU2NDNCIiwgIlgiOiAiMDQyNDY0OEVC
+ #OTg2QzJCRTBBRjYzNjQ1NUNFRjA1NTA2NzFENkJDRDhBQTI2RTBENzJGRkExQjFGRD
+ #EyQkE0RTBGNzhEQTJCNkQyMTg0RjMxQUYzOUU1NjZBRUYxMjcwMTRCNjkzNkM5QTM3
+ #MzQ2RDEwQTRBQjI1MTRGQUVGNTgzMSIsICJHLnNjYWxhcl9tdWx0KHMsWCkgKGZ1bG
+ #wgY29vcmRpbmF0ZXMpIjogIjA0RjVBMTkxRjA3OEM4N0MzNjYzM0I3OEM3MDE3NTEx
+ #NTlENTZDNTlGM0ZFOTEwNUI1NzIwNjczNDcwRjMwM0FCOTI1QjZBN0ZEMUNERDhGNj
+ #Q5QTIxQ0YzNkI2OEQ5RTlDNEExMTkxOUE5NTE4OTI1MTk3ODYxMDRCMjcwMzM3NTci
+ #LCAiRy5zY2FsYXJfbXVsdF92ZnkocyxYKSAob25seSBYLWNvb3JkaW5hdGUpIjogIk
+ #Y1QTE5MUYwNzhDODdDMzY2MzNCNzhDNzAxNzUxMTU5RDU2QzU5RjNGRTkxMDVCNTcy
+ #MDY3MzQ3MEYzMDNBQjkifSwgIkludmFsaWQgWTEiOiAiMDQyNDY0OEVCOTg2QzJCRT
+ #BBRjYzNjQ1NUNFRjA1NTA2NzFENkJDRDhBQTI2RTBENzJGRkExQjFGRDEyQkE0RTBG
+ #NzhEQTJCNkQyMTg0RjMxQUYzOUU1NjZBRUYxMjcwMTRCNjkzNkM5QTM3MzQ2RDEwQT
+ #RBQjI1MTRGQUVGNTg1NyIsICJJbnZhbGlkIFkyIjogIjAwIn0=
+
+
+
+
+
+
+
+
+
+
+

+B.6. Test vector for CPace using group NIST P-384 and hash SHA-384 +

+
+
+

+B.6.1. Test vectors for calculate_generator with group NIST P-384 +

+
+
+  Inputs
+    H   = SHA-384 with input block size 128 bytes.
+    PRS = b'Password' ; ZPAD length: 87 ;
+    DSI = b'CPaceP384_XMD:SHA-384_SSWU_NU_'
+    DST = b'CPaceP384_XMD:SHA-384_SSWU_NU__DST'
+    CI = b'oc\x0bB_responder\x0bA_initiator'
+    CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72
+    sid = 5b3773aa90e8f23c61563a4b645b276c
+  Outputs
+    generator_string(PRS,G.DSI,CI,sid,H.s_in_bytes):
+    (length: 172 bytes)
+      1e4350616365503338345f584d443a5348412d3338345f535357555f
+      4e555f0850617373776f726457000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      000000000000000000000000000000001a6f630b425f726573706f6e
+      6465720b415f696e69746961746f72105b3773aa90e8f23c61563a4b
+      645b276c
+    generator g: (length: 97 bytes)
+      04ffe1bdc3293fdbe31b2959916e52c018e923eac99836bd9a1cbeec
+      794a8d4d78baa32cdafc9685bc1067a780f4ad9c8a6c6e164aa42906
+      d1e27f782581adc8e0109219626a2b8fbdc34602e4084554bdd6c0c6
+      98dd657ac8e31b2bcce1c7b0d8
+
+
+
+
+
+B.6.1.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJIIjogIlNIQS0zODQiLCAiSC5zX2luX2J5dGVzIjogMTI4LCAiUFJTIjogIjUwNj
+ #E3MzczNzc2RjcyNjQiLCAiWlBBRCBsZW5ndGgiOiA4NywgIkRTSSI6ICI0MzUwNjE2
+ #MzY1NTAzMzM4MzQ1RjU4NEQ0NDNBNTM0ODQxMkQzMzM4MzQ1RjUzNTM1NzU1NUY0RT
+ #U1NUYiLCAiQ0kiOiAiNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0NjU3MjBCNDE1RjY5
+ #NkU2OTc0Njk2MTc0NkY3MiIsICJzaWQiOiAiNUIzNzczQUE5MEU4RjIzQzYxNTYzQT
+ #RCNjQ1QjI3NkMiLCAiZ2VuZXJhdG9yX3N0cmluZyhHLkRTSSxQUlMsQ0ksc2lkLEgu
+ #c19pbl9ieXRlcykiOiAiMUU0MzUwNjE2MzY1NTAzMzM4MzQ1RjU4NEQ0NDNBNTM0OD
+ #QxMkQzMzM4MzQ1RjUzNTM1NzU1NUY0RTU1NUYwODUwNjE3MzczNzc2RjcyNjQ1NzAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDFBNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0
+ #NjU3MjBCNDE1RjY5NkU2OTc0Njk2MTc0NkY3MjEwNUIzNzczQUE5MEU4RjIzQzYxNT
+ #YzQTRCNjQ1QjI3NkMiLCAiZ2VuZXJhdG9yIGciOiAiMDRGRkUxQkRDMzI5M0ZEQkUz
+ #MUIyOTU5OTE2RTUyQzAxOEU5MjNFQUM5OTgzNkJEOUExQ0JFRUM3OTRBOEQ0RDc4Qk
+ #FBMzJDREFGQzk2ODVCQzEwNjdBNzgwRjRBRDlDOEE2QzZFMTY0QUE0MjkwNkQxRTI3
+ #Rjc4MjU4MUFEQzhFMDEwOTIxOTYyNkEyQjhGQkRDMzQ2MDJFNDA4NDU1NEJERDZDME
+ #M2OThERDY1N0FDOEUzMUIyQkNDRTFDN0IwRDgifQ==
+
+
+
+
+
+
+
+
+

+B.6.2. Test vector for message from A +

+
+
+  Inputs
+    ADa = b'ADa'
+    ya (big endian): (length: 48 bytes)
+      ef433dd5ad142c860e7cb6400dd315d388d5ec5420c550e9d6f0907f
+      375d988bc4d704837e43561c497e7dd93edcdb9d
+  Outputs
+    Ya: (length: 97 bytes)
+      0434a04da121995d81d7c5ded02cf2e70954dca49059485ea38310b7
+      3b96fa1ec78619c5a1e524472778331fbe009fa1564a3203e42993a3
+      6285fa54e6c24184fd227458c87781be16fff46dbc970cc1b1770050
+      a94d6826d52f211b234792e66d
+    Alternative correct value for Ya: (-ya)*g:
+    (length: 97 bytes)
+      0434a04da121995d81d7c5ded02cf2e70954dca49059485ea38310b7
+      3b96fa1ec78619c5a1e524472778331fbe009fa156b5cdfc1bd66c5c
+      9d7a05ab193dbe7b02dd8ba737887e41e9000b924368f33e4d88ffaf
+      55b297d92ad0dee4ddb86d1992
+
+
+
+
+
+
+

+B.6.3. Test vector for message from B +

+
+
+  Inputs
+    ADb = b'ADb'
+    yb (big endian): (length: 48 bytes)
+      50b0e36b95a2edfaa8342b843dddc90b175330f2399c1b36586dedda
+      3c255975f30be6a750f9404fccc62a6323b5e471
+  Outputs
+    Yb: (length: 97 bytes)
+      040a6559147fd492ad74ab1f4def6196fd6399540e84706227a1f90d
+      104cdaeb630b7c5c18748deb25653ad2a4cb5e6274841cad328bb031
+      2628b9b1f51bea72b8c610999a6730f752649205ae85c452ef83f98b
+      e715cd0103186874b07cf02074
+    Alternative correct value for Yb: (-yb)*g:
+    (length: 97 bytes)
+      040a6559147fd492ad74ab1f4def6196fd6399540e84706227a1f90d
+      104cdaeb630b7c5c18748deb25653ad2a4cb5e62747be352cd744fce
+      d9d7464e0ae4158d4739ef666598cf08ad9b6dfa517a3bad0f7c0674
+      17ea32fefce7978b50830fdf8b
+
+
+
+
+
+
+

+B.6.4. Test vector for secret points K +

+
+
+    scalar_mult_vfy(ya,Yb): (length: 48 bytes)
+      a9acaea95692a64462067fe8e4321f2fca9793a8a0420f0e253ed0d6
+      db858fe161de7576206a8a35bd4a60e00724fd3e
+    scalar_mult_vfy(yb,Ya): (length: 48 bytes)
+      a9acaea95692a64462067fe8e4321f2fca9793a8a0420f0e253ed0d6
+      db858fe161de7576206a8a35bd4a60e00724fd3e
+
+
+
+
+
+
+

+B.6.5. Test vector for ISK calculation initiator/responder +

+
+
+    transcript_ir(Ya,ADa,Yb,ADb): (length: 204 bytes)
+      610434a04da121995d81d7c5ded02cf2e70954dca49059485ea38310
+      b73b96fa1ec78619c5a1e524472778331fbe009fa1564a3203e42993
+      a36285fa54e6c24184fd227458c87781be16fff46dbc970cc1b17700
+      50a94d6826d52f211b234792e66d0341446161040a6559147fd492ad
+      74ab1f4def6196fd6399540e84706227a1f90d104cdaeb630b7c5c18
+      748deb25653ad2a4cb5e6274841cad328bb0312628b9b1f51bea72b8
+      c610999a6730f752649205ae85c452ef83f98be715cd0103186874b0
+      7cf0207403414462
+    DSI = G.DSI_ISK, b'CPaceP384_XMD:SHA-384_SSWU_NU__ISK':
+    (length: 34 bytes)
+      4350616365503338345f584d443a5348412d3338345f535357555f4e
+      555f5f49534b
+    lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb):
+    (length: 305 bytes)
+      224350616365503338345f584d443a5348412d3338345f535357555f
+      4e555f5f49534b105b3773aa90e8f23c61563a4b645b276c30a9acae
+      a95692a64462067fe8e4321f2fca9793a8a0420f0e253ed0d6db858f
+      e161de7576206a8a35bd4a60e00724fd3e610434a04da121995d81d7
+      c5ded02cf2e70954dca49059485ea38310b73b96fa1ec78619c5a1e5
+      24472778331fbe009fa1564a3203e42993a36285fa54e6c24184fd22
+      7458c87781be16fff46dbc970cc1b1770050a94d6826d52f211b2347
+      92e66d0341446161040a6559147fd492ad74ab1f4def6196fd639954
+      0e84706227a1f90d104cdaeb630b7c5c18748deb25653ad2a4cb5e62
+      74841cad328bb0312628b9b1f51bea72b8c610999a6730f752649205
+      ae85c452ef83f98be715cd0103186874b07cf0207403414462
+    ISK result: (length: 48 bytes)
+      d1b74375c7d63d7de246cbf3fc2b3092645c73a0aa816989c0de6048
+      ed4ece6a54df82d05d2be3498cb9288be7bdbdb9
+
+
+
+
+
+
+

+B.6.6. Test vector for ISK calculation parallel execution +

+
+
+    transcript_oc(Ya,ADa,Yb,ADb): (length: 206 bytes)
+      6f63610434a04da121995d81d7c5ded02cf2e70954dca49059485ea3
+      8310b73b96fa1ec78619c5a1e524472778331fbe009fa1564a3203e4
+      2993a36285fa54e6c24184fd227458c87781be16fff46dbc970cc1b1
+      770050a94d6826d52f211b234792e66d0341446161040a6559147fd4
+      92ad74ab1f4def6196fd6399540e84706227a1f90d104cdaeb630b7c
+      5c18748deb25653ad2a4cb5e6274841cad328bb0312628b9b1f51bea
+      72b8c610999a6730f752649205ae85c452ef83f98be715cd01031868
+      74b07cf0207403414462
+    DSI = G.DSI_ISK, b'CPaceP384_XMD:SHA-384_SSWU_NU__ISK':
+    (length: 34 bytes)
+      4350616365503338345f584d443a5348412d3338345f535357555f4e
+      555f5f49534b
+    lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb):
+    (length: 307 bytes)
+      224350616365503338345f584d443a5348412d3338345f535357555f
+      4e555f5f49534b105b3773aa90e8f23c61563a4b645b276c30a9acae
+      a95692a64462067fe8e4321f2fca9793a8a0420f0e253ed0d6db858f
+      e161de7576206a8a35bd4a60e00724fd3e6f63610434a04da121995d
+      81d7c5ded02cf2e70954dca49059485ea38310b73b96fa1ec78619c5
+      a1e524472778331fbe009fa1564a3203e42993a36285fa54e6c24184
+      fd227458c87781be16fff46dbc970cc1b1770050a94d6826d52f211b
+      234792e66d0341446161040a6559147fd492ad74ab1f4def6196fd63
+      99540e84706227a1f90d104cdaeb630b7c5c18748deb25653ad2a4cb
+      5e6274841cad328bb0312628b9b1f51bea72b8c610999a6730f75264
+      9205ae85c452ef83f98be715cd0103186874b07cf0207403414462
+    ISK result: (length: 48 bytes)
+      a051d4532ca9fb6774e097ebac69c1d6a18144a15421dc155d0b1e8a
+      ef9f9d8c0fe86e85d3cbee7796ff50171f42801b
+
+
+
+
+
+
+

+B.6.7. Test vector for optional output of session id +

+
+
+    H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)):
+    (length: 48 bytes)
+      8d5a03946a69ffa12cd6efd469fe8671bbc25fad6db2656f3963c94e
+      9c940bdecc2bd555474c211817787d5cf7870ed1
+    H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)):
+    (length: 48 bytes)
+      c0729db25db40c48a35f787d5410b2cb9a2d9f5e9cf1cf159ed2f63c
+      6b2185e597e176cc221422e9496eeda2bf123c8b
+
+
+
+
+
+
+

+B.6.8. Corresponding C programming language initializers +

+
+
+const unsigned char tc_PRS[] = {
+ 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64,
+};
+const unsigned char tc_CI[] = {
+ 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64,
+ 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74,
+ 0x6f,0x72,
+};
+const unsigned char tc_sid[] = {
+ 0x5b,0x37,0x73,0xaa,0x90,0xe8,0xf2,0x3c,0x61,0x56,0x3a,0x4b,
+ 0x64,0x5b,0x27,0x6c,
+};
+const unsigned char tc_g[] = {
+ 0x04,0xff,0xe1,0xbd,0xc3,0x29,0x3f,0xdb,0xe3,0x1b,0x29,0x59,
+ 0x91,0x6e,0x52,0xc0,0x18,0xe9,0x23,0xea,0xc9,0x98,0x36,0xbd,
+ 0x9a,0x1c,0xbe,0xec,0x79,0x4a,0x8d,0x4d,0x78,0xba,0xa3,0x2c,
+ 0xda,0xfc,0x96,0x85,0xbc,0x10,0x67,0xa7,0x80,0xf4,0xad,0x9c,
+ 0x8a,0x6c,0x6e,0x16,0x4a,0xa4,0x29,0x06,0xd1,0xe2,0x7f,0x78,
+ 0x25,0x81,0xad,0xc8,0xe0,0x10,0x92,0x19,0x62,0x6a,0x2b,0x8f,
+ 0xbd,0xc3,0x46,0x02,0xe4,0x08,0x45,0x54,0xbd,0xd6,0xc0,0xc6,
+ 0x98,0xdd,0x65,0x7a,0xc8,0xe3,0x1b,0x2b,0xcc,0xe1,0xc7,0xb0,
+ 0xd8,
+};
+const unsigned char tc_ya[] = {
+ 0xef,0x43,0x3d,0xd5,0xad,0x14,0x2c,0x86,0x0e,0x7c,0xb6,0x40,
+ 0x0d,0xd3,0x15,0xd3,0x88,0xd5,0xec,0x54,0x20,0xc5,0x50,0xe9,
+ 0xd6,0xf0,0x90,0x7f,0x37,0x5d,0x98,0x8b,0xc4,0xd7,0x04,0x83,
+ 0x7e,0x43,0x56,0x1c,0x49,0x7e,0x7d,0xd9,0x3e,0xdc,0xdb,0x9d,
+};
+const unsigned char tc_ADa[] = {
+ 0x41,0x44,0x61,
+};
+const unsigned char tc_Ya[] = {
+ 0x04,0x34,0xa0,0x4d,0xa1,0x21,0x99,0x5d,0x81,0xd7,0xc5,0xde,
+ 0xd0,0x2c,0xf2,0xe7,0x09,0x54,0xdc,0xa4,0x90,0x59,0x48,0x5e,
+ 0xa3,0x83,0x10,0xb7,0x3b,0x96,0xfa,0x1e,0xc7,0x86,0x19,0xc5,
+ 0xa1,0xe5,0x24,0x47,0x27,0x78,0x33,0x1f,0xbe,0x00,0x9f,0xa1,
+ 0x56,0x4a,0x32,0x03,0xe4,0x29,0x93,0xa3,0x62,0x85,0xfa,0x54,
+ 0xe6,0xc2,0x41,0x84,0xfd,0x22,0x74,0x58,0xc8,0x77,0x81,0xbe,
+ 0x16,0xff,0xf4,0x6d,0xbc,0x97,0x0c,0xc1,0xb1,0x77,0x00,0x50,
+ 0xa9,0x4d,0x68,0x26,0xd5,0x2f,0x21,0x1b,0x23,0x47,0x92,0xe6,
+ 0x6d,
+};
+const unsigned char tc_yb[] = {
+ 0x50,0xb0,0xe3,0x6b,0x95,0xa2,0xed,0xfa,0xa8,0x34,0x2b,0x84,
+ 0x3d,0xdd,0xc9,0x0b,0x17,0x53,0x30,0xf2,0x39,0x9c,0x1b,0x36,
+ 0x58,0x6d,0xed,0xda,0x3c,0x25,0x59,0x75,0xf3,0x0b,0xe6,0xa7,
+ 0x50,0xf9,0x40,0x4f,0xcc,0xc6,0x2a,0x63,0x23,0xb5,0xe4,0x71,
+};
+const unsigned char tc_ADb[] = {
+ 0x41,0x44,0x62,
+};
+const unsigned char tc_Yb[] = {
+ 0x04,0x0a,0x65,0x59,0x14,0x7f,0xd4,0x92,0xad,0x74,0xab,0x1f,
+ 0x4d,0xef,0x61,0x96,0xfd,0x63,0x99,0x54,0x0e,0x84,0x70,0x62,
+ 0x27,0xa1,0xf9,0x0d,0x10,0x4c,0xda,0xeb,0x63,0x0b,0x7c,0x5c,
+ 0x18,0x74,0x8d,0xeb,0x25,0x65,0x3a,0xd2,0xa4,0xcb,0x5e,0x62,
+ 0x74,0x84,0x1c,0xad,0x32,0x8b,0xb0,0x31,0x26,0x28,0xb9,0xb1,
+ 0xf5,0x1b,0xea,0x72,0xb8,0xc6,0x10,0x99,0x9a,0x67,0x30,0xf7,
+ 0x52,0x64,0x92,0x05,0xae,0x85,0xc4,0x52,0xef,0x83,0xf9,0x8b,
+ 0xe7,0x15,0xcd,0x01,0x03,0x18,0x68,0x74,0xb0,0x7c,0xf0,0x20,
+ 0x74,
+};
+const unsigned char tc_K[] = {
+ 0xa9,0xac,0xae,0xa9,0x56,0x92,0xa6,0x44,0x62,0x06,0x7f,0xe8,
+ 0xe4,0x32,0x1f,0x2f,0xca,0x97,0x93,0xa8,0xa0,0x42,0x0f,0x0e,
+ 0x25,0x3e,0xd0,0xd6,0xdb,0x85,0x8f,0xe1,0x61,0xde,0x75,0x76,
+ 0x20,0x6a,0x8a,0x35,0xbd,0x4a,0x60,0xe0,0x07,0x24,0xfd,0x3e,
+};
+const unsigned char tc_ISK_IR[] = {
+ 0xd1,0xb7,0x43,0x75,0xc7,0xd6,0x3d,0x7d,0xe2,0x46,0xcb,0xf3,
+ 0xfc,0x2b,0x30,0x92,0x64,0x5c,0x73,0xa0,0xaa,0x81,0x69,0x89,
+ 0xc0,0xde,0x60,0x48,0xed,0x4e,0xce,0x6a,0x54,0xdf,0x82,0xd0,
+ 0x5d,0x2b,0xe3,0x49,0x8c,0xb9,0x28,0x8b,0xe7,0xbd,0xbd,0xb9,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0xa0,0x51,0xd4,0x53,0x2c,0xa9,0xfb,0x67,0x74,0xe0,0x97,0xeb,
+ 0xac,0x69,0xc1,0xd6,0xa1,0x81,0x44,0xa1,0x54,0x21,0xdc,0x15,
+ 0x5d,0x0b,0x1e,0x8a,0xef,0x9f,0x9d,0x8c,0x0f,0xe8,0x6e,0x85,
+ 0xd3,0xcb,0xee,0x77,0x96,0xff,0x50,0x17,0x1f,0x42,0x80,0x1b,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0xa0,0x51,0xd4,0x53,0x2c,0xa9,0xfb,0x67,0x74,0xe0,0x97,0xeb,
+ 0xac,0x69,0xc1,0xd6,0xa1,0x81,0x44,0xa1,0x54,0x21,0xdc,0x15,
+ 0x5d,0x0b,0x1e,0x8a,0xef,0x9f,0x9d,0x8c,0x0f,0xe8,0x6e,0x85,
+ 0xd3,0xcb,0xee,0x77,0x96,0xff,0x50,0x17,0x1f,0x42,0x80,0x1b,
+};
+const unsigned char tc_sid_out_ir[] = {
+ 0x8d,0x5a,0x03,0x94,0x6a,0x69,0xff,0xa1,0x2c,0xd6,0xef,0xd4,
+ 0x69,0xfe,0x86,0x71,0xbb,0xc2,0x5f,0xad,0x6d,0xb2,0x65,0x6f,
+ 0x39,0x63,0xc9,0x4e,0x9c,0x94,0x0b,0xde,0xcc,0x2b,0xd5,0x55,
+ 0x47,0x4c,0x21,0x18,0x17,0x78,0x7d,0x5c,0xf7,0x87,0x0e,0xd1,
+};
+const unsigned char tc_sid_out_oc[] = {
+ 0xc0,0x72,0x9d,0xb2,0x5d,0xb4,0x0c,0x48,0xa3,0x5f,0x78,0x7d,
+ 0x54,0x10,0xb2,0xcb,0x9a,0x2d,0x9f,0x5e,0x9c,0xf1,0xcf,0x15,
+ 0x9e,0xd2,0xf6,0x3c,0x6b,0x21,0x85,0xe5,0x97,0xe1,0x76,0xcc,
+ 0x22,0x14,0x22,0xe9,0x49,0x6e,0xed,0xa2,0xbf,0x12,0x3c,0x8b,
+};
+
+
+
+
+
+
+

+B.6.9. Testvectors as JSON file encoded as BASE64 +

+
+
+ #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT
+ #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI1
+ #QjM3NzNBQTkwRThGMjNDNjE1NjNBNEI2NDVCMjc2QyIsICJnIjogIjA0RkZFMUJEQz
+ #MyOTNGREJFMzFCMjk1OTkxNkU1MkMwMThFOTIzRUFDOTk4MzZCRDlBMUNCRUVDNzk0
+ #QThENEQ3OEJBQTMyQ0RBRkM5Njg1QkMxMDY3QTc4MEY0QUQ5QzhBNkM2RTE2NEFBND
+ #I5MDZEMUUyN0Y3ODI1ODFBREM4RTAxMDkyMTk2MjZBMkI4RkJEQzM0NjAyRTQwODQ1
+ #NTRCREQ2QzBDNjk4REQ2NTdBQzhFMzFCMkJDQ0UxQzdCMEQ4IiwgInlhIjogIkVGND
+ #MzREQ1QUQxNDJDODYwRTdDQjY0MDBERDMxNUQzODhENUVDNTQyMEM1NTBFOUQ2RjA5
+ #MDdGMzc1RDk4OEJDNEQ3MDQ4MzdFNDM1NjFDNDk3RTdERDkzRURDREI5RCIsICJBRG
+ #EiOiAiNDE0NDYxIiwgIllhIjogIjA0MzRBMDREQTEyMTk5NUQ4MUQ3QzVERUQwMkNG
+ #MkU3MDk1NERDQTQ5MDU5NDg1RUEzODMxMEI3M0I5NkZBMUVDNzg2MTlDNUExRTUyND
+ #Q3Mjc3ODMzMUZCRTAwOUZBMTU2NEEzMjAzRTQyOTkzQTM2Mjg1RkE1NEU2QzI0MTg0
+ #RkQyMjc0NThDODc3ODFCRTE2RkZGNDZEQkM5NzBDQzFCMTc3MDA1MEE5NEQ2ODI2RD
+ #UyRjIxMUIyMzQ3OTJFNjZEIiwgInliIjogIjUwQjBFMzZCOTVBMkVERkFBODM0MkI4
+ #NDNERERDOTBCMTc1MzMwRjIzOTlDMUIzNjU4NkRFRERBM0MyNTU5NzVGMzBCRTZBNz
+ #UwRjk0MDRGQ0NDNjJBNjMyM0I1RTQ3MSIsICJBRGIiOiAiNDE0NDYyIiwgIlliIjog
+ #IjA0MEE2NTU5MTQ3RkQ0OTJBRDc0QUIxRjRERUY2MTk2RkQ2Mzk5NTQwRTg0NzA2Mj
+ #I3QTFGOTBEMTA0Q0RBRUI2MzBCN0M1QzE4NzQ4REVCMjU2NTNBRDJBNENCNUU2Mjc0
+ #ODQxQ0FEMzI4QkIwMzEyNjI4QjlCMUY1MUJFQTcyQjhDNjEwOTk5QTY3MzBGNzUyNj
+ #Q5MjA1QUU4NUM0NTJFRjgzRjk4QkU3MTVDRDAxMDMxODY4NzRCMDdDRjAyMDc0Iiwg
+ #IksiOiAiQTlBQ0FFQTk1NjkyQTY0NDYyMDY3RkU4RTQzMjFGMkZDQTk3OTNBOEEwND
+ #IwRjBFMjUzRUQwRDZEQjg1OEZFMTYxREU3NTc2MjA2QThBMzVCRDRBNjBFMDA3MjRG
+ #RDNFIiwgIklTS19JUiI6ICJEMUI3NDM3NUM3RDYzRDdERTI0NkNCRjNGQzJCMzA5Mj
+ #Y0NUM3M0EwQUE4MTY5ODlDMERFNjA0OEVENEVDRTZBNTRERjgyRDA1RDJCRTM0OThD
+ #QjkyODhCRTdCREJEQjkiLCAiSVNLX1NZIjogIkEwNTFENDUzMkNBOUZCNjc3NEUwOT
+ #dFQkFDNjlDMUQ2QTE4MTQ0QTE1NDIxREMxNTVEMEIxRThBRUY5RjlEOEMwRkU4NkU4
+ #NUQzQ0JFRTc3OTZGRjUwMTcxRjQyODAxQiIsICJzaWRfb3V0cHV0X2lyIjogIjhENU
+ #EwMzk0NkE2OUZGQTEyQ0Q2RUZENDY5RkU4NjcxQkJDMjVGQUQ2REIyNjU2RjM5NjND
+ #OTRFOUM5NDBCREVDQzJCRDU1NTQ3NEMyMTE4MTc3ODdENUNGNzg3MEVEMSIsICJzaW
+ #Rfb3V0cHV0X29jIjogIkMwNzI5REIyNURCNDBDNDhBMzVGNzg3RDU0MTBCMkNCOUEy
+ #RDlGNUU5Q0YxQ0YxNTlFRDJGNjNDNkIyMTg1RTU5N0UxNzZDQzIyMTQyMkU5NDk2RU
+ #VEQTJCRjEyM0M4QiJ9
+
+
+
+
+
+
+

+B.6.10. Test case for scalar_mult_vfy with correct inputs +

+
+
+    s: (length: 48 bytes)
+      6e8a99a5cdd408eae98e1b8aed286e7b12adbbdac7f2c628d9060ce9
+      2ae0d90bd57a564fd3500fbcce3425dc94ba0ade
+    X: (length: 97 bytes)
+      045b4cd53c4506cc04ba4c44f2762d5d32c3e55df25b8baa5571b165
+      7ad9576efea8259f0684de065a470585b4be876748c7797054f3defe
+      f21b77f83d53bac57c89d52aa4d6dd5872bd281989b138359698009f
+      8ac1f301538badcce9d9f4036e
+    G.scalar_mult(s,X) (full coordinates): (length: 97 bytes)
+      0465c28db05fd9f9a93651c5cc31eae49c4e5246b46489b8f6105873
+      3173a033cda76c3e3ea5352b804e67fdbe2e334be8245dad5c8c993e
+      63bacf0456478f29b71b6c859f13676f84ff150d2741f028f560584a
+      0bdba19a63df62c08949c2fd6d
+    G.scalar_mult_vfy(s,X) (only X-coordinate):
+    (length: 48 bytes)
+      65c28db05fd9f9a93651c5cc31eae49c4e5246b46489b8f610587331
+      73a033cda76c3e3ea5352b804e67fdbe2e334be8
+
+
+
+
+
+
+

+B.6.11. Invalid inputs for scalar_mult_vfy +

+

For these test cases scalar_mult_vfy(y,.) MUST return the representation of the neutral element G.I. When including Y_i1 or Y_i2 in messages of A or B the protocol MUST abort.

+
+
+    s: (length: 48 bytes)
+      6e8a99a5cdd408eae98e1b8aed286e7b12adbbdac7f2c628d9060ce9
+      2ae0d90bd57a564fd3500fbcce3425dc94ba0ade
+    Y_i1: (length: 97 bytes)
+      045b4cd53c4506cc04ba4c44f2762d5d32c3e55df25b8baa5571b165
+      7ad9576efea8259f0684de065a470585b4be876748c7797054f3defe
+      f21b77f83d53bac57c89d52aa4d6dd5872bd281989b138359698009f
+      8ac1f301538badcce9d9f40302
+    Y_i2: (length: 1 bytes)
+      00
+    G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I
+
+
+
+
+
+B.6.11.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJWYWxpZCI6IHsicyI6ICI2RThBOTlBNUNERDQwOEVBRTk4RTFCOEFFRDI4NkU3Qj
+ #EyQURCQkRBQzdGMkM2MjhEOTA2MENFOTJBRTBEOTBCRDU3QTU2NEZEMzUwMEZCQ0NF
+ #MzQyNURDOTRCQTBBREUiLCAiWCI6ICIwNDVCNENENTNDNDUwNkNDMDRCQTRDNDRGMj
+ #c2MkQ1RDMyQzNFNTVERjI1QjhCQUE1NTcxQjE2NTdBRDk1NzZFRkVBODI1OUYwNjg0
+ #REUwNjVBNDcwNTg1QjRCRTg3Njc0OEM3Nzk3MDU0RjNERUZFRjIxQjc3RjgzRDUzQk
+ #FDNTdDODlENTJBQTRENkRENTg3MkJEMjgxOTg5QjEzODM1OTY5ODAwOUY4QUMxRjMw
+ #MTUzOEJBRENDRTlEOUY0MDM2RSIsICJHLnNjYWxhcl9tdWx0KHMsWCkgKGZ1bGwgY2
+ #9vcmRpbmF0ZXMpIjogIjA0NjVDMjhEQjA1RkQ5RjlBOTM2NTFDNUNDMzFFQUU0OUM0
+ #RTUyNDZCNDY0ODlCOEY2MTA1ODczMzE3M0EwMzNDREE3NkMzRTNFQTUzNTJCODA0RT
+ #Y3RkRCRTJFMzM0QkU4MjQ1REFENUM4Qzk5M0U2M0JBQ0YwNDU2NDc4RjI5QjcxQjZD
+ #ODU5RjEzNjc2Rjg0RkYxNTBEMjc0MUYwMjhGNTYwNTg0QTBCREJBMTlBNjNERjYyQz
+ #A4OTQ5QzJGRDZEIiwgIkcuc2NhbGFyX211bHRfdmZ5KHMsWCkgKG9ubHkgWC1jb29y
+ #ZGluYXRlKSI6ICI2NUMyOERCMDVGRDlGOUE5MzY1MUM1Q0MzMUVBRTQ5QzRFNTI0Nk
+ #I0NjQ4OUI4RjYxMDU4NzMzMTczQTAzM0NEQTc2QzNFM0VBNTM1MkI4MDRFNjdGREJF
+ #MkUzMzRCRTgifSwgIkludmFsaWQgWTEiOiAiMDQ1QjRDRDUzQzQ1MDZDQzA0QkE0Qz
+ #Q0RjI3NjJENUQzMkMzRTU1REYyNUI4QkFBNTU3MUIxNjU3QUQ5NTc2RUZFQTgyNTlG
+ #MDY4NERFMDY1QTQ3MDU4NUI0QkU4NzY3NDhDNzc5NzA1NEYzREVGRUYyMUI3N0Y4M0
+ #Q1M0JBQzU3Qzg5RDUyQUE0RDZERDU4NzJCRDI4MTk4OUIxMzgzNTk2OTgwMDlGOEFD
+ #MUYzMDE1MzhCQURDQ0U5RDlGNDAzMDIiLCAiSW52YWxpZCBZMiI6ICIwMCJ9
+
+
+
+
+
+
+
+
+
+
+

+B.7. Test vector for CPace using group NIST P-521 and hash SHA-512 +

+
+
+

+B.7.1. Test vectors for calculate_generator with group NIST P-521 +

+
+
+  Inputs
+    H   = SHA-512 with input block size 128 bytes.
+    PRS = b'Password' ; ZPAD length: 87 ;
+    DSI = b'CPaceP521_XMD:SHA-512_SSWU_NU_'
+    DST = b'CPaceP521_XMD:SHA-512_SSWU_NU__DST'
+    CI = b'oc\x0bB_responder\x0bA_initiator'
+    CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72
+    sid = 7e4b4791d6a8ef019b936c79fb7f2c57
+  Outputs
+    generator_string(PRS,G.DSI,CI,sid,H.s_in_bytes):
+    (length: 172 bytes)
+      1e4350616365503532315f584d443a5348412d3531325f535357555f
+      4e555f0850617373776f726457000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      00000000000000000000000000000000000000000000000000000000
+      000000000000000000000000000000001a6f630b425f726573706f6e
+      6465720b415f696e69746961746f72107e4b4791d6a8ef019b936c79
+      fb7f2c57
+    generator g: (length: 133 bytes)
+      0400e58a8fbf08b38e34a3676f6d690bed58aa4115ff32a57ec87172
+      fc2a1fb89d03258c6429c464981b3284b5fedbd1244bf27432008868
+      7065b9075dd558e14ed69901d2162db1ba3a49c97dca7c902cb1b96b
+      abe21a31942114c860665b35c46b8213f6de17194de54c441083dd11
+      63d5907adad8824bb1307dcf6a55c11a8f01d9789b
+
+
+
+
+
+B.7.1.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJIIjogIlNIQS01MTIiLCAiSC5zX2luX2J5dGVzIjogMTI4LCAiUFJTIjogIjUwNj
+ #E3MzczNzc2RjcyNjQiLCAiWlBBRCBsZW5ndGgiOiA4NywgIkRTSSI6ICI0MzUwNjE2
+ #MzY1NTAzNTMyMzE1RjU4NEQ0NDNBNTM0ODQxMkQzNTMxMzI1RjUzNTM1NzU1NUY0RT
+ #U1NUYiLCAiQ0kiOiAiNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0NjU3MjBCNDE1RjY5
+ #NkU2OTc0Njk2MTc0NkY3MiIsICJzaWQiOiAiN0U0QjQ3OTFENkE4RUYwMTlCOTM2Qz
+ #c5RkI3RjJDNTciLCAiZ2VuZXJhdG9yX3N0cmluZyhHLkRTSSxQUlMsQ0ksc2lkLEgu
+ #c19pbl9ieXRlcykiOiAiMUU0MzUwNjE2MzY1NTAzNTMyMzE1RjU4NEQ0NDNBNTM0OD
+ #QxMkQzNTMxMzI1RjUzNTM1NzU1NUY0RTU1NUYwODUwNjE3MzczNzc2RjcyNjQ1NzAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw
+ #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD
+ #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDFBNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0
+ #NjU3MjBCNDE1RjY5NkU2OTc0Njk2MTc0NkY3MjEwN0U0QjQ3OTFENkE4RUYwMTlCOT
+ #M2Qzc5RkI3RjJDNTciLCAiZ2VuZXJhdG9yIGciOiAiMDQwMEU1OEE4RkJGMDhCMzhF
+ #MzRBMzY3NkY2RDY5MEJFRDU4QUE0MTE1RkYzMkE1N0VDODcxNzJGQzJBMUZCODlEMD
+ #MyNThDNjQyOUM0NjQ5ODFCMzI4NEI1RkVEQkQxMjQ0QkYyNzQzMjAwODg2ODcwNjVC
+ #OTA3NURENTU4RTE0RUQ2OTkwMUQyMTYyREIxQkEzQTQ5Qzk3RENBN0M5MDJDQjFCOT
+ #ZCQUJFMjFBMzE5NDIxMTRDODYwNjY1QjM1QzQ2QjgyMTNGNkRFMTcxOTRERTU0QzQ0
+ #MTA4M0REMTE2M0Q1OTA3QURBRDg4MjRCQjEzMDdEQ0Y2QTU1QzExQThGMDFEOTc4OU
+ #IifQ==
+
+
+
+
+
+
+
+
+

+B.7.2. Test vector for message from A +

+
+
+  Inputs
+    ADa = b'ADa'
+    ya (big endian): (length: 66 bytes)
+      006367e9c2aeff9f1db19af600cca73343d47cbe446cebbd1ccd783f
+      82755a872da86fd0707eb3767c6114f1803deb62d63bdd1e613f67e6
+      3e8c141ee5310e3ee819
+  Outputs
+    Ya: (length: 133 bytes)
+      0400c2bfd794467f4438277e85a42e101fa4061e1ef6e05f81e5381f
+      30e73b341dd726089cb6a6bbe5a509fad009857488db7130ff768090
+      7312eb724cddb4dcce675b0098ad400fef80e1deb4bc1756c43961ef
+      60b85f2d62ed458454e11616a5d1df1e5809636821a73662f9f12254
+      e6f9950dd01fa8e26a8b20736fb63c63c81094f681
+    Alternative correct value for Ya: (-ya)*g:
+    (length: 133 bytes)
+      0400c2bfd794467f4438277e85a42e101fa4061e1ef6e05f81e5381f
+      30e73b341dd726089cb6a6bbe5a509fad009857488db7130ff768090
+      7312eb724cddb4dcce675b016752bff0107f1e214b43e8a93bc69e10
+      9f47a0d29d12ba7bab1ee9e95a2e20e1a7f69c97de58c99d060eddab
+      19066af22fe0571d9574df8c9049c39c37ef6b097e
+
+
+
+
+
+
+

+B.7.3. Test vector for message from B +

+
+
+  Inputs
+    ADb = b'ADb'
+    yb (big endian): (length: 66 bytes)
+      009227bf8dc741dacc9422f8bf3c0e96fce9587bc562eaafe0dc5f6f
+      82f28594e4a6f98553560c62b75fa4abb198cecbbb86ebd41b0ea025
+      4cde78ac68d39a240ae7
+  Outputs
+    Yb: (length: 133 bytes)
+      0400706ea69b2b7167773248ea6e69a574e9dd2ff8a3d04a6e07f70c
+      709869ca486827d59f9290599d1cf94e1a03fc242e2b1316afe2fa21
+      8bfaeb3e1ffd9f19bf062d01f6b15c9c3651be4c08baf01eec25c818
+      ee12c6edc4620644b1d97cf24f868732d56fe45ce78e302c221c92f4
+      03e0fa3207de8bb41b388d81046a298ed8ddac9b2a
+    Alternative correct value for Yb: (-yb)*g:
+    (length: 133 bytes)
+      0400706ea69b2b7167773248ea6e69a574e9dd2ff8a3d04a6e07f70c
+      709869ca486827d59f9290599d1cf94e1a03fc242e2b1316afe2fa21
+      8bfaeb3e1ffd9f19bf062d00094ea363c9ae41b3f7450fe113da37e7
+      11ed39123b9df9bb4e26830db07978cd2a901ba31871cfd3dde36d0b
+      fc1f05cdf821744be4c7727efb95d67127225364d5
+
+
+
+
+
+
+

+B.7.4. Test vector for secret points K +

+
+
+    scalar_mult_vfy(ya,Yb): (length: 66 bytes)
+      018e0e7e9ade74917c11c0f6b52f95ed871eab235437cbee8b5c2509
+      516e787a80e825ed5d539fa6a0ec32c48fa8fabe85809d000d0cfd30
+      832c23d477c991bea8e5
+    scalar_mult_vfy(yb,Ya): (length: 66 bytes)
+      018e0e7e9ade74917c11c0f6b52f95ed871eab235437cbee8b5c2509
+      516e787a80e825ed5d539fa6a0ec32c48fa8fabe85809d000d0cfd30
+      832c23d477c991bea8e5
+
+
+
+
+
+
+

+B.7.5. Test vector for ISK calculation initiator/responder +

+
+
+    transcript_ir(Ya,ADa,Yb,ADb): (length: 278 bytes)
+      85010400c2bfd794467f4438277e85a42e101fa4061e1ef6e05f81e5
+      381f30e73b341dd726089cb6a6bbe5a509fad009857488db7130ff76
+      80907312eb724cddb4dcce675b0098ad400fef80e1deb4bc1756c439
+      61ef60b85f2d62ed458454e11616a5d1df1e5809636821a73662f9f1
+      2254e6f9950dd01fa8e26a8b20736fb63c63c81094f6810341446185
+      010400706ea69b2b7167773248ea6e69a574e9dd2ff8a3d04a6e07f7
+      0c709869ca486827d59f9290599d1cf94e1a03fc242e2b1316afe2fa
+      218bfaeb3e1ffd9f19bf062d01f6b15c9c3651be4c08baf01eec25c8
+      18ee12c6edc4620644b1d97cf24f868732d56fe45ce78e302c221c92
+      f403e0fa3207de8bb41b388d81046a298ed8ddac9b2a03414462
+    DSI = G.DSI_ISK, b'CPaceP521_XMD:SHA-512_SSWU_NU__ISK':
+    (length: 34 bytes)
+      4350616365503532315f584d443a5348412d3531325f535357555f4e
+      555f5f49534b
+    lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb):
+    (length: 397 bytes)
+      224350616365503532315f584d443a5348412d3531325f535357555f
+      4e555f5f49534b107e4b4791d6a8ef019b936c79fb7f2c5742018e0e
+      7e9ade74917c11c0f6b52f95ed871eab235437cbee8b5c2509516e78
+      7a80e825ed5d539fa6a0ec32c48fa8fabe85809d000d0cfd30832c23
+      d477c991bea8e585010400c2bfd794467f4438277e85a42e101fa406
+      1e1ef6e05f81e5381f30e73b341dd726089cb6a6bbe5a509fad00985
+      7488db7130ff7680907312eb724cddb4dcce675b0098ad400fef80e1
+      deb4bc1756c43961ef60b85f2d62ed458454e11616a5d1df1e580963
+      6821a73662f9f12254e6f9950dd01fa8e26a8b20736fb63c63c81094
+      f6810341446185010400706ea69b2b7167773248ea6e69a574e9dd2f
+      f8a3d04a6e07f70c709869ca486827d59f9290599d1cf94e1a03fc24
+      2e2b1316afe2fa218bfaeb3e1ffd9f19bf062d01f6b15c9c3651be4c
+      08baf01eec25c818ee12c6edc4620644b1d97cf24f868732d56fe45c
+      e78e302c221c92f403e0fa3207de8bb41b388d81046a298ed8ddac9b
+      2a03414462
+    ISK result: (length: 64 bytes)
+      1669a0a29726adc7eea2510d6f7e004a135fa63ac3c9f9e6ce53cba5
+      d5e3781aced515956041e43358409a13ef90ddc3c36fd8d7d81424c8
+      e94592e21854260a
+
+
+
+
+
+
+

+B.7.6. Test vector for ISK calculation parallel execution +

+
+
+    transcript_oc(Ya,ADa,Yb,ADb): (length: 280 bytes)
+      6f6385010400c2bfd794467f4438277e85a42e101fa4061e1ef6e05f
+      81e5381f30e73b341dd726089cb6a6bbe5a509fad009857488db7130
+      ff7680907312eb724cddb4dcce675b0098ad400fef80e1deb4bc1756
+      c43961ef60b85f2d62ed458454e11616a5d1df1e5809636821a73662
+      f9f12254e6f9950dd01fa8e26a8b20736fb63c63c81094f681034144
+      6185010400706ea69b2b7167773248ea6e69a574e9dd2ff8a3d04a6e
+      07f70c709869ca486827d59f9290599d1cf94e1a03fc242e2b1316af
+      e2fa218bfaeb3e1ffd9f19bf062d01f6b15c9c3651be4c08baf01eec
+      25c818ee12c6edc4620644b1d97cf24f868732d56fe45ce78e302c22
+      1c92f403e0fa3207de8bb41b388d81046a298ed8ddac9b2a03414462
+    DSI = G.DSI_ISK, b'CPaceP521_XMD:SHA-512_SSWU_NU__ISK':
+    (length: 34 bytes)
+      4350616365503532315f584d443a5348412d3531325f535357555f4e
+      555f5f49534b
+    lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb):
+    (length: 399 bytes)
+      224350616365503532315f584d443a5348412d3531325f535357555f
+      4e555f5f49534b107e4b4791d6a8ef019b936c79fb7f2c5742018e0e
+      7e9ade74917c11c0f6b52f95ed871eab235437cbee8b5c2509516e78
+      7a80e825ed5d539fa6a0ec32c48fa8fabe85809d000d0cfd30832c23
+      d477c991bea8e56f6385010400c2bfd794467f4438277e85a42e101f
+      a4061e1ef6e05f81e5381f30e73b341dd726089cb6a6bbe5a509fad0
+      09857488db7130ff7680907312eb724cddb4dcce675b0098ad400fef
+      80e1deb4bc1756c43961ef60b85f2d62ed458454e11616a5d1df1e58
+      09636821a73662f9f12254e6f9950dd01fa8e26a8b20736fb63c63c8
+      1094f6810341446185010400706ea69b2b7167773248ea6e69a574e9
+      dd2ff8a3d04a6e07f70c709869ca486827d59f9290599d1cf94e1a03
+      fc242e2b1316afe2fa218bfaeb3e1ffd9f19bf062d01f6b15c9c3651
+      be4c08baf01eec25c818ee12c6edc4620644b1d97cf24f868732d56f
+      e45ce78e302c221c92f403e0fa3207de8bb41b388d81046a298ed8dd
+      ac9b2a03414462
+    ISK result: (length: 64 bytes)
+      f2f3bd8cd442a4e16659b47a7b7a84f29be75893ed2e5f772d7a3c8b
+      779eb0df937a4ec50a4f1ff01ebbaa97d80e090ea69b00a95200ed25
+      8e48c6f7e9d8fbc2
+
+
+
+
+
+
+

+B.7.7. Test vector for optional output of session id +

+
+
+    H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      56cc3cd8be77cdc84c0d1906de1ffc8ef7cbb326a3f05267b6e8c634
+      4e2781eb20ef725e84cb1bb45927435051b4e0fae78e975bf15099f9
+      e38d755413eee2fd
+    H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)):
+    (length: 64 bytes)
+      a46c7189ba6a36c4447741e057da39c885b7d59e08bd2df1852a5271
+      f2a8a2e9b187ccd07325a3eede646adee0c06fe58da77f74177896b2
+      1053c5d107de006d
+
+
+
+
+
+
+

+B.7.8. Corresponding C programming language initializers +

+
+
+const unsigned char tc_PRS[] = {
+ 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64,
+};
+const unsigned char tc_CI[] = {
+ 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64,
+ 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74,
+ 0x6f,0x72,
+};
+const unsigned char tc_sid[] = {
+ 0x7e,0x4b,0x47,0x91,0xd6,0xa8,0xef,0x01,0x9b,0x93,0x6c,0x79,
+ 0xfb,0x7f,0x2c,0x57,
+};
+const unsigned char tc_g[] = {
+ 0x04,0x00,0xe5,0x8a,0x8f,0xbf,0x08,0xb3,0x8e,0x34,0xa3,0x67,
+ 0x6f,0x6d,0x69,0x0b,0xed,0x58,0xaa,0x41,0x15,0xff,0x32,0xa5,
+ 0x7e,0xc8,0x71,0x72,0xfc,0x2a,0x1f,0xb8,0x9d,0x03,0x25,0x8c,
+ 0x64,0x29,0xc4,0x64,0x98,0x1b,0x32,0x84,0xb5,0xfe,0xdb,0xd1,
+ 0x24,0x4b,0xf2,0x74,0x32,0x00,0x88,0x68,0x70,0x65,0xb9,0x07,
+ 0x5d,0xd5,0x58,0xe1,0x4e,0xd6,0x99,0x01,0xd2,0x16,0x2d,0xb1,
+ 0xba,0x3a,0x49,0xc9,0x7d,0xca,0x7c,0x90,0x2c,0xb1,0xb9,0x6b,
+ 0xab,0xe2,0x1a,0x31,0x94,0x21,0x14,0xc8,0x60,0x66,0x5b,0x35,
+ 0xc4,0x6b,0x82,0x13,0xf6,0xde,0x17,0x19,0x4d,0xe5,0x4c,0x44,
+ 0x10,0x83,0xdd,0x11,0x63,0xd5,0x90,0x7a,0xda,0xd8,0x82,0x4b,
+ 0xb1,0x30,0x7d,0xcf,0x6a,0x55,0xc1,0x1a,0x8f,0x01,0xd9,0x78,
+ 0x9b,
+};
+const unsigned char tc_ya[] = {
+ 0x00,0x63,0x67,0xe9,0xc2,0xae,0xff,0x9f,0x1d,0xb1,0x9a,0xf6,
+ 0x00,0xcc,0xa7,0x33,0x43,0xd4,0x7c,0xbe,0x44,0x6c,0xeb,0xbd,
+ 0x1c,0xcd,0x78,0x3f,0x82,0x75,0x5a,0x87,0x2d,0xa8,0x6f,0xd0,
+ 0x70,0x7e,0xb3,0x76,0x7c,0x61,0x14,0xf1,0x80,0x3d,0xeb,0x62,
+ 0xd6,0x3b,0xdd,0x1e,0x61,0x3f,0x67,0xe6,0x3e,0x8c,0x14,0x1e,
+ 0xe5,0x31,0x0e,0x3e,0xe8,0x19,
+};
+const unsigned char tc_ADa[] = {
+ 0x41,0x44,0x61,
+};
+const unsigned char tc_Ya[] = {
+ 0x04,0x00,0xc2,0xbf,0xd7,0x94,0x46,0x7f,0x44,0x38,0x27,0x7e,
+ 0x85,0xa4,0x2e,0x10,0x1f,0xa4,0x06,0x1e,0x1e,0xf6,0xe0,0x5f,
+ 0x81,0xe5,0x38,0x1f,0x30,0xe7,0x3b,0x34,0x1d,0xd7,0x26,0x08,
+ 0x9c,0xb6,0xa6,0xbb,0xe5,0xa5,0x09,0xfa,0xd0,0x09,0x85,0x74,
+ 0x88,0xdb,0x71,0x30,0xff,0x76,0x80,0x90,0x73,0x12,0xeb,0x72,
+ 0x4c,0xdd,0xb4,0xdc,0xce,0x67,0x5b,0x00,0x98,0xad,0x40,0x0f,
+ 0xef,0x80,0xe1,0xde,0xb4,0xbc,0x17,0x56,0xc4,0x39,0x61,0xef,
+ 0x60,0xb8,0x5f,0x2d,0x62,0xed,0x45,0x84,0x54,0xe1,0x16,0x16,
+ 0xa5,0xd1,0xdf,0x1e,0x58,0x09,0x63,0x68,0x21,0xa7,0x36,0x62,
+ 0xf9,0xf1,0x22,0x54,0xe6,0xf9,0x95,0x0d,0xd0,0x1f,0xa8,0xe2,
+ 0x6a,0x8b,0x20,0x73,0x6f,0xb6,0x3c,0x63,0xc8,0x10,0x94,0xf6,
+ 0x81,
+};
+const unsigned char tc_yb[] = {
+ 0x00,0x92,0x27,0xbf,0x8d,0xc7,0x41,0xda,0xcc,0x94,0x22,0xf8,
+ 0xbf,0x3c,0x0e,0x96,0xfc,0xe9,0x58,0x7b,0xc5,0x62,0xea,0xaf,
+ 0xe0,0xdc,0x5f,0x6f,0x82,0xf2,0x85,0x94,0xe4,0xa6,0xf9,0x85,
+ 0x53,0x56,0x0c,0x62,0xb7,0x5f,0xa4,0xab,0xb1,0x98,0xce,0xcb,
+ 0xbb,0x86,0xeb,0xd4,0x1b,0x0e,0xa0,0x25,0x4c,0xde,0x78,0xac,
+ 0x68,0xd3,0x9a,0x24,0x0a,0xe7,
+};
+const unsigned char tc_ADb[] = {
+ 0x41,0x44,0x62,
+};
+const unsigned char tc_Yb[] = {
+ 0x04,0x00,0x70,0x6e,0xa6,0x9b,0x2b,0x71,0x67,0x77,0x32,0x48,
+ 0xea,0x6e,0x69,0xa5,0x74,0xe9,0xdd,0x2f,0xf8,0xa3,0xd0,0x4a,
+ 0x6e,0x07,0xf7,0x0c,0x70,0x98,0x69,0xca,0x48,0x68,0x27,0xd5,
+ 0x9f,0x92,0x90,0x59,0x9d,0x1c,0xf9,0x4e,0x1a,0x03,0xfc,0x24,
+ 0x2e,0x2b,0x13,0x16,0xaf,0xe2,0xfa,0x21,0x8b,0xfa,0xeb,0x3e,
+ 0x1f,0xfd,0x9f,0x19,0xbf,0x06,0x2d,0x01,0xf6,0xb1,0x5c,0x9c,
+ 0x36,0x51,0xbe,0x4c,0x08,0xba,0xf0,0x1e,0xec,0x25,0xc8,0x18,
+ 0xee,0x12,0xc6,0xed,0xc4,0x62,0x06,0x44,0xb1,0xd9,0x7c,0xf2,
+ 0x4f,0x86,0x87,0x32,0xd5,0x6f,0xe4,0x5c,0xe7,0x8e,0x30,0x2c,
+ 0x22,0x1c,0x92,0xf4,0x03,0xe0,0xfa,0x32,0x07,0xde,0x8b,0xb4,
+ 0x1b,0x38,0x8d,0x81,0x04,0x6a,0x29,0x8e,0xd8,0xdd,0xac,0x9b,
+ 0x2a,
+};
+const unsigned char tc_K[] = {
+ 0x01,0x8e,0x0e,0x7e,0x9a,0xde,0x74,0x91,0x7c,0x11,0xc0,0xf6,
+ 0xb5,0x2f,0x95,0xed,0x87,0x1e,0xab,0x23,0x54,0x37,0xcb,0xee,
+ 0x8b,0x5c,0x25,0x09,0x51,0x6e,0x78,0x7a,0x80,0xe8,0x25,0xed,
+ 0x5d,0x53,0x9f,0xa6,0xa0,0xec,0x32,0xc4,0x8f,0xa8,0xfa,0xbe,
+ 0x85,0x80,0x9d,0x00,0x0d,0x0c,0xfd,0x30,0x83,0x2c,0x23,0xd4,
+ 0x77,0xc9,0x91,0xbe,0xa8,0xe5,
+};
+const unsigned char tc_ISK_IR[] = {
+ 0x16,0x69,0xa0,0xa2,0x97,0x26,0xad,0xc7,0xee,0xa2,0x51,0x0d,
+ 0x6f,0x7e,0x00,0x4a,0x13,0x5f,0xa6,0x3a,0xc3,0xc9,0xf9,0xe6,
+ 0xce,0x53,0xcb,0xa5,0xd5,0xe3,0x78,0x1a,0xce,0xd5,0x15,0x95,
+ 0x60,0x41,0xe4,0x33,0x58,0x40,0x9a,0x13,0xef,0x90,0xdd,0xc3,
+ 0xc3,0x6f,0xd8,0xd7,0xd8,0x14,0x24,0xc8,0xe9,0x45,0x92,0xe2,
+ 0x18,0x54,0x26,0x0a,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0xf2,0xf3,0xbd,0x8c,0xd4,0x42,0xa4,0xe1,0x66,0x59,0xb4,0x7a,
+ 0x7b,0x7a,0x84,0xf2,0x9b,0xe7,0x58,0x93,0xed,0x2e,0x5f,0x77,
+ 0x2d,0x7a,0x3c,0x8b,0x77,0x9e,0xb0,0xdf,0x93,0x7a,0x4e,0xc5,
+ 0x0a,0x4f,0x1f,0xf0,0x1e,0xbb,0xaa,0x97,0xd8,0x0e,0x09,0x0e,
+ 0xa6,0x9b,0x00,0xa9,0x52,0x00,0xed,0x25,0x8e,0x48,0xc6,0xf7,
+ 0xe9,0xd8,0xfb,0xc2,
+};
+const unsigned char tc_ISK_SY[] = {
+ 0xf2,0xf3,0xbd,0x8c,0xd4,0x42,0xa4,0xe1,0x66,0x59,0xb4,0x7a,
+ 0x7b,0x7a,0x84,0xf2,0x9b,0xe7,0x58,0x93,0xed,0x2e,0x5f,0x77,
+ 0x2d,0x7a,0x3c,0x8b,0x77,0x9e,0xb0,0xdf,0x93,0x7a,0x4e,0xc5,
+ 0x0a,0x4f,0x1f,0xf0,0x1e,0xbb,0xaa,0x97,0xd8,0x0e,0x09,0x0e,
+ 0xa6,0x9b,0x00,0xa9,0x52,0x00,0xed,0x25,0x8e,0x48,0xc6,0xf7,
+ 0xe9,0xd8,0xfb,0xc2,
+};
+const unsigned char tc_sid_out_ir[] = {
+ 0x56,0xcc,0x3c,0xd8,0xbe,0x77,0xcd,0xc8,0x4c,0x0d,0x19,0x06,
+ 0xde,0x1f,0xfc,0x8e,0xf7,0xcb,0xb3,0x26,0xa3,0xf0,0x52,0x67,
+ 0xb6,0xe8,0xc6,0x34,0x4e,0x27,0x81,0xeb,0x20,0xef,0x72,0x5e,
+ 0x84,0xcb,0x1b,0xb4,0x59,0x27,0x43,0x50,0x51,0xb4,0xe0,0xfa,
+ 0xe7,0x8e,0x97,0x5b,0xf1,0x50,0x99,0xf9,0xe3,0x8d,0x75,0x54,
+ 0x13,0xee,0xe2,0xfd,
+};
+const unsigned char tc_sid_out_oc[] = {
+ 0xa4,0x6c,0x71,0x89,0xba,0x6a,0x36,0xc4,0x44,0x77,0x41,0xe0,
+ 0x57,0xda,0x39,0xc8,0x85,0xb7,0xd5,0x9e,0x08,0xbd,0x2d,0xf1,
+ 0x85,0x2a,0x52,0x71,0xf2,0xa8,0xa2,0xe9,0xb1,0x87,0xcc,0xd0,
+ 0x73,0x25,0xa3,0xee,0xde,0x64,0x6a,0xde,0xe0,0xc0,0x6f,0xe5,
+ 0x8d,0xa7,0x7f,0x74,0x17,0x78,0x96,0xb2,0x10,0x53,0xc5,0xd1,
+ 0x07,0xde,0x00,0x6d,
+};
+
+
+
+
+
+
+

+B.7.9. Testvectors as JSON file encoded as BASE64 +

+
+
+ #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT
+ #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI3
+ #RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJnIjogIjA0MDBFNThBOE
+ #ZCRjA4QjM4RTM0QTM2NzZGNkQ2OTBCRUQ1OEFBNDExNUZGMzJBNTdFQzg3MTcyRkMy
+ #QTFGQjg5RDAzMjU4QzY0MjlDNDY0OTgxQjMyODRCNUZFREJEMTI0NEJGMjc0MzIwMD
+ #g4Njg3MDY1QjkwNzVERDU1OEUxNEVENjk5MDFEMjE2MkRCMUJBM0E0OUM5N0RDQTdD
+ #OTAyQ0IxQjk2QkFCRTIxQTMxOTQyMTE0Qzg2MDY2NUIzNUM0NkI4MjEzRjZERTE3MT
+ #k0REU1NEM0NDEwODNERDExNjNENTkwN0FEQUQ4ODI0QkIxMzA3RENGNkE1NUMxMUE4
+ #RjAxRDk3ODlCIiwgInlhIjogIjAwNjM2N0U5QzJBRUZGOUYxREIxOUFGNjAwQ0NBNz
+ #MzNDNENDdDQkU0NDZDRUJCRDFDQ0Q3ODNGODI3NTVBODcyREE4NkZEMDcwN0VCMzc2
+ #N0M2MTE0RjE4MDNERUI2MkQ2M0JERDFFNjEzRjY3RTYzRThDMTQxRUU1MzEwRTNFRT
+ #gxOSIsICJBRGEiOiAiNDE0NDYxIiwgIllhIjogIjA0MDBDMkJGRDc5NDQ2N0Y0NDM4
+ #Mjc3RTg1QTQyRTEwMUZBNDA2MUUxRUY2RTA1RjgxRTUzODFGMzBFNzNCMzQxREQ3Mj
+ #YwODlDQjZBNkJCRTVBNTA5RkFEMDA5ODU3NDg4REI3MTMwRkY3NjgwOTA3MzEyRUI3
+ #MjRDRERCNERDQ0U2NzVCMDA5OEFENDAwRkVGODBFMURFQjRCQzE3NTZDNDM5NjFFRj
+ #YwQjg1RjJENjJFRDQ1ODQ1NEUxMTYxNkE1RDFERjFFNTgwOTYzNjgyMUE3MzY2MkY5
+ #RjEyMjU0RTZGOTk1MEREMDFGQThFMjZBOEIyMDczNkZCNjNDNjNDODEwOTRGNjgxIi
+ #wgInliIjogIjAwOTIyN0JGOERDNzQxREFDQzk0MjJGOEJGM0MwRTk2RkNFOTU4N0JD
+ #NTYyRUFBRkUwREM1RjZGODJGMjg1OTRFNEE2Rjk4NTUzNTYwQzYyQjc1RkE0QUJCMT
+ #k4Q0VDQkJCODZFQkQ0MUIwRUEwMjU0Q0RFNzhBQzY4RDM5QTI0MEFFNyIsICJBRGIi
+ #OiAiNDE0NDYyIiwgIlliIjogIjA0MDA3MDZFQTY5QjJCNzE2Nzc3MzI0OEVBNkU2OU
+ #E1NzRFOUREMkZGOEEzRDA0QTZFMDdGNzBDNzA5ODY5Q0E0ODY4MjdENTlGOTI5MDU5
+ #OUQxQ0Y5NEUxQTAzRkMyNDJFMkIxMzE2QUZFMkZBMjE4QkZBRUIzRTFGRkQ5RjE5Qk
+ #YwNjJEMDFGNkIxNUM5QzM2NTFCRTRDMDhCQUYwMUVFQzI1QzgxOEVFMTJDNkVEQzQ2
+ #MjA2NDRCMUQ5N0NGMjRGODY4NzMyRDU2RkU0NUNFNzhFMzAyQzIyMUM5MkY0MDNFME
+ #ZBMzIwN0RFOEJCNDFCMzg4RDgxMDQ2QTI5OEVEOEREQUM5QjJBIiwgIksiOiAiMDE4
+ #RTBFN0U5QURFNzQ5MTdDMTFDMEY2QjUyRjk1RUQ4NzFFQUIyMzU0MzdDQkVFOEI1Qz
+ #I1MDk1MTZFNzg3QTgwRTgyNUVENUQ1MzlGQTZBMEVDMzJDNDhGQThGQUJFODU4MDlE
+ #MDAwRDBDRkQzMDgzMkMyM0Q0NzdDOTkxQkVBOEU1IiwgIklTS19JUiI6ICIxNjY5QT
+ #BBMjk3MjZBREM3RUVBMjUxMEQ2RjdFMDA0QTEzNUZBNjNBQzNDOUY5RTZDRTUzQ0JB
+ #NUQ1RTM3ODFBQ0VENTE1OTU2MDQxRTQzMzU4NDA5QTEzRUY5MEREQzNDMzZGRDhEN0
+ #Q4MTQyNEM4RTk0NTkyRTIxODU0MjYwQSIsICJJU0tfU1kiOiAiRjJGM0JEOENENDQy
+ #QTRFMTY2NTlCNDdBN0I3QTg0RjI5QkU3NTg5M0VEMkU1Rjc3MkQ3QTNDOEI3NzlFQj
+ #BERjkzN0E0RUM1MEE0RjFGRjAxRUJCQUE5N0Q4MEUwOTBFQTY5QjAwQTk1MjAwRUQy
+ #NThFNDhDNkY3RTlEOEZCQzIiLCAic2lkX291dHB1dF9pciI6ICI1NkNDM0NEOEJFNz
+ #dDREM4NEMwRDE5MDZERTFGRkM4RUY3Q0JCMzI2QTNGMDUyNjdCNkU4QzYzNDRFMjc4
+ #MUVCMjBFRjcyNUU4NENCMUJCNDU5Mjc0MzUwNTFCNEUwRkFFNzhFOTc1QkYxNTA5OU
+ #Y5RTM4RDc1NTQxM0VFRTJGRCIsICJzaWRfb3V0cHV0X29jIjogIkE0NkM3MTg5QkE2
+ #QTM2QzQ0NDc3NDFFMDU3REEzOUM4ODVCN0Q1OUUwOEJEMkRGMTg1MkE1MjcxRjJBOE
+ #EyRTlCMTg3Q0NEMDczMjVBM0VFREU2NDZBREVFMEMwNkZFNThEQTc3Rjc0MTc3ODk2
+ #QjIxMDUzQzVEMTA3REUwMDZEIn0=
+
+
+
+
+
+
+

+B.7.10. Test case for scalar_mult_vfy with correct inputs +

+
+
+    s: (length: 66 bytes)
+      0182dd7925f1753419e4bf83429763acd37d64000cd5a175edf53a15
+      87dd986bc95acc1506991702b6ba1a9ee2458fee8efc00198cf0088c
+      480965ef65ff2048b856
+    X: (length: 133 bytes)
+      0400dc5078b24c4af1620cc10fbecc6cd8cf1cab0b011efb73c782f2
+      26dc21c7ca7eb406be74a69ecba5b4a87c07cfc6e687b4beca9a6eda
+      c95940a3b4120573b26a80005e697833b0ba285fce7b3f1f25243008
+      860b8f1de710a0dcc05b0d20341efe90eb2bcca26797c2d85ae6ca74
+      c00696cb1b13e40bda15b27964d7670576647bfab9
+    G.scalar_mult(s,X) (full coordinates): (length: 133 bytes)
+      040122f88ce73ec5aa2d1c8c5d04148760c3d97ba87daa10d8cb8bb7
+      c73cf6e951fc922721bf1437995cfb13e132a78beb86389e60d3517c
+      df6d99a8a2d6db19ef27bd0055af9e8ddcf337ce0a7c22a9c8099bc4
+      a44faeded1eb72effd26e4f322217b67d60b944b267b3df5046078fd
+      577f1785728f49b241fd5e8c83223a994a2d219281
+    G.scalar_mult_vfy(s,X) (only X-coordinate):
+    (length: 66 bytes)
+      0122f88ce73ec5aa2d1c8c5d04148760c3d97ba87daa10d8cb8bb7c7
+      3cf6e951fc922721bf1437995cfb13e132a78beb86389e60d3517cdf
+      6d99a8a2d6db19ef27bd
+
+
+
+
+
+
+

+B.7.11. Invalid inputs for scalar_mult_vfy +

+

For these test cases scalar_mult_vfy(y,.) MUST return the representation of the neutral element G.I. When including Y_i1 or Y_i2 in messages of A or B the protocol MUST abort.

+
+
+    s: (length: 66 bytes)
+      0182dd7925f1753419e4bf83429763acd37d64000cd5a175edf53a15
+      87dd986bc95acc1506991702b6ba1a9ee2458fee8efc00198cf0088c
+      480965ef65ff2048b856
+    Y_i1: (length: 133 bytes)
+      0400dc5078b24c4af1620cc10fbecc6cd8cf1cab0b011efb73c782f2
+      26dc21c7ca7eb406be74a69ecba5b4a87c07cfc6e687b4beca9a6eda
+      c95940a3b4120573b26a80005e697833b0ba285fce7b3f1f25243008
+      860b8f1de710a0dcc05b0d20341efe90eb2bcca26797c2d85ae6ca74
+      c00696cb1b13e40bda15b27964d7670576647bfaf9
+    Y_i2: (length: 1 bytes)
+      00
+    G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I
+
+
+
+
+
+B.7.11.1. Testvectors as JSON file encoded as BASE64 +
+
+
+ #eyJWYWxpZCI6IHsicyI6ICIwMTgyREQ3OTI1RjE3NTM0MTlFNEJGODM0Mjk3NjNBQ0
+ #QzN0Q2NDAwMENENUExNzVFREY1M0ExNTg3REQ5ODZCQzk1QUNDMTUwNjk5MTcwMkI2
+ #QkExQTlFRTI0NThGRUU4RUZDMDAxOThDRjAwODhDNDgwOTY1RUY2NUZGMjA0OEI4NT
+ #YiLCAiWCI6ICIwNDAwREM1MDc4QjI0QzRBRjE2MjBDQzEwRkJFQ0M2Q0Q4Q0YxQ0FC
+ #MEIwMTFFRkI3M0M3ODJGMjI2REMyMUM3Q0E3RUI0MDZCRTc0QTY5RUNCQTVCNEE4N0
+ #MwN0NGQzZFNjg3QjRCRUNBOUE2RURBQzk1OTQwQTNCNDEyMDU3M0IyNkE4MDAwNUU2
+ #OTc4MzNCMEJBMjg1RkNFN0IzRjFGMjUyNDMwMDg4NjBCOEYxREU3MTBBMERDQzA1Qj
+ #BEMjAzNDFFRkU5MEVCMkJDQ0EyNjc5N0MyRDg1QUU2Q0E3NEMwMDY5NkNCMUIxM0U0
+ #MEJEQTE1QjI3OTY0RDc2NzA1NzY2NDdCRkFCOSIsICJHLnNjYWxhcl9tdWx0KHMsWC
+ #kgKGZ1bGwgY29vcmRpbmF0ZXMpIjogIjA0MDEyMkY4OENFNzNFQzVBQTJEMUM4QzVE
+ #MDQxNDg3NjBDM0Q5N0JBODdEQUExMEQ4Q0I4QkI3QzczQ0Y2RTk1MUZDOTIyNzIxQk
+ #YxNDM3OTk1Q0ZCMTNFMTMyQTc4QkVCODYzODlFNjBEMzUxN0NERjZEOTlBOEEyRDZE
+ #QjE5RUYyN0JEMDA1NUFGOUU4RERDRjMzN0NFMEE3QzIyQTlDODA5OUJDNEE0NEZBRU
+ #RFRDFFQjcyRUZGRDI2RTRGMzIyMjE3QjY3RDYwQjk0NEIyNjdCM0RGNTA0NjA3OEZE
+ #NTc3RjE3ODU3MjhGNDlCMjQxRkQ1RThDODMyMjNBOTk0QTJEMjE5MjgxIiwgIkcuc2
+ #NhbGFyX211bHRfdmZ5KHMsWCkgKG9ubHkgWC1jb29yZGluYXRlKSI6ICIwMTIyRjg4
+ #Q0U3M0VDNUFBMkQxQzhDNUQwNDE0ODc2MEMzRDk3QkE4N0RBQTEwRDhDQjhCQjdDNz
+ #NDRjZFOTUxRkM5MjI3MjFCRjE0Mzc5OTVDRkIxM0UxMzJBNzhCRUI4NjM4OUU2MEQz
+ #NTE3Q0RGNkQ5OUE4QTJENkRCMTlFRjI3QkQifSwgIkludmFsaWQgWTEiOiAiMDQwME
+ #RDNTA3OEIyNEM0QUYxNjIwQ0MxMEZCRUNDNkNEOENGMUNBQjBCMDExRUZCNzNDNzgy
+ #RjIyNkRDMjFDN0NBN0VCNDA2QkU3NEE2OUVDQkE1QjRBODdDMDdDRkM2RTY4N0I0Qk
+ #VDQTlBNkVEQUM5NTk0MEEzQjQxMjA1NzNCMjZBODAwMDVFNjk3ODMzQjBCQTI4NUZD
+ #RTdCM0YxRjI1MjQzMDA4ODYwQjhGMURFNzEwQTBEQ0MwNUIwRDIwMzQxRUZFOTBFQj
+ #JCQ0NBMjY3OTdDMkQ4NUFFNkNBNzRDMDA2OTZDQjFCMTNFNDBCREExNUIyNzk2NEQ3
+ #NjcwNTc2NjQ3QkZBRjkiLCAiSW52YWxpZCBZMiI6ICIwMCJ9
+
+
+
+
+
+
+
+
+
+
+
+
+

+Authors' Addresses +

+
+
Michel Abdalla
+
Nexus - San Francisco
+ +
+
+
Bjoern Haase
+
Endress + Hauser Liquid Analysis - Gerlingen
+ +
+
+
Julia Hesse
+
IBM Research Europe - Zurich
+ +
+
+
+ + + diff --git a/draft-irtf-cfrg-cpace-13/draft-irtf-cfrg-cpace.txt b/draft-irtf-cfrg-cpace-13/draft-irtf-cfrg-cpace.txt new file mode 100644 index 0000000..8251f8e --- /dev/null +++ b/draft-irtf-cfrg-cpace-13/draft-irtf-cfrg-cpace.txt @@ -0,0 +1,4152 @@ + + + + +CFRG M. Abdalla +Internet-Draft Nexus - San Francisco +Intended status: Informational B. Haase +Expires: 18 April 2025 Endress + Hauser Liquid Analysis - Gerlingen + J. Hesse + IBM Research Europe - Zurich + 15 October 2024 + + + CPace, a balanced composable PAKE + draft-irtf-cfrg-cpace-latest + +Abstract + + This document describes CPace which is a protocol that allows two + parties that share a low-entropy secret (password) to derive a strong + shared key without disclosing the secret to offline dictionary + attacks. The CPace protocol was tailored for constrained devices and + can be used on groups of prime- and non-prime order. + +Discussion Venues + + This note is to be removed before publishing as an RFC. + + Discussion of this document takes place on the Crypto Forum Research + Group mailing list (cfrg@ietf.org), which is archived at + https://mailarchive.ietf.org/arch/search/?email_list=cfrg. + + Source for this draft and an issue tracker can be found at + https://github.com/cfrg/draft-irtf-cfrg-cpace. + +Status of This Memo + + This Internet-Draft is submitted in full conformance with the + provisions of BCP 78 and BCP 79. + + Internet-Drafts are working documents of the Internet Engineering + Task Force (IETF). Note that other groups may also distribute + working documents as Internet-Drafts. The list of current Internet- + Drafts is at https://datatracker.ietf.org/drafts/current/. + + Internet-Drafts are draft documents valid for a maximum of six months + and may be updated, replaced, or obsoleted by other documents at any + time. It is inappropriate to use Internet-Drafts as reference + material or to cite them other than as "work in progress." + + This Internet-Draft will expire on 18 April 2025. + +Copyright Notice + + Copyright (c) 2024 IETF Trust and the persons identified as the + document authors. All rights reserved. + + This document is subject to BCP 78 and the IETF Trust's Legal + Provisions Relating to IETF Documents (https://trustee.ietf.org/ + license-info) in effect on the date of publication of this document. + Please review these documents carefully, as they describe your rights + and restrictions with respect to this document. + +Table of Contents + + 1. Introduction + 1.1. Outline of this document + 2. Requirements Notation + 3. High-level application perspective + 3.1. Optional CPace inputs + 3.2. Optional CPace outputs + 3.3. Responsibilities of the application layer + 4. CPace cipher suites + 5. Definitions and notation + 5.1. Hash function H + 5.2. Group environment G + 5.3. Notation for string operations + 5.4. Notation for group operations + 6. The CPace protocol + 6.1. Protocol flow + 6.2. CPace protocol instructions + 7. Implementation of recommended CPace cipher suites + 7.1. Common function for computing generators + 7.2. CPace group objects G_X25519 and G_X448 for + single-coordinate Ladders on Montgomery curves + 7.2.1. Verification tests + 7.3. CPace group objects G_Ristretto255 and G_Decaf448 for + prime-order group abstractions + 7.3.1. Verification tests + 7.4. CPace group objects for curves in Short-Weierstrass + representation + 7.4.1. Curves and associated functions + 7.4.2. Suitable encode_to_curve methods + 7.4.3. Definition of the group environment G for + Short-Weierstrass curves + 7.4.4. Verification tests + 8. Implementation verification + 9. Security Considerations + 9.1. Party identifiers and relay attacks + 9.2. Hashing protocol transcripts + 9.3. Key derivation + 9.4. Key confirmation + 9.5. Integrating CPace in higher-level protocols such as TLS1.3 + 9.6. Calculating a session identifier alongside with the CPace + run + 9.7. Sampling of scalars + 9.8. Preconditions for using the simplified CPace specification + from Section 7.2 + 9.9. Nonce values + 9.10. Side channel attacks + 9.11. Quantum computers + 10. IANA Considerations + 11. Reference implementation and test vector generation + 12. Acknowledgements + 13. References + 13.1. Normative References + 13.2. Informative References + Appendix A. CPace function definitions + A.1. Definition and test vectors for string utility functions + A.1.1. prepend_len function + A.1.2. prepend_len test vectors + A.1.3. lv_cat function + A.1.4. Testvector for lv_cat() + A.2. Definition of generator_string function. + A.3. Definitions and test vector ordered concatenation + A.3.1. Definitions for lexiographical ordering + A.3.2. Definitions for ordered concatenation + A.3.3. Test vectors ordered concatenation + A.3.4. Definitions for transcript_ir function + A.3.5. Test vectors transcript_ir function + A.3.6. Definitions for transcript_oc function + A.3.7. Test vectors for transcript_oc function + A.4. Decoding and Encoding functions according to RFC7748 + A.5. Elligator 2 reference implementation + Appendix B. Test vectors + B.1. Test vector for CPace using group X25519 and hash SHA-512 + B.1.1. Test vectors for calculate_generator with group X25519 + B.1.2. Test vector for message from A + B.1.3. Test vector for message from B + B.1.4. Test vector for secret points K + B.1.5. Test vector for ISK calculation initiator/responder + B.1.6. Test vector for ISK calculation parallel execution + B.1.7. Test vector for optional output of session id + B.1.8. Corresponding C programming language initializers + B.1.9. Testvectors as JSON file encoded as BASE64 + B.1.10. Test vectors for G_X25519.scalar_mult_vfy: low order + points + B.2. Test vector for CPace using group X448 and hash SHAKE-256 + B.2.1. Test vectors for calculate_generator with group X448 + B.2.2. Test vector for message from A + B.2.3. Test vector for message from B + B.2.4. Test vector for secret points K + B.2.5. Test vector for ISK calculation initiator/responder + B.2.6. Test vector for ISK calculation parallel execution + B.2.7. Test vector for optional output of session id + B.2.8. Corresponding C programming language initializers + B.2.9. Testvectors as JSON file encoded as BASE64 + B.2.10. Test vectors for G_X448.scalar_mult_vfy: low order + points + B.3. Test vector for CPace using group ristretto255 and hash + SHA-512 + B.3.1. Test vectors for calculate_generator with group + ristretto255 + B.3.2. Test vector for message from A + B.3.3. Test vector for message from B + B.3.4. Test vector for secret points K + B.3.5. Test vector for ISK calculation initiator/responder + B.3.6. Test vector for ISK calculation parallel execution + B.3.7. Test vector for optional output of session id + B.3.8. Corresponding C programming language initializers + B.3.9. Testvectors as JSON file encoded as BASE64 + B.3.10. Test case for scalar_mult with valid inputs + B.3.11. Invalid inputs for scalar_mult_vfy + B.4. Test vector for CPace using group decaf448 and hash + SHAKE-256 + B.4.1. Test vectors for calculate_generator with group + decaf448 + B.4.2. Test vector for message from A + B.4.3. Test vector for message from B + B.4.4. Test vector for secret points K + B.4.5. Test vector for ISK calculation initiator/responder + B.4.6. Test vector for ISK calculation parallel execution + B.4.7. Test vector for optional output of session id + B.4.8. Corresponding C programming language initializers + B.4.9. Testvectors as JSON file encoded as BASE64 + B.4.10. Test case for scalar_mult with valid inputs + B.4.11. Invalid inputs for scalar_mult_vfy + B.5. Test vector for CPace using group NIST P-256 and hash + SHA-256 + B.5.1. Test vectors for calculate_generator with group NIST + P-256 + B.5.2. Test vector for message from A + B.5.3. Test vector for message from B + B.5.4. Test vector for secret points K + B.5.5. Test vector for ISK calculation initiator/responder + B.5.6. Test vector for ISK calculation parallel execution + B.5.7. Test vector for optional output of session id + B.5.8. Corresponding C programming language initializers + B.5.9. Testvectors as JSON file encoded as BASE64 + B.5.10. Test case for scalar_mult_vfy with correct inputs + B.5.11. Invalid inputs for scalar_mult_vfy + B.6. Test vector for CPace using group NIST P-384 and hash + SHA-384 + B.6.1. Test vectors for calculate_generator with group NIST + P-384 + B.6.2. Test vector for message from A + B.6.3. Test vector for message from B + B.6.4. Test vector for secret points K + B.6.5. Test vector for ISK calculation initiator/responder + B.6.6. Test vector for ISK calculation parallel execution + B.6.7. Test vector for optional output of session id + B.6.8. Corresponding C programming language initializers + B.6.9. Testvectors as JSON file encoded as BASE64 + B.6.10. Test case for scalar_mult_vfy with correct inputs + B.6.11. Invalid inputs for scalar_mult_vfy + B.7. Test vector for CPace using group NIST P-521 and hash + SHA-512 + B.7.1. Test vectors for calculate_generator with group NIST + P-521 + B.7.2. Test vector for message from A + B.7.3. Test vector for message from B + B.7.4. Test vector for secret points K + B.7.5. Test vector for ISK calculation initiator/responder + B.7.6. Test vector for ISK calculation parallel execution + B.7.7. Test vector for optional output of session id + B.7.8. Corresponding C programming language initializers + B.7.9. Testvectors as JSON file encoded as BASE64 + B.7.10. Test case for scalar_mult_vfy with correct inputs + B.7.11. Invalid inputs for scalar_mult_vfy + Authors' Addresses + +1. Introduction + + This document describes CPace which is a balanced Password- + Authenticated-Key-Establishment (PAKE) protocol for two parties where + both parties derive a cryptographic key of high entropy from a shared + secret of low-entropy. CPace protects the passwords against offline + dictionary attacks by requiring adversaries to actively interact with + a protocol party and by allowing for at most one single password + guess per active interaction. + + The CPace design was tailored considering the following main + objectives: + + * Efficiency: Deployment of CPace is feasible on resource- + constrained devices. + + * Versatility: CPace supports different application scenarios via + versatile input formats, and by supporting applications with and + without clear initiator and responder roles. + + * Implementation error resistance: CPace aims at avoiding common + implementation pitfalls already by design, such as avoiding + incentives for insecure execution-time speed optimizations. For + smooth integration into different cryptographic library + ecosystems, this document provides a variety of cipher suites. + + * Post-quantum annoyance: CPace comes with measures to slow down + adversaries capable of breaking the discrete logarithm problem on + elliptic curves. + +1.1. Outline of this document + + * Section 3 describes the expected properties of an application + using CPace, and discusses in particular which application-level + aspects are relevant for CPace's security. + + * Section 4 gives an overview of the recommended cipher suites for + CPace which were optimized for different types of cryptographic + library ecosystems. + + * Section 5 introduces the notation used throughout this document. + + * Section 6 specifies the CPace protocol. + + * The appendix provides code and test vectors of all of the + functions defined for CPace. + + As this document is primarily written for implementers and + application designers, we would like to refer the theory-inclined + reader to the scientific paper [AHH21] which covers the detailed + security analysis of the different CPace instantiations as defined in + this document via the cipher suites. + +2. Requirements Notation + + The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", + "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and + "OPTIONAL" in this document are to be interpreted as described in + BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all + capitals, as shown here. + +3. High-level application perspective + + CPace enables balanced password-authenticated key establishment. + I.e. with CPace the parties start the protocol with a shared secret + octet string, namely the password-related string (PRS). PRS can be a + low-entropy secret itself, for instance a clear-text password encoded + according to [RFC8265], or any string derived from a common secret, + for instance by use of a key derivation function. + + Applications with clients and servers where the server side is + storing account and password information in its persistent memory are + recommended to use _augmented_ PAKE protocols such as OPAQUE + [I-D.irtf-cfrg-opaque]. + + In the course of the CPace protocol, A sends one message to B and B + sends one message to A. CPace does not mandate any ordering of these + two messages. We use the term "initiator-responder" for CPace where + A always speaks first, and the term "symmetric" setting where anyone + can speak first. + + CPace's output is an intermediate session key (ISK), but any party + might abort in case of an invalid received message. A and B will + produce the same ISK value if and only if both sides did initiate the + protocol using the same protocol inputs, specifically the same PRS + and the same value for the optional input parameters CI, ADa, ADb and + sid that will be specified in section Section 3.1. + + The naming of ISK as "intermediate" session key highlights the fact + that it is RECOMMENDED that applications process ISK by use of a + suitable strong key derivation function KDF (such as defined in + [RFC5869]) before using the key in a higher-level protocol. + +3.1. Optional CPace inputs + + For accommodating different application settings, CPace offers the + following OPTIONAL inputs, i.e. inputs which MAY also be the empty + string: + + * Party identity strings (A,B). In CPace each party can be given a + party identity string which might be a device name a user name or + an URL. CPace offers two alternative options for authenticating + the party identifiers in the course of the protocol run. The + RECOMMENDED option is to integrate both, A and B, into the channel + identifier string CI. This option is to be preferred as A and B + will be kept confidential and as this provides security advantages + (see Section 9.11 and Section 9.1). Integrating A,B into CI, + however, requires that both parties know the party identity string + of the communication partner before starting the protocol. If + this requirement is not fulfilled in an application setting then + CPace offers the alternative of integrating A as part of the + optional input ADa and B as part of the optional input ADb. If + the key exchange is successful, parties are guaranteed to learn + each other's identity string. + + * Channel identifier (CI). CI can be used to bind a session key + exchanged with CPace to a specific networking channel which + interconnects the protocol parties. CI could for instance include + networking addresses of both parties or party identity strings. + Both parties are required to have the same view of CI. CI will + not be publicly sent on the wire and may also include confidential + information. Both parties will only establish a common session + key if they initiated the protocol with the same view of CI. + + * Associated data fields (ADa and ADb). These fields can be used + for authenticating associated data alongside the CPace protocol. + The ADa and ADb will be sent in clear text as part of the protocol + messages. ADa and ADb will become authenticated in a CPace + protocol run as both parties will only agree on a common key if + they have had the same view on ADa and ADb. + + If an application cannot integrate the party identities (A,B) as + part of CI, A SHOULD BE included in ADa and B SHOULD BE included + in ADb instead (see Section 9.1). + + In a setting with clear initiator and responder roles, identity + information in ADa sent by the initiator can be used by the + responder for choosing the appropriate PRS (respectively password) + for this identity. ADa and ADb could also include application + protocol version information (e.g. to avoid downgrade attacks). + + * Session identifier (sid). If both parties have access to the same + unique public octet string sid being specific for a communication + session before starting the protocol, it is RECOMMENDED to use + this sid value as an additional input for the protocol as this + provides security advantages and will bind the CPace run to this + communication session (see Section 9). + +3.2. Optional CPace outputs + + If a session identifier is not available as input at protocol start + CPace can optionally produce a unique public session identifier + sid_output as output that might be helpful for the application for + actions subsequent to the CPace protocol step (see Section 9.6, + [BGHJ24]). + +3.3. Responsibilities of the application layer + + The following tasks are out of the scope of this document and left to + the application layer + + * Setup phase: The application layer is responsible for the + handshake that makes parties agree on a common CPace cipher suite. + + * This document does not specify which encodings applications use + for the mandatory PRS input and the optional inputs CI, sid, ADa + and ADb. If PRS is a clear-text password or an octet string + derived from a clear-text password, e.g. by use of a key- + derivation function, the clear-text password SHOULD BE encoded + according to [RFC8265]. + + * The application needs to settle whether CPace is used in the + initiator-responder or the symmetric setting, as in the symmetric + setting transcripts ordered string concatenation must be used for + generating protocol transcripts and when integrating the identity + strings A and B into the channel identifier CI. In this document + we will provide test vectors for both, initiator-responder and + symmetric settings. + +4. CPace cipher suites + + In the setup phase of CPace, both communication partners need to + agree on a common cipher suite. Cipher suites consist of a + combination of a hash function H and an elliptic curve environment G. + + For naming cipher suites we use the convention "CPACE-G-H". We + RECOMMEND the following cipher suites: + + * CPACE-X25519-SHA512. This suite uses the group environment + G_X25519 defined in Section 7.2 and SHA-512 as hash function. + This cipher suite comes with the smallest messages on the wire and + a low computational cost. + + * CPACE-P256_XMD:SHA-256_SSWU_NU_-SHA256. This suite instantiates + the group environment G as specified in Section 7.4 using the + encode_to_curve function P256_XMD:SHA-256_SSWU_NU_ from [RFC9380] + on curve NIST-P256, and hash function SHA-256. + + The following RECOMMENDED cipher suites provide higher security + margins. + + * CPACE-X448-SHAKE256. This suite uses the group environment G_X448 + defined in Section 7.2 and SHAKE-256 as hash function. + + * CPACE-P384_XMD:SHA-384_SSWU_NU_-SHA384. This suite instantiates G + as specified in Section 7.4 using the encode_to_curve function + P384_XMD:SHA-384_SSWU_NU_ from [RFC9380] on curve NIST-P384 with H + = SHA-384. + + * CPACE-P521_XMD:SHA-512_SSWU_NU_-SHA512. This suite instantiates G + as specified in Section 7.4 using the encode_to_curve function + P521_XMD:SHA-512_SSWU_NU_ from [RFC9380] on curve NIST-P521 with H + = SHA-512. + + CPace can also securely be implemented using the cipher suites CPACE- + RISTR255-SHA512 and CPACE-DECAF448-SHAKE256 defined in Section 7.3. + Section 9 gives guidance on how to implement CPace on further + elliptic curves. + +5. Definitions and notation + +5.1. Hash function H + + Common choices for H are SHA-512 [RFC6234] or SHAKE-256 [FIPS202]. + (I.e., the hash function outputs octet strings, and not group + elements.) For considering both variable-output-length hashes and + fixed-output-length hashes, we use the following convention. + + We use the following notation for referring to the specific + properties of a hash function H: + + * H.hash(m,l) is a function that operates on an input octet string m + and returns the first l octets of the hash of m. + + * H.b_in_bytes denotes the _minimum_ output size in bytes for + collision resistance for the security level target of the hash + function. E.g. H.b_in_bytes = 64 for SHA-512 and SHAKE-256 and + H.b_in_bytes = 32 for SHA-256 and SHAKE-128. We use the notation + H.hash(m) = H.hash(m, H.b_in_bytes) and let the hash operation + output the default length if no explicit length parameter is + given. + + * H.bmax_in_bytes denotes the _maximum_ output size in octets + supported by the hash function. In case of fixed-size hashes such + as SHA-256, this is the same as H.b_in_bytes, while there is no + such limit for hash functions such as SHAKE-256. + + * H.s_in_bytes denotes the _input block size_ used by H. This + number denotes the maximum number of bytes that can be processed + in a single block before applying the compression function or + permutation becomes necessary. (See also [RFC2104] for the + corresponding block size concepts). For instance, for SHA-512 the + input block size s_in_bytes is 128 as the compression function can + process up to 128 bytes, while for SHAKE-256 the input block size + amounts to 136 bytes before the permutation of the sponge state + needs to be applied. + +5.2. Group environment G + + The group environment G specifies an elliptic curve group (also + denoted G for convenience) and associated constants and functions as + detailed below. In this document we use additive notation for the + group operation. + + * G.calculate_generator(H,PRS,CI,sid) denotes a function that + outputs a representation of a generator (referred to as + "generator" from now on) of the group which is derived from input + octet strings PRS, CI, and sid and with the help of a hash + function H. + + * G.sample_scalar() is a function returning a representation of an + integer (referred to as "scalar" from now on) appropriate as a + private Diffie-Hellman key for the group. + + * G.scalar_mult(y,g) is a function operating on a scalar y and a + group element g. It returns an octet string representation of the + group element Y = y*g. + + * G.I denotes a unique octet string representation of the neutral + element of the group. G.I is used for detecting and signaling + certain error conditions. + + * G.scalar_mult_vfy(y,g) is a function operating on a scalar y and a + group element g. It returns an octet string representation of the + group element y*g. Additionally, scalar_mult_vfy specifies + validity conditions for y,g and y*g and outputs G.I in case they + are not met. + + * G.DSI denotes a domain-separation identifier octet string which + SHALL be uniquely identifying the group environment G. + +5.3. Notation for string operations + + * bytes1 || bytes2 denotes concatenation of octet strings. + + * len(S) denotes the number of octets in an octet string S. + + * This document uses quotation marks "" both for general language + (e.g. for citation of notation used in other documents) and as + syntax for specifying octet strings as in b"CPace25519". + + We use a preceding lowercase letter b"" in front of the quotation + marks if a character sequence is representing an octet string + sequence. I.e., we use the notation convention for byte string + representations with single-byte ASCII character encodings from + the python programming language. b"" denotes the empty string of + length 0. + + * LEB128 denotes an algorithm that converts an integer to a variable + sized string. The algorithm encodes 7 bits per byte starting with + the least significant bits in bits #0 to #6. As long as + significant bits remain, bit #7 will be set. This will result in + a single-byte encoding for values below 128. Test vectors and + reference code for LEB128 encoding are available in the appendix. + + * prepend_len(octet_string) denotes the octet sequence that is + obtained from prepending the length of the octet string to the + string itself. The length is encoded using LEB128. Test vectors + and code for prepend_len are available in the appendix. + + * lv_cat(a0,a1, ...) is the "length-value" encoding function which + returns the concatenation of the input strings with an encoding of + their respective length prepended. E.g., lv_cat(a0,a1) returns + prepend_len(a0) || prepend_len(a1). The detailed specification of + lv_cat and reference code is available in the appendix. + + * sample_random_bytes(n) denotes a function that returns n octets, + each of which is to be independently sampled from a uniform + distribution between 0 and 255. + + * zero_bytes(n) denotes a function that returns n octets with value + 0. + + * o_cat(bytes1,bytes2) denotes a function for ordered concatenation + of octet strings. It places the lexicographically larger octet + string first and prepends the two bytes from the octet string + b"oc" to the result. Reference code for this function is + available in the appendix. + + * transcript(Ya,ADa,Yb,ADb) denotes a function outputting an octet + string for the protocol transcript. In applications where CPace + is used without clear initiator and responder roles, i.e. where + the ordering of messages is not enforced by the protocol flow, + transcript_oc(Ya,Yb,ADa,ADb) = o_cat(lv_cat(Ya,ADa),lv_cat(Yb, + ADb)) SHALL be used. In the initiator-responder setting the + implementation transcript_ir(Ya,Yb,ADa,ADb) = lv_cat(Ya,ADa) || + lv_cat(Yb, ADb) SHALL be used. + +5.4. Notation for group operations + + We use additive notation for the group, i.e., 2*X denotes the element + that is obtained by computing X+X, for group element X and group + operation +. + +6. The CPace protocol + + CPace is a one round protocol between two parties, A and B. At + invocation, A and B are provisioned with PRS,G and H. Parties will + also be provisioned with OPTIONAL CI,sid,ADa (for A) and CI,sid,ADb + (for B) which will default to the empty string b"" if not used. A + sends the public share Ya and optional associated data ADa to B. + Likewise, B sends the public share Yb and optional associated data + ADb to A. Both A and B use the received messages for deriving a + shared intermediate session key, ISK. + +6.1. Protocol flow + + Optional parameters and messages are denoted with []. + + public: G, H + + A: PRS,[ADa],[CI],[sid] B: PRS,[ADb],[CI],[sid] + --------------------------------------- + compute Ya | Ya,[ADa] | compute Yb + |----------------->| + | Yb,[ADb] | + verify inputs |<-----------------| verify inputs + derive ISK | | derive ISK + --------------------------------------- + output ISK output ISK + +6.2. CPace protocol instructions + + A computes a generator g = G.calculate_generator(H,PRS,CI,sid), + scalar ya = G.sample_scalar() and group element Ya = G.scalar_mult + (ya,g). A then transmits Ya and optional associated data ADa to B. + + B computes a generator g = G.calculate_generator(H,PRS,CI,sid), + scalar yb = G.sample_scalar() and group element Yb = + G.scalar_mult(yb,g). B sends Yb and optional associated data ADb to + A. + + B then computes K = G.scalar_mult_vfy(yb,Ya). B MUST abort if K=G.I. + Otherwise B calculates ISK = H.hash(lv_cat(G.DSI || b"_ISK", sid, + K)||transcript(Ya,ADa,Yb,ADb)). B returns ISK and terminates. + + Likewise upon reception of the message from B, A computes K = + G.scalar_mult_vfy(ya,Yb). A MUST abort if K=G.I. + + Otherwise A calculates ISK = H.hash(lv_cat(G.DSI || b"_ISK", sid, + K) || transcript(Ya,ADa,Yb,ADb)). A returns ISK and terminates. + + The session key ISK returned by A and B is identical if and only if + the supplied input parameters PRS, CI and sid match on both sides and + the transcript views of both parties match. + +7. Implementation of recommended CPace cipher suites + +7.1. Common function for computing generators + + The different cipher suites for CPace defined in the upcoming + sections share the following method for deterministically combining + the individual strings PRS, CI, sid and the domain-separation + identifier DSI to a generator string: + + * generator_string(DSI, PRS, CI, sid, s_in_bytes) denotes a function + that returns the string lv_cat(DSI, PRS, zero_bytes(len_zpad), CI, + sid). + + * len_zpad = MAX(0, s_in_bytes - len(prepend_len(PRS)) - + len(prepend_len(G.DSI)) - 1) + + The zero padding of length len_zpad is designed such that the + encoding of DSI and PRS together with the zero padding field + completely fills at least the first input block (of length + s_in_bytes) of the hash. As a result for the common case of short + PRS the number of bytes to hash becomes independent of the actual + length of the password (PRS). (Code and test vectors are provided in + the appendix.) + + The introduction of a zero-padding within the generator string also + helps mitigating attacks of a side-channel adversary that analyzes + correlations between publicly known variable information with a short + low-entropy PRS string. Note that the hash of the first block is + intentionally made independent of session-specific inputs, such as + sid or CI and that there is no limitation regarding the maximum + length of the PRS string. + +7.2. CPace group objects G_X25519 and G_X448 for single-coordinate + Ladders on Montgomery curves + + In this section we consider the case of CPace when using the X25519 + and X448 Diffie-Hellman functions from [RFC7748] operating on the + Montgomery curves Curve25519 and Curve448 [RFC7748]. CPace + implementations using single-coordinate ladders on further Montgomery + curves SHALL use the definitions in line with the specifications for + X25519 and X448 and review the guidance given in Section 9. + + For the group environment G_X25519 the following definitions apply: + + * G_X25519.field_size_bytes = 32 + + * G_X25519.field_size_bits = 255 + + * G_X25519.sample_scalar() = sample_random_bytes(G.field_size_bytes) + + * G_X25519.scalar_mult(y,g) = G.scalar_mult_vfy(y,g) = X25519(y,g) + + * G_X25519.I = zero_bytes(G.field_size_bytes) + + * G_X25519.DSI = b"CPace255" + + CPace cipher suites using G_X25519 MUST use a hash function producing + at least H.b_max_in_bytes >= 32 bytes of output. It is RECOMMENDED + to use G_X25519 in combination with SHA-512. + + For X448 the following definitions apply: + + * G_X448.field_size_bytes = 56 + + * G_X448.field_size_bits = 448 + + * G_X448.sample_scalar() = sample_random_bytes(G.field_size_bytes) + + * G_X448.scalar_mult(y,g) = G.scalar_mult_vfy(y,g) = X448(y,g) + + * G_X448.I = zero_bytes(G.field_size_bytes) + + * G_X448.DSI = b"CPace448" + + CPace cipher suites using G_X448 MUST use a hash function producing + at least H.b_max_in_bytes >= 56 bytes of output. It is RECOMMENDED + to use G_X448 in combination with SHAKE-256. + + For both G_X448 and G_X25519 the G.calculate_generator(H, PRS,sid,CI) + function shall be implemented as follows. + + * First gen_str = generator_string(G.DSI,PRS,CI,sid, H.s_in_bytes) + SHALL BE calculated using the input block size of the chosen hash + function. + + * This string SHALL then BE hashed to the required length + gen_str_hash = H.hash(gen_str, G.field_size_bytes). Note that + this implies that the permissible output length H.maxb_in_bytes + MUST BE larger or equal to the field size of the group G for + making a hashing function suitable. + + * This result is then considered as a field coordinate using the u = + decodeUCoordinate(gen_str_hash, G.field_size_bits) function from + [RFC7748] which we repeat in the appendix for convenience. + + * The result point g is then calculated as (g,v) = + map_to_curve_elligator2(u) using the function from [RFC9380]. + Note that the v coordinate produced by the map_to_curve_elligator2 + function is not required for CPace and discarded. The appendix + repeats the definitions from [RFC9380] for convenience. + + Code for the functions above is available in the appendix. + +7.2.1. Verification tests + + For single-coordinate Montgomery ladders on Montgomery curves, + verification tests according to Section 8 SHALL check for proper + handling of the abort conditions, when a party is receiving u + coordinate values that encode a low-order point on either the curve + or the quadratic twist. + + In addition to that, in case of G_X25519, the tests SHALL also verify + that the implementation of G.scalar_mult_vfy(y,g) produces the + expected results for non-canonical u coordinate values with bit #255 + set, which may also encode low-order points. + + Corresponding test vectors are provided in the appendix. + +7.3. CPace group objects G_Ristretto255 and G_Decaf448 for prime-order + group abstractions + + In this section we consider the case of CPace using the Ristretto255 + and Decaf448 group abstractions + [I-D.draft-irtf-cfrg-ristretto255-decaf448]. These abstractions + define an encode and decode function, group operations using an + internal encoding and an element-derivation function that maps a byte + string to a group element. With the group abstractions there is a + distinction between an internal representation of group elements and + an external encoding of the same group element. In order to + distinguish between these different representations, we prepend an + underscore before values using the internal representation within + this section. + + For Ristretto255 the following definitions apply: + + * G_Ristretto255.DSI = b"CPaceRistretto255" + + * G_Ristretto255.field_size_bytes = 32 + + * G_Ristretto255.group_size_bits = 252 + + * G_Ristretto255.group_order = 2^252 + + 27742317777372353535851937790883648493 + + CPace cipher suites using G_Ristretto255 MUST use a hash function + producing at least H.b_max_in_bytes >= 64 bytes of output. It is + RECOMMENDED to use G_Ristretto255 in combination with SHA-512. + + For decaf448 the following definitions apply: + + * G_Decaf448.DSI = b"CPaceDecaf448" + + * G_Decaf448.field_size_bytes = 56 + + * G_Decaf448.group_size_bits = 445 + + * G_Decaf448.group_order = l = 2^446 - + 1381806680989511535200738674851542 + 6880336692474882178609894547503885 + + CPace cipher suites using G_Decaf448 MUST use a hash function + producing at least H.b_max_in_bytes >= 112 bytes of output. It is + RECOMMENDED to use G_Decaf448 in combination with SHAKE-256. + + For both abstractions the following definitions apply: + + * It is RECOMMENDED to implement G.sample_scalar() as follows. + + - Set scalar = sample_random_bytes(G.group_size_bytes). + + - Then clear the most significant bits larger than + G.group_size_bits. + + - Interpret the result as the little-endian encoding of an + integer value and return the result. + + * Alternatively, if G.sample_scalar() is not implemented according + to the above recommendation, it SHALL be implemented using uniform + sampling between 1 and (G.group_order - 1). Note that the more + complex uniform sampling process can provide a larger side-channel + attack surface for embedded systems in hostile environments. + + * G.scalar_mult(y,_g) SHALL operate on a scalar y and a group + element _g in the internal representation of the group abstraction + environment. It returns the value Y = encode(y * (_g)), i.e. it + returns a value using the public encoding. + + * G.I = is the public encoding representation of the identity + element. + + * G.scalar_mult_vfy(y,X) operates on a value using the public + encoding and a scalar and is implemented as follows. If the + decode(X) function fails, it returns G.I. Otherwise it returns + encode( y * decode(X) ). + + * The G.calculate_generator(H, PRS,sid,CI) function SHALL return a + decoded point and SHALL BE implemented as follows. + + - First gen_str = generator_string(G.DSI,PRS,CI,sid, + H.s_in_bytes) is calculated using the input block size of the + chosen hash function. + + - This string is then hashed to the required length gen_str_hash + = H.hash(gen_str, 2 * G.field_size_bytes). Note that this + implies that the permissible output length H.maxb_in_bytes MUST + BE larger or equal to twice the field size of the group G for + making a hash function suitable. + + - Finally the internal representation of the generator _g is + calculated as _g = element_derivation(gen_str_hash) using the + element derivation function from the abstraction. + + Note that with these definitions the scalar_mult function operates on + a decoded point _g and returns an encoded point, while the + scalar_mult_vfy(y,X) function operates on an encoded point X (and + also returns an encoded point). + +7.3.1. Verification tests + + For group abstractions verification tests according to Section 8 + SHALL check for proper handling of the abort conditions, when a party + is receiving encodings of the neutral element or receives an octet + string that does not decode to a valid group element. + +7.4. CPace group objects for curves in Short-Weierstrass representation + + The group environment objects G defined in this section for use with + Short-Weierstrass curves, are parametrized by the choice of an + elliptic curve and by choice of a suitable encode_to_curve function. + encode_to_curve must map an octet string to a point on the curve. + +7.4.1. Curves and associated functions + + Elliptic curves in Short-Weierstrass form are considered in + [IEEE1363]. [IEEE1363] allows for both, curves of prime and non- + prime order. However, for the procedures described in this section + any suitable group MUST BE of prime order. + + The specification for the group environment objects specified in this + section closely follow the ECKAS-DH1 method from [IEEE1363]. I.e. we + use the same methods and encodings and protocol sub steps as employed + in the TLS [RFC5246] [RFC8446] protocol family. + + For CPace only the uncompressed full-coordinate encodings from [SEC1] + (x and y coordinate) SHOULD be used. Commonly used curve groups are + specified in [SEC2] and [RFC5639]. A typical representative of such + a Short-Weierstrass curve is NIST-P256. Point verification as used + in ECKAS-DH1 is described in Annex A.16.10. of [IEEE1363]. + + For deriving Diffie-Hellman shared secrets ECKAS-DH1 from [IEEE1363] + specifies the use of an ECSVDP-DH method. We use ECSVDP-DH in + combination with the identity map such that it either returns "error" + or the x-coordinate of the Diffie-Hellman result point as shared + secret in big endian format (fixed length output by FE2OSP without + truncating leading zeros). + +7.4.2. Suitable encode_to_curve methods + + All the encode_to_curve methods specified in [RFC9380] are suitable + for CPace. For Short-Weierstrass curves it is RECOMMENDED to use the + non-uniform variant of the SSWU mapping primitive from [RFC9380] if a + SSWU mapping is available for the chosen curve. (We recommend non- + uniform maps in order to give implementations the flexibility to opt + for x-coordinate-only scalar multiplication algorithms.) + +7.4.3. Definition of the group environment G for Short-Weierstrass + curves + + In this paragraph we use the following notation for defining the + group object G for a selected curve and encode_to_curve method: + + * With G.group_order we denote the order of the elliptic curve which + MUST BE a prime. + + * With is_valid(X) we denote a method which operates on an octet + stream according to [SEC1] of a point on the group and returns + true if the point is valid and returns false otherwise. This + is_valid(X) method SHALL be implemented according to Annex + A.16.10. of [IEEE1363]. I.e. it shall return false if X encodes + either the neutral element on the group or does not form a valid + encoding of a point on the group. + + * With encode_to_curve(str,DST) we denote a mapping function from + [RFC9380]. I.e. a function that maps octet string str to a point + on the group using the domain separation tag DST. [RFC9380] + considers both, uniform and non-uniform mappings based on several + different strategies. It is RECOMMENDED to use the nonuniform + variant of the SSWU mapping primitive within [RFC9380]. + + * G.DSI denotes a domain-separation identifier octet string. G.DSI + which SHALL BE obtained by the concatenation of b"CPace" and the + associated name of the cipher suite used for the encode_to_curve + function as specified in [RFC9380]. E.g. when using the map with + the name P384_XMD:SHA-384_SSWU_NU_ on curve NIST-P384 the + resulting value SHALL BE G.DSI = b"CPaceP384_XMD:SHA- + 384_SSWU_NU_". + + Using the above definitions, the CPace functions required for the + group object G are defined as follows. + + * G.DST denotes the domain-separation tag value to use in + conjunction with the encode_to_curve function from [RFC9380]. + G.DST shall be obtained by concatenating G.DSI and b"_DST". + + * G.sample_scalar() SHALL return a value between 1 and + (G.group_order - 1). The sampling SHALL BE indistinguishable from + uniform random selection between 1 and (G.group_order - 1). It is + RECOMMENDED to use a constant-time rejection sampling algorithm + for converting a uniform bitstring to a uniform value between 1 + and (G.group_order - 1). + + * G.calculate_generator(H, PRS,sid,CI) function SHALL be implemented + as follows. + + - First gen_str = generator_string(G.DSI,PRS,CI,sid, + H.s_in_bytes) is calculated. + + - Then the output of a call to encode_to_curve(gen_str, G.DST) is + returned, using the selected suite from [RFC9380]. + + * G.scalar_mult(s,X) is a function that operates on a scalar s and + an input point X. The input X shall use the same encoding as + produced by the G.calculate_generator method above. + G.scalar_mult(s,X) SHALL return an encoding of either the point + s*X or the point (-s)*X according to [SEC1]. Implementations + SHOULD use the full-coordinate format without compression, as + important protocols such as TLS 1.3 removed support for + compression. Implementations of scalar_mult(s,X) MAY output + either s*X or (-s)*X as both points s*X and (-s)*X have the same + x-coordinate and result in the same Diffie-Hellman shared secrets + K. (This allows implementations to opt for x-coordinate-only + scalar multiplication algorithms.) + + * G.scalar_mult_vfy(s,X) merges verification of point X according to + [IEEE1363] A.16.10. and the the ECSVDP-DH procedure from + [IEEE1363]. It SHALL BE implemented as follows: + + - If is_valid(X) = False then G.scalar_mult_vfy(s,X) SHALL return + "error" as specified in [IEEE1363] A.16.10 and 7.2.1. + + - Otherwise G.scalar_mult_vfy(s,X) SHALL return the result of the + ECSVDP-DH procedure from [IEEE1363] (section 7.2.1). I.e. it + shall either return "error" (in case that s*X is the neutral + element) or the secret shared value "z" defined in [IEEE1363] + (otherwise). "z" SHALL be encoded by using the big-endian + encoding of the x-coordinate of the result point s*X according + to [SEC1]. + + * We represent the neutral element G.I by using the representation + of the "error" result case from [IEEE1363] as used in the + G.scalar_mult_vfy method above. + +7.4.4. Verification tests + + For Short-Weierstrass curves verification tests according to + Section 8 SHALL check for proper handling of the abort conditions, + when a party is receiving an encoding of the point at infinity and an + encoding of a point not on the group. + +8. Implementation verification + + Any CPace implementation MUST be tested against invalid or weak point + attacks. Implementation MUST be verified to abort upon conditions + where G.scalar_mult_vfy functions outputs G.I. For testing an + implementation it is RECOMMENDED to include weak or invalid point + encodings within the messages of party A and B and introduce this in + a protocol run. It SHALL be verified that the abort condition is + properly handled. + + Corresponding test vectors are given in the appendix for all + recommended cipher suites. + +9. Security Considerations + + A security proof of CPace is found in [AHH21]. This proof covers all + recommended cipher suites included in this document. The security + analysis in [BGHJ24] extends the analysis from [AHH21] by covering + the case that no pre-agreed session identifier is available. + [BGHJ24] also shows how a unique session id sid_output can be + generated along with the protocol for applications that do not have a + session identifier input available. + +9.1. Party identifiers and relay attacks + + If unique strings identifying the protocol partners are included + either as part of the channel identifier CI or the associated data + fields ADa, ADb, then ISK will provide implicit authentication also + regarding the party identities. + + Incorporating party identifier strings is important for fending off + relay attacks. Such attacks become relevant in a setting where + several parties, say, A, B and C, share the same password PRS. An + adversary might relay messages from an honest user A, who aims at + interacting with user B, to a party C instead. If no party + identifier strings are used and B and C share the same PRS value then + A might be using CPace for establishing a common ISK key with C while + assuming to interact with party B. Including and checking party + identifiers can fend off such relay attacks. + + The following guidance SHOULD be followed regarding party + identifiers. + + * If an application layer has party identifiers available, it SHOULD + integrate party identifiers in the CPace protocol run, either + within CI or ADa/ADb. + + * The application SHOULD give preference to the option of + integrating party identifiers in CI. This avoids the need of an + explicit check for the identity strings. + + * Otherwise A SHOULD integrate its party identifiers in ADa and ADb, + such that A integrates its identifier in ADa and B integrates its + party identifier as part of ADb. In this case the application + layer will have to add an explicit check for the identity string + of the actual communication partner for fending off relay attacks. + +9.2. Hashing protocol transcripts + + CPace prepends the length of all variable-size input strings before + hashing data. Prepending the length of all variable-size input + strings results in a so-called prefix-free encoding of transcript + strings, using terminology introduced in [CDMP05]. This property + allows for disregarding length-extension imperfections that come with + the commonly used Merkle-Damgard hash function constructions such as + SHA256 and SHA512 [CDMP05]. + +9.3. Key derivation + + A CPace implementation SHALL output ISK but MUST NOT expose K, + because a leaked K may enable offline dictionary attack on the + password, and a matching value for K does not provide authentication + of ADa and ADb. + + As noted already in Section 6 it is RECOMMENDED to process ISK by use + of a suitable strong key derivation function KDF (such as defined in + [RFC5869]) first, before using the key in a higher-level protocol. + +9.4. Key confirmation + + In many applications it is advisable to add an explicit key + confirmation round after the CPace protocol flow. However, as some + applications might only require implicit authentication and as + explicit authentication messages are already a built-in feature in + many higher-level protocols (e.g. TLS 1.3), the CPace protocol + described here does not mandate key confirmation. + + Already without explicit key confirmation, CPace enjoys weak forward + security under the sCDH and sSDH assumptions [AHH21]. With added + explicit confirmation, CPace enjoys perfect forward security also + under the strong sCDH and sSDH assumptions [AHH21]. + + Note that in [ABKLX21] it was shown that an idealized variant of + CPace also enjoys perfect forward security without explicit key + confirmation. However this proof does not explicitly cover the + recommended cipher suites in this document and requires the stronger + assumption of an algebraic adversary model. For this reason, we + recommend adding explicit key confirmation if perfect forward + security is required. + + When implementing explicit key confirmation, it is recommended to use + an appropriate message-authentication code (MAC) such as HMAC + [RFC2104] or CMAC [RFC4493] using a key mac_key derived from ISK. + + One suitable option that works also in the parallel setting without + message ordering is to proceed as follows. + + * First calculate mac_key as mac_key = H.hash(b"CPaceMac" || sid || + ISK). + + * Then let each party send an authenticator tag calculated over the + protocol message that it has sent previously. I.e. let party A + calculate its authentication tag Ta as Ta = MAC(mac_key, + lv_cat(Ya,ADa)) and let party B calculate its authentication tag + Tb as Tb = MAC(mac_key, lv_cat(Yb,ADb)). + + * Let the receiving party check the remote authentication tag for + the correct value and abort in case that it's incorrect. + +9.5. Integrating CPace in higher-level protocols such as TLS1.3 + + When integrating CPace into a higher-level protocol such as TLS1.3 + [RFC8446] it is recommended to use ISK as shared secret (which might + otherwise be generated as part of a Diffie-Hellman key exchange + output for other cipher suites). + + Note that unlike the shared secret of a Diffie-Hellman protocol run, + ISK will also provide mutual implicit authentication of the protocol + partners. For providing explicit authentication, it is recommended + to add a key confirmation round along the lines in Section 9.4, such + as e.g. done in the "Finished" messages in TLS1.3 [RFC8446]. + + If an embedding protocol uses more than two messages (e.g. four + message TLS1.3 [RFC8446] flows involving a hello-retry message and a + repeated client-hello message) it is suggested that the CPace layer + only considers the two messages used for the CPace run. I.e., it is + suggested that authenticating the full message sequence involving + also the additional messages that might precede the two CPace + messages is done under the responsibility of the embedding + application protocol. This could be done by integrating the full + protocol transcript as part of a final explicit key confirmation + round (as commonly done by TLS 1.3 as part of the "Finished" + messages). Alternatively, information on communication rounds + preceding the CPace flows can also be integrated as part of the CI + field, as this will authenticate the information and will not require + both communication partners to keep state information regarding + preceding messages in memory until after the CPace run. + + In case of TLS 1.3 [RFC8446] it is suggested to integrate Ya into the + client-hello message and Yb into the server-hello message. Also + party identifiers might best be added to the client-hello and server- + hello messages as part of extension fields. It is recommended to use + the full octet stream encoding of the client-hello message as + parameter ADa. Likewise it is recommended to use the encoding of the + server-hello message for the parameter ADb. This approach has the + drawback that the public points Ya and Yb might show up redundantly + duplicated in the hashing operation for CPace's transcript strings + but has the advantage of simplicity and the advantage that all meta- + information in the extension fields within the client- and server + hello fields will always become authenticated as part of the ISK. + +9.6. Calculating a session identifier alongside with the CPace run + + If CPace was run with an empty string sid available as input, both + parties can produce a public session identifier string sid_output = + H.hash(b"CPaceSidOutput" || transcript(Ya,ADa,Yb,ADb)) which will be + unique for honest parties [BGHJ24]. + +9.7. Sampling of scalars + + For curves over fields F_q where q is a prime close to a power of + two, we recommend sampling scalars as a uniform bit string of length + field_size_bits. We do so in order to reduce both, complexity of the + implementation and the attack surface with respect to side-channels + for embedded systems in hostile environments. [AHH21] demonstrated + that non-uniform sampling did not negatively impact security for the + case of Curve25519 and Curve448. This analysis however does not + transfer to most curves in Short-Weierstrass form. + + As a result, we recommend rejection sampling if G is as in + Section 7.4. Alternatively an algorithm designed along the lines of + the hash_to_field() function from [RFC9380] can also be used. There, + oversampling to an integer significantly larger than the curve order + is followed by a modular reduction to the group order. + +9.8. Preconditions for using the simplified CPace specification from + Section 7.2 + + The security of the algorithms used for the recommended cipher suites + for the Montgomery curves Curve25519 and Curve448 in Section 7.2 rely + on the following properties [AHH21]: + + * The curve has order (p * c) with p prime and c a small cofactor. + Also the curve's quadratic twist must be of order (p' * c') with + p' prime and c' a cofactor. + + * The cofactor c of the curve MUST BE equal to or an integer + multiple of the cofactor c' of the curve's quadratic twist. Also, + importantly, the implementation of the scalar_mult and + scalar_mult_vfy functions must ensure that all scalars actually + used for the group operation are integer multiples of c (e.g. such + as asserted by the specification of the decodeScalar functions in + [RFC7748]). + + * Both field order q and group order p MUST BE close to a power of + two along the lines of [AHH21], Appendix E. Otherwise the + simplified scalar sampling specified in Section 7.2 needs to be + changed. + + * The representation of the neutral element G.I MUST BE the same for + both, the curve and its twist. + + * The implementation of G.scalar_mult_vfy(y,X) MUST map all c low- + order points on the curve and all c' low-order points on the twist + to G.I. + + Algorithms for curves other than the ones recommended here can be + based on the principles from Section 7.2 given that the above + properties hold. + +9.9. Nonce values + + Secret scalars ya and yb MUST NOT be reused. Values for sid SHOULD + NOT be reused since the composability guarantees established by the + simulation-based proof rely on the uniqueness of session ids [AHH21]. + + If the higher-level protocol that integrates CPace is able to + establish a unique sid identifier for the communication session, it + is RECOMMENDED that this is passed to CPace as sid parameter. One + suitable option for generating sid is concatenation of ephemeral + random strings contributed by both parties. + +9.10. Side channel attacks + + All state-of-the art methods for realizing constant-time execution + SHOULD be used. Special care is RECOMMENDED specifically for + elliptic curves in Short-Weierstrass form as important standard + documents including [IEEE1363] describe curve operations with non- + constant-time algorithms. + + In case that side channel attacks are to be considered practical for + a given application, it is RECOMMENDED to pay special attention on + computing the secret generator G.calculate_generator(PRS,CI,sid). + The most critical substep to consider might be the processing of the + first block of the hash that includes the PRS string. The zero- + padding introduced when hashing the sensitive PRS string can be + expected to make the task for a side-channel attack somewhat more + complex. Still this feature alone is not sufficient for ruling out + power analysis attacks. + + Even though the calculate_generator operation might be considered to + form the primary target for side-channel attacks as information on + long-term secrets might be exposed, also the subsequent operations on + ephemeral values, such as scalar sampling and scalar multiplication + should be protected from side-channels. + +9.11. Quantum computers + + CPace is proven secure under the hardness of the strong computational + Simultaneous Diffie-Hellmann (sSDH) and strong computational Diffie- + Hellmann (sCDH) assumptions in the group G (as defined in [AHH21]). + These assumptions are not expected to hold any longer when large- + scale quantum computers (LSQC) are available. Still, even in case + that LSQC emerge, it is reasonable to assume that discrete-logarithm + computations will remain costly. CPace with ephemeral pre- + established session id values sid forces the adversary to solve one + computational Diffie-Hellman problem per password guess [ES21]. If + party identifiers are included as part of CI then the adversary is + forced to solve one computational Diffie-Hellman problem per password + guess and party identifier pair. For this reason it is RECOMMENDED + to use the optional inputs sid if available in an application + setting. For the same reason it is RECOMMENDED to integrate party + identity strings A,B into CI. + + In this sense, using the wording suggested by Steve Thomas on the + CFRG mailing list, CPace is "quantum-annoying". + +10. IANA Considerations + + No IANA action is required. + +11. Reference implementation and test vector generation + + The reference implementation that was used for deriving test vectors + is available at [REFIMP]. The embedded base64-encoded test vectors + will decode to JSON files having the test vector's octet strings + encoded as base16 (i.e. hexadecimal) strings. + +12. Acknowledgements + + We would like to thank the participants on the CFRG list for comments + and advice. Any comment and advice is appreciated. + +13. References + +13.1. Normative References + + [I-D.draft-irtf-cfrg-ristretto255-decaf448] + de Valence, H., Grigg, J., Hamburg, M., Lovecruft, I., + Tankersley, G., and F. Valsorda, "The ristretto255 and + decaf448 Groups", Work in Progress, Internet-Draft, draft- + irtf-cfrg-ristretto255-decaf448-08, 5 September 2023, + . + + [IEEE1363] "Standard Specifications for Public Key Cryptography, IEEE + 1363", 2000. + + [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate + Requirement Levels", BCP 14, RFC 2119, + DOI 10.17487/RFC2119, March 1997, + . + + [RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves + for Security", RFC 7748, DOI 10.17487/RFC7748, January + 2016, . + + [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC + 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, + May 2017, . + + [SEC1] Standards for Efficient Cryptography Group (SECG), "SEC 1: + Elliptic Curve Cryptography", May 2009, + . + +13.2. Informative References + + [ABKLX21] Abdalla, M., Barbosa, M., Katz, J., Loss, J., and J. Xu, + "Algebraic Adversaries in the Universal Composability + Framework.", n.d., . + + [AHH21] Abdalla, M., Haase, B., and J. Hesse, "Security analysis + of CPace", n.d., . + + [BGHJ24] Barbosa, M., Gellert, K., Hesse, J., and S. Jarecki, "Bare + PAKE: Universally Composable Key Exchange from Just + Passwords", n.d., . + + [CDMP05] Coron, J.-S., Dodis, Y., Malinaud, C., and P. Puniya, + "Merkle-Damgaard Revisited: How to Construct a Hash + Function", In Advances in Cryptology - CRYPTO 2005, + pages 430-448, DOI 10.1007/11535218_26, 2005, + . + + [ES21] Eaton, E. and D. Stebila, "The 'quantum annoying' property + of password-authenticated key exchange protocols.", n.d., + . + + [FIPS202] National Institute of Standards and Technology (NIST), + "SHA-3 Standard: Permutation-Based Hash and Extendable- + Output Functions", August 2015, + . + + [I-D.irtf-cfrg-opaque] + Bourdrez, D., Krawczyk, H., Lewi, K., and C. A. Wood, "The + OPAQUE Augmented PAKE Protocol", Work in Progress, + Internet-Draft, draft-irtf-cfrg-opaque-17, 27 September + 2024, . + + [REFIMP] "CPace reference implementation (sage)", September 2024, + . + + [RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed- + Hashing for Message Authentication", RFC 2104, + DOI 10.17487/RFC2104, February 1997, + . + + [RFC4493] Song, JH., Poovendran, R., Lee, J., and T. Iwata, "The + AES-CMAC Algorithm", RFC 4493, DOI 10.17487/RFC4493, June + 2006, . + + [RFC5246] Dierks, T. and E. Rescorla, "The Transport Layer Security + (TLS) Protocol Version 1.2", RFC 5246, + DOI 10.17487/RFC5246, August 2008, + . + + [RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography + (ECC) Brainpool Standard Curves and Curve Generation", + RFC 5639, DOI 10.17487/RFC5639, March 2010, + . + + [RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand + Key Derivation Function (HKDF)", RFC 5869, + DOI 10.17487/RFC5869, May 2010, + . + + [RFC6234] Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms + (SHA and SHA-based HMAC and HKDF)", RFC 6234, + DOI 10.17487/RFC6234, May 2011, + . + + [RFC8265] Saint-Andre, P. and A. Melnikov, "Preparation, + Enforcement, and Comparison of Internationalized Strings + Representing Usernames and Passwords", RFC 8265, + DOI 10.17487/RFC8265, October 2017, + . + + [RFC8446] Rescorla, E., "The Transport Layer Security (TLS) Protocol + Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018, + . + + [RFC9380] Faz-Hernandez, A., Scott, S., Sullivan, N., Wahby, R. S., + and C. A. Wood, "Hashing to Elliptic Curves", RFC 9380, + DOI 10.17487/RFC9380, August 2023, + . + + [SEC2] Standards for Efficient Cryptography Group (SECG), "SEC 2: + Recommended Elliptic Curve Domain Parameters", January + 2010, . + +Appendix A. CPace function definitions + +A.1. Definition and test vectors for string utility functions + +A.1.1. prepend_len function + + def prepend_len(data): + "prepend LEB128 encoding of length" + length = len(data) + length_encoded = b"" + while True: + if length < 128: + length_encoded += bytes([length]) + else: + length_encoded += bytes([(length & 0x7f) + 0x80]) + length = int(length >> 7) + if length == 0: + break; + return length_encoded + data + +A.1.2. prepend_len test vectors + + prepend_len(b""): (length: 1 bytes) + 00 + prepend_len(b"1234"): (length: 5 bytes) + 0431323334 + prepend_len(bytes(range(127))): (length: 128 bytes) + 7f000102030405060708090a0b0c0d0e0f101112131415161718191a1b + 1c1d1e1f202122232425262728292a2b2c2d2e2f303132333435363738 + 393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f505152535455 + 565758595a5b5c5d5e5f606162636465666768696a6b6c6d6e6f707172 + 737475767778797a7b7c7d7e + prepend_len(bytes(range(128))): (length: 130 bytes) + 8001000102030405060708090a0b0c0d0e0f101112131415161718191a + 1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334353637 + 38393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f5051525354 + 55565758595a5b5c5d5e5f606162636465666768696a6b6c6d6e6f7071 + 72737475767778797a7b7c7d7e7f + +A.1.2.1. Testvectors as JSON file encoded as BASE64 + + #eyJwcmVwZW5kX2xlbihiJycpIjogIjAwIiwgImInMTIzNCciOiAiMzEzMjMzMzQiLC + #AicHJlcGVuZF9sZW4oYicxMjM0JykiOiAiMDQzMTMyMzMzNCIsICJwcmVwZW5kX2xl + #bihieXRlcyhyYW5nZSgxMjcpKSkiOiAiN0YwMDAxMDIwMzA0MDUwNjA3MDgwOTBBME + #IwQzBEMEUwRjEwMTExMjEzMTQxNTE2MTcxODE5MUExQjFDMUQxRTFGMjAyMTIyMjMy + #NDI1MjYyNzI4MjkyQTJCMkMyRDJFMkYzMDMxMzIzMzM0MzUzNjM3MzgzOTNBM0IzQz + #NEM0UzRjQwNDE0MjQzNDQ0NTQ2NDc0ODQ5NEE0QjRDNEQ0RTRGNTA1MTUyNTM1NDU1 + #NTY1NzU4NTk1QTVCNUM1RDVFNUY2MDYxNjI2MzY0NjU2NjY3Njg2OTZBNkI2QzZENk + #U2RjcwNzE3MjczNzQ3NTc2Nzc3ODc5N0E3QjdDN0Q3RSIsICJwcmVwZW5kX2xlbihi + #eXRlcyhyYW5nZSgxMjgpKSkiOiAiODAwMTAwMDEwMjAzMDQwNTA2MDcwODA5MEEwQj + #BDMEQwRTBGMTAxMTEyMTMxNDE1MTYxNzE4MTkxQTFCMUMxRDFFMUYyMDIxMjIyMzI0 + #MjUyNjI3MjgyOTJBMkIyQzJEMkUyRjMwMzEzMjMzMzQzNTM2MzczODM5M0EzQjNDM0 + #QzRTNGNDA0MTQyNDM0NDQ1NDY0NzQ4NDk0QTRCNEM0RDRFNEY1MDUxNTI1MzU0NTU1 + #NjU3NTg1OTVBNUI1QzVENUU1RjYwNjE2MjYzNjQ2NTY2Njc2ODY5NkE2QjZDNkQ2RT + #ZGNzA3MTcyNzM3NDc1NzY3Nzc4Nzk3QTdCN0M3RDdFN0YifQ== + +A.1.3. lv_cat function + + def lv_cat(*args): + result = b"" + for arg in args: + result += prepend_len(arg) + return result + +A.1.4. Testvector for lv_cat() + + lv_cat(b"1234",b"5",b"",b"678"): (length: 12 bytes) + 043132333401350003363738 + +A.1.4.1. Testvectors as JSON file encoded as BASE64 + + #eyJiJzEyMzQnIjogIjMxMzIzMzM0IiwgImInNSciOiAiMzUiLCAiYic2NzgnIjogIj + #M2MzczOCIsICJsdl9jYXQoYicxMjM0JyxiJzUnLGInJyxiJzY3OCcpIjogIjA0MzEz + #MjMzMzQwMTM1MDAwMzM2MzczOCJ9 + +A.2. Definition of generator_string function. + + def generator_string(DSI,PRS,CI,sid,s_in_bytes): + # Concat all input fields with prepended length information. + # Add zero padding in the first hash block after DSI and PRS. + len_zpad = max(0,s_in_bytes - 1 - len(prepend_len(PRS)) + - len(prepend_len(DSI))) + return lv_cat(DSI, PRS, zero_bytes(len_zpad), + CI, sid) + +A.3. Definitions and test vector ordered concatenation + +A.3.1. Definitions for lexiographical ordering + + For ordered concatenation lexiographical ordering of byte sequences + is used: + + def lexiographically_larger(bytes1,bytes2): + "Returns True if bytes1>bytes2 using lexiographical ordering." + min_len = min (len(bytes1), len(bytes2)) + for m in range(min_len): + if bytes1[m] > bytes2[m]: + return True; + elif bytes1[m] < bytes2[m]: + return False; + return len(bytes1) > len(bytes2) + +A.3.2. Definitions for ordered concatenation + + With the above definition of lexiographical ordering ordered + concatenation is specified as follows. + + def o_cat(bytes1,bytes2): + if lexiographically_larger(bytes1,bytes2): + return b"oc" + bytes1 + bytes2 + else: + return b"oc" + bytes2 + bytes1 + +A.3.3. Test vectors ordered concatenation + + string comparison for o_cat: + lexiographically_larger(b"\0", b"\0\0") == False + lexiographically_larger(b"\1", b"\0\0") == True + lexiographically_larger(b"\0\0", b"\0") == True + lexiographically_larger(b"\0\0", b"\1") == False + lexiographically_larger(b"\0\1", b"\1") == False + lexiographically_larger(b"ABCD", b"BCD") == False + + o_cat(b"ABCD",b"BCD"): (length: 9 bytes) + 6f6342434441424344 + o_cat(b"BCD",b"ABCDE"): (length: 10 bytes) + 6f634243444142434445 + +A.3.3.1. Testvectors as JSON file encoded as BASE64 + + #eyJiJ0FCQ0QnIjogIjQxNDI0MzQ0IiwgImInQkNEJyI6ICI0MjQzNDQiLCAiYidBQk + #NERSciOiAiNDE0MjQzNDQ0NSIsICJvX2NhdChiJ0FCQ0QnLGInQkNEJykiOiAiNkY2 + #MzQyNDM0NDQxNDI0MzQ0IiwgIm9fY2F0KGInQkNEJyxiJ0FCQ0RFJykiOiAiNkY2Mz + #QyNDM0NDQxNDI0MzQ0NDUifQ== + +A.3.4. Definitions for transcript_ir function + + def transcript_ir(Ya,ADa,Yb,ADb): + result = lv_cat(Ya,ADa) + lv_cat(Yb,ADb) + return result + +A.3.5. Test vectors transcript_ir function + + transcript_ir(b"123", b"PartyA", b"234",b"PartyB"): + (length: 22 bytes) + 03313233065061727479410332333406506172747942 + transcript_ir(b"3456",b"PartyA",b"2345",b"PartyB"): + (length: 24 bytes) + 043334353606506172747941043233343506506172747942 + +A.3.5.1. Testvectors as JSON file encoded as BASE64 + + #eyJiJzEyMyciOiAiMzEzMjMzIiwgImInMjM0JyI6ICIzMjMzMzQiLCAiYidQYXJ0eU + #EnIjogIjUwNjE3Mjc0Nzk0MSIsICJiJ1BhcnR5QiciOiAiNTA2MTcyNzQ3OTQyIiwg + #ImInMzQ1NiciOiAiMzMzNDM1MzYiLCAiYicyMzQ1JyI6ICIzMjMzMzQzNSIsICJ0cm + #Fuc2NyaXB0X2lyKGInMTIzJyxiJ1BhcnR5QScsYicyMzQnLGInUGFydHlCJykiOiAi + #MDMzMTMyMzMwNjUwNjE3Mjc0Nzk0MTAzMzIzMzM0MDY1MDYxNzI3NDc5NDIiLCAidH + #JhbnNjcmlwdF9pcihiJzM0NTYnLGInUGFydHlBJyxiJzIzNDUnLGInUGFydHlCJyki + #OiAiMDQzMzM0MzUzNjA2NTA2MTcyNzQ3OTQxMDQzMjMzMzQzNTA2NTA2MTcyNzQ3OT + #QyIn0= + +A.3.6. Definitions for transcript_oc function + + def transcript_oc(Ya,ADa,Yb,ADb): + result = o_cat(lv_cat(Ya,ADa),lv_cat(Yb,ADb)) + return result + +A.3.7. Test vectors for transcript_oc function + + transcript_oc(b"123", b"PartyA", b"234",b"PartyB"): + (length: 24 bytes) + 6f6303323334065061727479420331323306506172747941 + transcript_oc(b"3456",b"PartyA",b"2345",b"PartyB"): + (length: 26 bytes) + 6f63043334353606506172747941043233343506506172747942 + +A.3.7.1. Testvectors as JSON file encoded as BASE64 + + #eyJiJzEyMyciOiAiMzEzMjMzIiwgImInMjM0JyI6ICIzMjMzMzQiLCAiYidQYXJ0eU + #EnIjogIjUwNjE3Mjc0Nzk0MSIsICJiJ1BhcnR5QiciOiAiNTA2MTcyNzQ3OTQyIiwg + #ImInMzQ1NiciOiAiMzMzNDM1MzYiLCAiYicyMzQ1JyI6ICIzMjMzMzQzNSIsICJ0cm + #Fuc2NyaXB0X29jKGInMTIzJyxiJ1BhcnR5QScsYicyMzQnLGInUGFydHlCJykiOiAi + #NkY2MzAzMzIzMzM0MDY1MDYxNzI3NDc5NDIwMzMxMzIzMzA2NTA2MTcyNzQ3OTQxIi + #wgInRyYW5zY3JpcHRfb2MoYiczNDU2JyxiJ1BhcnR5QScsYicyMzQ1JyxiJ1BhcnR5 + #QicpIjogIjZGNjMwNDMzMzQzNTM2MDY1MDYxNzI3NDc5NDEwNDMyMzMzNDM1MDY1MD + #YxNzI3NDc5NDIifQ== + +A.4. Decoding and Encoding functions according to RFC7748 + + def decodeLittleEndian(b, bits): + return sum([b[i] << 8*i for i in range((bits+7)/8)]) + + def decodeUCoordinate(u, bits): + u_list = [ord(b) for b in u] + # Ignore any unused bits. + if bits % 8: + u_list[-1] &= (1<<(bits%8))-1 + return decodeLittleEndian(u_list, bits) + + def encodeUCoordinate(u, bits): + return ''.join([chr((u >> 8*i) & 0xff) + for i in range((bits+7)/8)]) + +A.5. Elligator 2 reference implementation + + The Elligator 2 map requires a non-square field element Z which shall + be calculated as follows. + + def find_z_ell2(F): + # Find nonsquare for Elligator2 + # Argument: F, a field object, e.g., F = GF(2^255 - 19) + ctr = F.gen() + while True: + for Z_cand in (F(ctr), F(-ctr)): + # Z must be a non-square in F. + if is_square(Z_cand): + continue + return Z_cand + ctr += 1 + + The values of the non-square Z only depend on the curve. The + algorithm above results in a value of Z = 2 for Curve25519 and Z=-1 + for Ed448. + + The following code maps a field element r to an encoded field element + which is a valid u-coordinate of a Montgomery curve with curve + parameter A. + + def elligator2(r, q, A, field_size_bits): + # Inputs: field element r, field order q, + # curve parameter A and field size in bits + Fq = GF(q); A = Fq(A); B = Fq(1); + + # get non-square z as specified in the hash2curve draft. + z = Fq(find_z_ell2(Fq)) + powerForLegendreSymbol = floor((q-1)/2) + + v = - A / (1 + z * r^2) + epsilon = (v^3 + A * v^2 + B * v)^powerForLegendreSymbol + x = epsilon * v - (1 - epsilon) * A/2 + return encodeUCoordinate(Integer(x), field_size_bits) + +Appendix B. Test vectors + +B.1. Test vector for CPace using group X25519 and hash SHA-512 + +B.1.1. Test vectors for calculate_generator with group X25519 + + Inputs + H = SHA-512 with input block size 128 bytes. + PRS = b'Password' ; ZPAD length: 109 ; DSI = b'CPace255' + CI = b'oc\x0bB_responder\x0bA_initiator' + CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72 + sid = 7e4b4791d6a8ef019b936c79fb7f2c57 + Outputs + generator_string(G.DSI,PRS,CI,sid,H.s_in_bytes): + (length: 172 bytes) + 0843506163653235350850617373776f72646d000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000001a6f630b425f726573706f6e + 6465720b415f696e69746961746f72107e4b4791d6a8ef019b936c79 + fb7f2c57 + hash generator string: (length: 32 bytes) + 92806dc608984dbf4e4aae478c6ec453ae979cc01ecc1a2a7cf49f5c + ee56551b + decoded field element of 255 bits: (length: 32 bytes) + 92806dc608984dbf4e4aae478c6ec453ae979cc01ecc1a2a7cf49f5c + ee56551b + generator g: (length: 32 bytes) + 64e8099e3ea682cfdc5cb665c057ebb514d06bf23ebc9f743b51b822 + 42327074 + +B.1.1.1. Testvectors as JSON file encoded as BASE64 + + #eyJIIjogIlNIQS01MTIiLCAiSC5zX2luX2J5dGVzIjogMTI4LCAiUFJTIjogIjUwNj + #E3MzczNzc2RjcyNjQiLCAiWlBBRCBsZW5ndGgiOiAxMDksICJEU0kiOiAiNDM1MDYx + #NjM2NTMyMzUzNSIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NTczNzA2RjZFNjQ2NTcyME + #I0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI3RTRCNDc5MUQ2QThFRjAx + #OUI5MzZDNzlGQjdGMkM1NyIsICJnZW5lcmF0b3Jfc3RyaW5nKEcuRFNJLFBSUyxDSS + #xzaWQsSC5zX2luX2J5dGVzKSI6ICIwODQzNTA2MTYzNjUzMjM1MzUwODUwNjE3Mzcz + #Nzc2RjcyNjQ2RDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMUE2RjYzMEI0MjVGNzI2NTczNz + #A2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyMTA3RTRCNDc5MUQ2QThF + #RjAxOUI5MzZDNzlGQjdGMkM1NyIsICJoYXNoIGdlbmVyYXRvciBzdHJpbmciOiAiOT + #I4MDZEQzYwODk4NERCRjRFNEFBRTQ3OEM2RUM0NTNBRTk3OUNDMDFFQ0MxQTJBN0NG + #NDlGNUNFRTU2NTUxQiIsICJkZWNvZGVkIGZpZWxkIGVsZW1lbnQgb2YgMjU1IGJpdH + #MiOiAiOTI4MDZEQzYwODk4NERCRjRFNEFBRTQ3OEM2RUM0NTNBRTk3OUNDMDFFQ0Mx + #QTJBN0NGNDlGNUNFRTU2NTUxQiIsICJnZW5lcmF0b3IgZyI6ICI2NEU4MDk5RTNFQT + #Y4MkNGREM1Q0I2NjVDMDU3RUJCNTE0RDA2QkYyM0VCQzlGNzQzQjUxQjgyMjQyMzI3 + #MDc0In0= + +B.1.2. Test vector for message from A + + Inputs + ADa = b'ADa' + ya (little endian): (length: 32 bytes) + 21b4f4bd9e64ed355c3eb676a28ebedaf6d8f17bdc365995b3190971 + 53044080 + Outputs + Ya: (length: 32 bytes) + 1b02dad6dbd29a07b6d28c9e04cb2f184f0734350e32bb7e62ff9dbc + fdb63d15 + +B.1.3. Test vector for message from B + + Inputs + ADb = b'ADb' + yb (little endian): (length: 32 bytes) + 848b0779ff415f0af4ea14df9dd1d3c29ac41d836c7808896c4eba19 + c51ac40a + Outputs + Yb: (length: 32 bytes) + 20cda5955f82c4931545bcbf40758ce1010d7db4db2a907013d79c7a + 8fcf957f + +B.1.4. Test vector for secret points K + + scalar_mult_vfy(ya,Yb): (length: 32 bytes) + f97fdfcfff1c983ed6283856a401de3191ca919902b323c5f950c970 + 3df7297a + scalar_mult_vfy(yb,Ya): (length: 32 bytes) + f97fdfcfff1c983ed6283856a401de3191ca919902b323c5f950c970 + 3df7297a + +B.1.5. Test vector for ISK calculation initiator/responder + + transcript_ir(Ya,ADa,Yb,ADb): (length: 74 bytes) + 201b02dad6dbd29a07b6d28c9e04cb2f184f0734350e32bb7e62ff9d + bcfdb63d15034144612020cda5955f82c4931545bcbf40758ce1010d + 7db4db2a907013d79c7a8fcf957f03414462 + DSI = G.DSI_ISK, b'CPace255_ISK': (length: 12 bytes) + 43506163653235355f49534b + lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb): + (length: 137 bytes) + 0c43506163653235355f49534b107e4b4791d6a8ef019b936c79fb7f + 2c5720f97fdfcfff1c983ed6283856a401de3191ca919902b323c5f9 + 50c9703df7297a201b02dad6dbd29a07b6d28c9e04cb2f184f073435 + 0e32bb7e62ff9dbcfdb63d15034144612020cda5955f82c4931545bc + bf40758ce1010d7db4db2a907013d79c7a8fcf957f03414462 + ISK result: (length: 64 bytes) + a051ee5ee2499d16da3f69f430218b8ea94a18a45b67f9e86495b382 + c33d14a5c38cecc0cc834f960e39e0d1bf7d76b9ef5d54eecc5e0f38 + 6c97ad12da8c3d5f + +B.1.6. Test vector for ISK calculation parallel execution + + transcript_oc(Ya,ADa,Yb,ADb): (length: 76 bytes) + 6f632020cda5955f82c4931545bcbf40758ce1010d7db4db2a907013 + d79c7a8fcf957f03414462201b02dad6dbd29a07b6d28c9e04cb2f18 + 4f0734350e32bb7e62ff9dbcfdb63d1503414461 + DSI = G.DSI_ISK, b'CPace255_ISK': (length: 12 bytes) + 43506163653235355f49534b + lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb): + (length: 139 bytes) + 0c43506163653235355f49534b107e4b4791d6a8ef019b936c79fb7f + 2c5720f97fdfcfff1c983ed6283856a401de3191ca919902b323c5f9 + 50c9703df7297a6f632020cda5955f82c4931545bcbf40758ce1010d + 7db4db2a907013d79c7a8fcf957f03414462201b02dad6dbd29a07b6 + d28c9e04cb2f184f0734350e32bb7e62ff9dbcfdb63d1503414461 + ISK result: (length: 64 bytes) + 5cc27e49679423f81a37d7521d9fb1327c840d2ea4a1543652e7de5c + abb89ebad27d24761b3288a3fd5764b441ecb78d30abc26161ff45ea + 297bb311dde04727 + +B.1.7. Test vector for optional output of session id + + H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + f7ae11ac3ee85c3c42d8bd51ba823fbe17158f43d34a1296f1cb2567 + bcc71dc8b201a134b566b468aad8fd04f02f96e3caf9d5601f7ed760 + a0a951a5a861b5e7 + H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + a38389e34fa492788c1df43b06b427710491174e53c33b01362a490d + 116fe1b7e870aa6e2a7fc018725e3b7f969f7508042e44cd3863f39a + a75026a190d1902b + +B.1.8. Corresponding C programming language initializers + + const unsigned char tc_PRS[] = { + 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64, + }; + const unsigned char tc_CI[] = { + 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64, + 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74, + 0x6f,0x72, + }; + const unsigned char tc_sid[] = { + 0x7e,0x4b,0x47,0x91,0xd6,0xa8,0xef,0x01,0x9b,0x93,0x6c,0x79, + 0xfb,0x7f,0x2c,0x57, + }; + const unsigned char tc_g[] = { + 0x64,0xe8,0x09,0x9e,0x3e,0xa6,0x82,0xcf,0xdc,0x5c,0xb6,0x65, + 0xc0,0x57,0xeb,0xb5,0x14,0xd0,0x6b,0xf2,0x3e,0xbc,0x9f,0x74, + 0x3b,0x51,0xb8,0x22,0x42,0x32,0x70,0x74, + }; + const unsigned char tc_ya[] = { + 0x21,0xb4,0xf4,0xbd,0x9e,0x64,0xed,0x35,0x5c,0x3e,0xb6,0x76, + 0xa2,0x8e,0xbe,0xda,0xf6,0xd8,0xf1,0x7b,0xdc,0x36,0x59,0x95, + 0xb3,0x19,0x09,0x71,0x53,0x04,0x40,0x80, + }; + const unsigned char tc_ADa[] = { + 0x41,0x44,0x61, + }; + const unsigned char tc_Ya[] = { + 0x1b,0x02,0xda,0xd6,0xdb,0xd2,0x9a,0x07,0xb6,0xd2,0x8c,0x9e, + 0x04,0xcb,0x2f,0x18,0x4f,0x07,0x34,0x35,0x0e,0x32,0xbb,0x7e, + 0x62,0xff,0x9d,0xbc,0xfd,0xb6,0x3d,0x15, + }; + const unsigned char tc_yb[] = { + 0x84,0x8b,0x07,0x79,0xff,0x41,0x5f,0x0a,0xf4,0xea,0x14,0xdf, + 0x9d,0xd1,0xd3,0xc2,0x9a,0xc4,0x1d,0x83,0x6c,0x78,0x08,0x89, + 0x6c,0x4e,0xba,0x19,0xc5,0x1a,0xc4,0x0a, + }; + const unsigned char tc_ADb[] = { + 0x41,0x44,0x62, + }; + const unsigned char tc_Yb[] = { + 0x20,0xcd,0xa5,0x95,0x5f,0x82,0xc4,0x93,0x15,0x45,0xbc,0xbf, + 0x40,0x75,0x8c,0xe1,0x01,0x0d,0x7d,0xb4,0xdb,0x2a,0x90,0x70, + 0x13,0xd7,0x9c,0x7a,0x8f,0xcf,0x95,0x7f, + }; + const unsigned char tc_K[] = { + 0xf9,0x7f,0xdf,0xcf,0xff,0x1c,0x98,0x3e,0xd6,0x28,0x38,0x56, + 0xa4,0x01,0xde,0x31,0x91,0xca,0x91,0x99,0x02,0xb3,0x23,0xc5, + 0xf9,0x50,0xc9,0x70,0x3d,0xf7,0x29,0x7a, + }; + const unsigned char tc_ISK_IR[] = { + 0xa0,0x51,0xee,0x5e,0xe2,0x49,0x9d,0x16,0xda,0x3f,0x69,0xf4, + 0x30,0x21,0x8b,0x8e,0xa9,0x4a,0x18,0xa4,0x5b,0x67,0xf9,0xe8, + 0x64,0x95,0xb3,0x82,0xc3,0x3d,0x14,0xa5,0xc3,0x8c,0xec,0xc0, + 0xcc,0x83,0x4f,0x96,0x0e,0x39,0xe0,0xd1,0xbf,0x7d,0x76,0xb9, + 0xef,0x5d,0x54,0xee,0xcc,0x5e,0x0f,0x38,0x6c,0x97,0xad,0x12, + 0xda,0x8c,0x3d,0x5f, + }; + const unsigned char tc_ISK_SY[] = { + 0x5c,0xc2,0x7e,0x49,0x67,0x94,0x23,0xf8,0x1a,0x37,0xd7,0x52, + 0x1d,0x9f,0xb1,0x32,0x7c,0x84,0x0d,0x2e,0xa4,0xa1,0x54,0x36, + 0x52,0xe7,0xde,0x5c,0xab,0xb8,0x9e,0xba,0xd2,0x7d,0x24,0x76, + 0x1b,0x32,0x88,0xa3,0xfd,0x57,0x64,0xb4,0x41,0xec,0xb7,0x8d, + 0x30,0xab,0xc2,0x61,0x61,0xff,0x45,0xea,0x29,0x7b,0xb3,0x11, + 0xdd,0xe0,0x47,0x27, + }; + const unsigned char tc_ISK_SY[] = { + 0x5c,0xc2,0x7e,0x49,0x67,0x94,0x23,0xf8,0x1a,0x37,0xd7,0x52, + 0x1d,0x9f,0xb1,0x32,0x7c,0x84,0x0d,0x2e,0xa4,0xa1,0x54,0x36, + 0x52,0xe7,0xde,0x5c,0xab,0xb8,0x9e,0xba,0xd2,0x7d,0x24,0x76, + 0x1b,0x32,0x88,0xa3,0xfd,0x57,0x64,0xb4,0x41,0xec,0xb7,0x8d, + 0x30,0xab,0xc2,0x61,0x61,0xff,0x45,0xea,0x29,0x7b,0xb3,0x11, + 0xdd,0xe0,0x47,0x27, + }; + const unsigned char tc_sid_out_ir[] = { + 0xf7,0xae,0x11,0xac,0x3e,0xe8,0x5c,0x3c,0x42,0xd8,0xbd,0x51, + 0xba,0x82,0x3f,0xbe,0x17,0x15,0x8f,0x43,0xd3,0x4a,0x12,0x96, + 0xf1,0xcb,0x25,0x67,0xbc,0xc7,0x1d,0xc8,0xb2,0x01,0xa1,0x34, + 0xb5,0x66,0xb4,0x68,0xaa,0xd8,0xfd,0x04,0xf0,0x2f,0x96,0xe3, + 0xca,0xf9,0xd5,0x60,0x1f,0x7e,0xd7,0x60,0xa0,0xa9,0x51,0xa5, + 0xa8,0x61,0xb5,0xe7, + }; + const unsigned char tc_sid_out_oc[] = { + 0xa3,0x83,0x89,0xe3,0x4f,0xa4,0x92,0x78,0x8c,0x1d,0xf4,0x3b, + 0x06,0xb4,0x27,0x71,0x04,0x91,0x17,0x4e,0x53,0xc3,0x3b,0x01, + 0x36,0x2a,0x49,0x0d,0x11,0x6f,0xe1,0xb7,0xe8,0x70,0xaa,0x6e, + 0x2a,0x7f,0xc0,0x18,0x72,0x5e,0x3b,0x7f,0x96,0x9f,0x75,0x08, + 0x04,0x2e,0x44,0xcd,0x38,0x63,0xf3,0x9a,0xa7,0x50,0x26,0xa1, + 0x90,0xd1,0x90,0x2b, + }; + +B.1.9. Testvectors as JSON file encoded as BASE64 + + #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT + #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI3 + #RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJnIjogIjY0RTgwOTlFM0 + #VBNjgyQ0ZEQzVDQjY2NUMwNTdFQkI1MTREMDZCRjIzRUJDOUY3NDNCNTFCODIyNDIz + #MjcwNzQiLCAieWEiOiAiMjFCNEY0QkQ5RTY0RUQzNTVDM0VCNjc2QTI4RUJFREFGNk + #Q4RjE3QkRDMzY1OTk1QjMxOTA5NzE1MzA0NDA4MCIsICJBRGEiOiAiNDE0NDYxIiwg + #IllhIjogIjFCMDJEQUQ2REJEMjlBMDdCNkQyOEM5RTA0Q0IyRjE4NEYwNzM0MzUwRT + #MyQkI3RTYyRkY5REJDRkRCNjNEMTUiLCAieWIiOiAiODQ4QjA3NzlGRjQxNUYwQUY0 + #RUExNERGOUREMUQzQzI5QUM0MUQ4MzZDNzgwODg5NkM0RUJBMTlDNTFBQzQwQSIsIC + #JBRGIiOiAiNDE0NDYyIiwgIlliIjogIjIwQ0RBNTk1NUY4MkM0OTMxNTQ1QkNCRjQw + #NzU4Q0UxMDEwRDdEQjREQjJBOTA3MDEzRDc5QzdBOEZDRjk1N0YiLCAiSyI6ICJGOT + #dGREZDRkZGMUM5ODNFRDYyODM4NTZBNDAxREUzMTkxQ0E5MTk5MDJCMzIzQzVGOTUw + #Qzk3MDNERjcyOTdBIiwgIklTS19JUiI6ICJBMDUxRUU1RUUyNDk5RDE2REEzRjY5Rj + #QzMDIxOEI4RUE5NEExOEE0NUI2N0Y5RTg2NDk1QjM4MkMzM0QxNEE1QzM4Q0VDQzBD + #QzgzNEY5NjBFMzlFMEQxQkY3RDc2QjlFRjVENTRFRUNDNUUwRjM4NkM5N0FEMTJEQT + #hDM0Q1RiIsICJJU0tfU1kiOiAiNUNDMjdFNDk2Nzk0MjNGODFBMzdENzUyMUQ5RkIx + #MzI3Qzg0MEQyRUE0QTE1NDM2NTJFN0RFNUNBQkI4OUVCQUQyN0QyNDc2MUIzMjg4QT + #NGRDU3NjRCNDQxRUNCNzhEMzBBQkMyNjE2MUZGNDVFQTI5N0JCMzExRERFMDQ3Mjci + #LCAic2lkX291dHB1dF9pciI6ICJGN0FFMTFBQzNFRTg1QzNDNDJEOEJENTFCQTgyM0 + #ZCRTE3MTU4RjQzRDM0QTEyOTZGMUNCMjU2N0JDQzcxREM4QjIwMUExMzRCNTY2QjQ2 + #OEFBRDhGRDA0RjAyRjk2RTNDQUY5RDU2MDFGN0VENzYwQTBBOTUxQTVBODYxQjVFNy + #IsICJzaWRfb3V0cHV0X29jIjogIkEzODM4OUUzNEZBNDkyNzg4QzFERjQzQjA2QjQy + #NzcxMDQ5MTE3NEU1M0MzM0IwMTM2MkE0OTBEMTE2RkUxQjdFODcwQUE2RTJBN0ZDMD + #E4NzI1RTNCN0Y5NjlGNzUwODA0MkU0NENEMzg2M0YzOUFBNzUwMjZBMTkwRDE5MDJC + #In0= + +B.1.10. Test vectors for G_X25519.scalar_mult_vfy: low order points + + Test vectors for which G_X25519.scalar_mult_vfy(s_in,ux) must return + the neutral element or would return the neutral element if bit #255 + of field element representation was not correctly cleared. (The + decodeUCoordinate function from RFC7748 mandates clearing bit #255 + for field element representations for use in the X25519 function.). + + u0: 0000000000000000000000000000000000000000000000000000000000000000 + u1: 0100000000000000000000000000000000000000000000000000000000000000 + u2: ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f + u3: e0eb7a7c3b41b8ae1656e3faf19fc46ada098deb9c32b1fd866205165f49b800 + u4: 5f9c95bca3508c24b1d0b1559c83ef5b04445cc4581c8e86d8224eddd09f1157 + u5: edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f + u6: daffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff + u7: eeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f + u8: dbffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff + u9: d9ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff + ua: cdeb7a7c3b41b8ae1656e3faf19fc46ada098deb9c32b1fd866205165f49b880 + ub: 4c9c95bca3508c24b1d0b1559c83ef5b04445cc4581c8e86d8224eddd09f11d7 + + u0 ... ub MUST be verified to produce the correct results q0 ... qb: + + Additionally, u0,u1,u2,u3,u4,u5 and u7 MUST trigger the abort case + when included in message from A or B. + + s = af46e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449aff + qN = G_X25519.scalar_mult_vfy(s, uX) + q0: 0000000000000000000000000000000000000000000000000000000000000000 + q1: 0000000000000000000000000000000000000000000000000000000000000000 + q2: 0000000000000000000000000000000000000000000000000000000000000000 + q3: 0000000000000000000000000000000000000000000000000000000000000000 + q4: 0000000000000000000000000000000000000000000000000000000000000000 + q5: 0000000000000000000000000000000000000000000000000000000000000000 + q6: d8e2c776bbacd510d09fd9278b7edcd25fc5ae9adfba3b6e040e8d3b71b21806 + q7: 0000000000000000000000000000000000000000000000000000000000000000 + q8: c85c655ebe8be44ba9c0ffde69f2fe10194458d137f09bbff725ce58803cdb38 + q9: db64dafa9b8fdd136914e61461935fe92aa372cb056314e1231bc4ec12417456 + qa: e062dcd5376d58297be2618c7498f55baa07d7e03184e8aada20bca28888bf7a + qb: 993c6ad11c4c29da9a56f7691fd0ff8d732e49de6250b6c2e80003ff4629a175 + +B.1.10.1. Testvectors as JSON file encoded as BASE64 + + #eyJJbnZhbGlkIFkwIjogIjAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAiLCAiSW52YWxpZCBZMSI6ICIw + #MTAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwIiwgIkludmFsaWQgWTIiOiAiRUNGRkZGRkZGRkZGRkZGRkZG + #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkY3RiIsIC + #JJbnZhbGlkIFkzIjogIkUwRUI3QTdDM0I0MUI4QUUxNjU2RTNGQUYxOUZDNDZBREEw + #OThERUI5QzMyQjFGRDg2NjIwNTE2NUY0OUI4MDAiLCAiSW52YWxpZCBZNCI6ICI1Rj + #lDOTVCQ0EzNTA4QzI0QjFEMEIxNTU5QzgzRUY1QjA0NDQ1Q0M0NTgxQzhFODZEODIy + #NEVEREQwOUYxMTU3IiwgIkludmFsaWQgWTUiOiAiRURGRkZGRkZGRkZGRkZGRkZGRk + #ZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkY3RiIsICJJ + #bnZhbGlkIFk2IjogIkRBRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRk + #ZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkYiLCAiSW52YWxpZCBZNyI6ICJFRUZG + #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRk + #ZGRkZGRkZGRjdGIiwgIkludmFsaWQgWTgiOiAiREJGRkZGRkZGRkZGRkZGRkZGRkZG + #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRiIsICJJbn + #ZhbGlkIFk5IjogIkQ5RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZG + #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkYiLCAiSW52YWxpZCBZMTAiOiAiQ0RFQj + #dBN0MzQjQxQjhBRTE2NTZFM0ZBRjE5RkM0NkFEQTA5OERFQjlDMzJCMUZEODY2MjA1 + #MTY1RjQ5Qjg4MCIsICJJbnZhbGlkIFkxMSI6ICI0QzlDOTVCQ0EzNTA4QzI0QjFEME + #IxNTU5QzgzRUY1QjA0NDQ1Q0M0NTgxQzhFODZEODIyNEVEREQwOUYxMUQ3In0= + +B.2. Test vector for CPace using group X448 and hash SHAKE-256 + +B.2.1. Test vectors for calculate_generator with group X448 + + Inputs + H = SHAKE-256 with input block size 136 bytes. + PRS = b'Password' ; ZPAD length: 117 ; DSI = b'CPace448' + CI = b'oc\x0bB_responder\x0bA_initiator' + CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72 + sid = 5223e0cdc45d6575668d64c552004124 + Outputs + generator_string(G.DSI,PRS,CI,sid,H.s_in_bytes): + (length: 180 bytes) + 0843506163653434380850617373776f726475000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 0000000000000000000000000000000000000000000000001a6f630b + 425f726573706f6e6465720b415f696e69746961746f72105223e0cd + c45d6575668d64c552004124 + hash generator string: (length: 56 bytes) + 98b713f84529194d719a7d86cb0f504b8afeb05354d68747e18b2e7c + c8b6da526085e4263bd8bea7d69e479ebad09e30ae062e5d089da7f3 + decoded field element of 448 bits: (length: 56 bytes) + 98b713f84529194d719a7d86cb0f504b8afeb05354d68747e18b2e7c + c8b6da526085e4263bd8bea7d69e479ebad09e30ae062e5d089da7f3 + generator g: (length: 56 bytes) + e293b7ccf61ca7eb928a26391cf38b660f874a001fdf0bf3a91fd182 + f2b6d83e61a9377ede127eba7e0d4c08592eaff33d4aa705d6ce54bb + +B.2.1.1. Testvectors as JSON file encoded as BASE64 + + #eyJIIjogIlNIQUtFLTI1NiIsICJILnNfaW5fYnl0ZXMiOiAxMzYsICJQUlMiOiAiNT + #A2MTczNzM3NzZGNzI2NCIsICJaUEFEIGxlbmd0aCI6IDExNywgIkRTSSI6ICI0MzUw + #NjE2MzY1MzQzNDM4IiwgIkNJIjogIjZGNjMwQjQyNUY3MjY1NzM3MDZGNkU2NDY1Nz + #IwQjQxNUY2OTZFNjk3NDY5NjE3NDZGNzIiLCAic2lkIjogIjUyMjNFMENEQzQ1RDY1 + #NzU2NjhENjRDNTUyMDA0MTI0IiwgImdlbmVyYXRvcl9zdHJpbmcoRy5EU0ksUFJTLE + #NJLHNpZCxILnNfaW5fYnl0ZXMpIjogIjA4NDM1MDYxNjM2NTM0MzQzODA4NTA2MTcz + #NzM3NzZGNzI2NDc1MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMU + #E2RjYzMEI0MjVGNzI2NTczNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2 + #RjcyMTA1MjIzRTBDREM0NUQ2NTc1NjY4RDY0QzU1MjAwNDEyNCIsICJoYXNoIGdlbm + #VyYXRvciBzdHJpbmciOiAiOThCNzEzRjg0NTI5MTk0RDcxOUE3RDg2Q0IwRjUwNEI4 + #QUZFQjA1MzU0RDY4NzQ3RTE4QjJFN0NDOEI2REE1MjYwODVFNDI2M0JEOEJFQTdENj + #lFNDc5RUJBRDA5RTMwQUUwNjJFNUQwODlEQTdGMyIsICJkZWNvZGVkIGZpZWxkIGVs + #ZW1lbnQgb2YgNDQ4IGJpdHMiOiAiOThCNzEzRjg0NTI5MTk0RDcxOUE3RDg2Q0IwRj + #UwNEI4QUZFQjA1MzU0RDY4NzQ3RTE4QjJFN0NDOEI2REE1MjYwODVFNDI2M0JEOEJF + #QTdENjlFNDc5RUJBRDA5RTMwQUUwNjJFNUQwODlEQTdGMyIsICJnZW5lcmF0b3IgZy + #I6ICJFMjkzQjdDQ0Y2MUNBN0VCOTI4QTI2MzkxQ0YzOEI2NjBGODc0QTAwMUZERjBC + #RjNBOTFGRDE4MkYyQjZEODNFNjFBOTM3N0VERTEyN0VCQTdFMEQ0QzA4NTkyRUFGRj + #MzRDRBQTcwNUQ2Q0U1NEJCIn0= + +B.2.2. Test vector for message from A + + Inputs + ADa = b'ADa' + ya (little endian): (length: 56 bytes) + 21b4f4bd9e64ed355c3eb676a28ebedaf6d8f17bdc365995b3190971 + 53044080516bd083bfcce66121a3072646994c8430cc382b8dc543e8 + Outputs + Ya: (length: 56 bytes) + 7f645772cc209bf9fd9d76dbb10283bea71b12235e3bb21878d5e56a + 70506e165743a632de98eca9932c5d2efe36500a59b2fdaed0d8a148 + +B.2.3. Test vector for message from B + + Inputs + ADb = b'ADb' + yb (little endian): (length: 56 bytes) + 848b0779ff415f0af4ea14df9dd1d3c29ac41d836c7808896c4eba19 + c51ac40a439caf5e61ec88c307c7d619195229412eaa73fb2a5ea20d + Outputs + Yb: (length: 56 bytes) + a4690a0750c42b288ddd0ba08e3f4902dfe70bae5c9e2c6ee95844de + f2692be77646b20d3b429f8da00d21433ee0891c667658d8d0c48e38 + +B.2.4. Test vector for secret points K + + scalar_mult_vfy(ya,Yb): (length: 56 bytes) + db3fff9da59576715b04d4df8dc8d18db2430e57bbed337dbeee5bb2 + d6ab6ceddc9c75c5c0b17fad7eb724daa12f8f1903dd6c2cede6135a + scalar_mult_vfy(yb,Ya): (length: 56 bytes) + db3fff9da59576715b04d4df8dc8d18db2430e57bbed337dbeee5bb2 + d6ab6ceddc9c75c5c0b17fad7eb724daa12f8f1903dd6c2cede6135a + +B.2.5. Test vector for ISK calculation initiator/responder + + transcript_ir(Ya,ADa,Yb,ADb): (length: 122 bytes) + 387f645772cc209bf9fd9d76dbb10283bea71b12235e3bb21878d5e5 + 6a70506e165743a632de98eca9932c5d2efe36500a59b2fdaed0d8a1 + 480341446138a4690a0750c42b288ddd0ba08e3f4902dfe70bae5c9e + 2c6ee95844def2692be77646b20d3b429f8da00d21433ee0891c6676 + 58d8d0c48e3803414462 + DSI = G.DSI_ISK, b'CPace448_ISK': (length: 12 bytes) + 43506163653434385f49534b + lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb): + (length: 209 bytes) + 0c43506163653434385f49534b105223e0cdc45d6575668d64c55200 + 412438db3fff9da59576715b04d4df8dc8d18db2430e57bbed337dbe + ee5bb2d6ab6ceddc9c75c5c0b17fad7eb724daa12f8f1903dd6c2ced + e6135a387f645772cc209bf9fd9d76dbb10283bea71b12235e3bb218 + 78d5e56a70506e165743a632de98eca9932c5d2efe36500a59b2fdae + d0d8a1480341446138a4690a0750c42b288ddd0ba08e3f4902dfe70b + ae5c9e2c6ee95844def2692be77646b20d3b429f8da00d21433ee089 + 1c667658d8d0c48e3803414462 + ISK result: (length: 64 bytes) + 599892a2078a8c988181625e1e5e5f7a6163f7d72f21b93ebefba0f1 + 7ff7ea3aa0594bd569cf74264157b3c0087bdccf2f59c77156628487 + f5ca1645b8e9d05b + +B.2.6. Test vector for ISK calculation parallel execution + + transcript_oc(Ya,ADa,Yb,ADb): (length: 124 bytes) + 6f6338a4690a0750c42b288ddd0ba08e3f4902dfe70bae5c9e2c6ee9 + 5844def2692be77646b20d3b429f8da00d21433ee0891c667658d8d0 + c48e3803414462387f645772cc209bf9fd9d76dbb10283bea71b1223 + 5e3bb21878d5e56a70506e165743a632de98eca9932c5d2efe36500a + 59b2fdaed0d8a14803414461 + DSI = G.DSI_ISK, b'CPace448_ISK': (length: 12 bytes) + 43506163653434385f49534b + lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb): + (length: 211 bytes) + 0c43506163653434385f49534b105223e0cdc45d6575668d64c55200 + 412438db3fff9da59576715b04d4df8dc8d18db2430e57bbed337dbe + ee5bb2d6ab6ceddc9c75c5c0b17fad7eb724daa12f8f1903dd6c2ced + e6135a6f6338a4690a0750c42b288ddd0ba08e3f4902dfe70bae5c9e + 2c6ee95844def2692be77646b20d3b429f8da00d21433ee0891c6676 + 58d8d0c48e3803414462387f645772cc209bf9fd9d76dbb10283bea7 + 1b12235e3bb21878d5e56a70506e165743a632de98eca9932c5d2efe + 36500a59b2fdaed0d8a14803414461 + ISK result: (length: 64 bytes) + 3ac73f03030296aa591f01326b18afa47e1189129cd06ae8dfb05e6e + b1310cde948b59eef0755365c06a339266afe594948c56a538d98a65 + 767113938a9a78d8 + +B.2.7. Test vector for optional output of session id + + H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + 00a2333a79481abe71efd6594d7bbaac55c808482e869c9b65c4b53d + 7100d3da8f3cabd59fa0c1f22d6d2f9ac0c093962292798fca2c0b93 + 268974cad75d575a + H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + a1ce90537a8d53b06d77e79fe719461cc5ed8300d21d1866a59f9638 + 601833f57a8b5e88db9a52abfa1b4e8a651a400bc9205082aad81eb3 + 11c44373b9a19eff + +B.2.8. Corresponding C programming language initializers + + const unsigned char tc_PRS[] = { + 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64, + }; + const unsigned char tc_CI[] = { + 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64, + 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74, + 0x6f,0x72, + }; + const unsigned char tc_sid[] = { + 0x52,0x23,0xe0,0xcd,0xc4,0x5d,0x65,0x75,0x66,0x8d,0x64,0xc5, + 0x52,0x00,0x41,0x24, + }; + const unsigned char tc_g[] = { + 0xe2,0x93,0xb7,0xcc,0xf6,0x1c,0xa7,0xeb,0x92,0x8a,0x26,0x39, + 0x1c,0xf3,0x8b,0x66,0x0f,0x87,0x4a,0x00,0x1f,0xdf,0x0b,0xf3, + 0xa9,0x1f,0xd1,0x82,0xf2,0xb6,0xd8,0x3e,0x61,0xa9,0x37,0x7e, + 0xde,0x12,0x7e,0xba,0x7e,0x0d,0x4c,0x08,0x59,0x2e,0xaf,0xf3, + 0x3d,0x4a,0xa7,0x05,0xd6,0xce,0x54,0xbb, + }; + const unsigned char tc_ya[] = { + 0x21,0xb4,0xf4,0xbd,0x9e,0x64,0xed,0x35,0x5c,0x3e,0xb6,0x76, + 0xa2,0x8e,0xbe,0xda,0xf6,0xd8,0xf1,0x7b,0xdc,0x36,0x59,0x95, + 0xb3,0x19,0x09,0x71,0x53,0x04,0x40,0x80,0x51,0x6b,0xd0,0x83, + 0xbf,0xcc,0xe6,0x61,0x21,0xa3,0x07,0x26,0x46,0x99,0x4c,0x84, + 0x30,0xcc,0x38,0x2b,0x8d,0xc5,0x43,0xe8, + }; + const unsigned char tc_ADa[] = { + 0x41,0x44,0x61, + }; + const unsigned char tc_Ya[] = { + 0x7f,0x64,0x57,0x72,0xcc,0x20,0x9b,0xf9,0xfd,0x9d,0x76,0xdb, + 0xb1,0x02,0x83,0xbe,0xa7,0x1b,0x12,0x23,0x5e,0x3b,0xb2,0x18, + 0x78,0xd5,0xe5,0x6a,0x70,0x50,0x6e,0x16,0x57,0x43,0xa6,0x32, + 0xde,0x98,0xec,0xa9,0x93,0x2c,0x5d,0x2e,0xfe,0x36,0x50,0x0a, + 0x59,0xb2,0xfd,0xae,0xd0,0xd8,0xa1,0x48, + }; + const unsigned char tc_yb[] = { + 0x84,0x8b,0x07,0x79,0xff,0x41,0x5f,0x0a,0xf4,0xea,0x14,0xdf, + 0x9d,0xd1,0xd3,0xc2,0x9a,0xc4,0x1d,0x83,0x6c,0x78,0x08,0x89, + 0x6c,0x4e,0xba,0x19,0xc5,0x1a,0xc4,0x0a,0x43,0x9c,0xaf,0x5e, + 0x61,0xec,0x88,0xc3,0x07,0xc7,0xd6,0x19,0x19,0x52,0x29,0x41, + 0x2e,0xaa,0x73,0xfb,0x2a,0x5e,0xa2,0x0d, + }; + const unsigned char tc_ADb[] = { + 0x41,0x44,0x62, + }; + const unsigned char tc_Yb[] = { + 0xa4,0x69,0x0a,0x07,0x50,0xc4,0x2b,0x28,0x8d,0xdd,0x0b,0xa0, + 0x8e,0x3f,0x49,0x02,0xdf,0xe7,0x0b,0xae,0x5c,0x9e,0x2c,0x6e, + 0xe9,0x58,0x44,0xde,0xf2,0x69,0x2b,0xe7,0x76,0x46,0xb2,0x0d, + 0x3b,0x42,0x9f,0x8d,0xa0,0x0d,0x21,0x43,0x3e,0xe0,0x89,0x1c, + 0x66,0x76,0x58,0xd8,0xd0,0xc4,0x8e,0x38, + }; + const unsigned char tc_K[] = { + 0xdb,0x3f,0xff,0x9d,0xa5,0x95,0x76,0x71,0x5b,0x04,0xd4,0xdf, + 0x8d,0xc8,0xd1,0x8d,0xb2,0x43,0x0e,0x57,0xbb,0xed,0x33,0x7d, + 0xbe,0xee,0x5b,0xb2,0xd6,0xab,0x6c,0xed,0xdc,0x9c,0x75,0xc5, + 0xc0,0xb1,0x7f,0xad,0x7e,0xb7,0x24,0xda,0xa1,0x2f,0x8f,0x19, + 0x03,0xdd,0x6c,0x2c,0xed,0xe6,0x13,0x5a, + }; + const unsigned char tc_ISK_IR[] = { + 0x59,0x98,0x92,0xa2,0x07,0x8a,0x8c,0x98,0x81,0x81,0x62,0x5e, + 0x1e,0x5e,0x5f,0x7a,0x61,0x63,0xf7,0xd7,0x2f,0x21,0xb9,0x3e, + 0xbe,0xfb,0xa0,0xf1,0x7f,0xf7,0xea,0x3a,0xa0,0x59,0x4b,0xd5, + 0x69,0xcf,0x74,0x26,0x41,0x57,0xb3,0xc0,0x08,0x7b,0xdc,0xcf, + 0x2f,0x59,0xc7,0x71,0x56,0x62,0x84,0x87,0xf5,0xca,0x16,0x45, + 0xb8,0xe9,0xd0,0x5b, + }; + const unsigned char tc_ISK_SY[] = { + 0x3a,0xc7,0x3f,0x03,0x03,0x02,0x96,0xaa,0x59,0x1f,0x01,0x32, + 0x6b,0x18,0xaf,0xa4,0x7e,0x11,0x89,0x12,0x9c,0xd0,0x6a,0xe8, + 0xdf,0xb0,0x5e,0x6e,0xb1,0x31,0x0c,0xde,0x94,0x8b,0x59,0xee, + 0xf0,0x75,0x53,0x65,0xc0,0x6a,0x33,0x92,0x66,0xaf,0xe5,0x94, + 0x94,0x8c,0x56,0xa5,0x38,0xd9,0x8a,0x65,0x76,0x71,0x13,0x93, + 0x8a,0x9a,0x78,0xd8, + }; + const unsigned char tc_ISK_SY[] = { + 0x3a,0xc7,0x3f,0x03,0x03,0x02,0x96,0xaa,0x59,0x1f,0x01,0x32, + 0x6b,0x18,0xaf,0xa4,0x7e,0x11,0x89,0x12,0x9c,0xd0,0x6a,0xe8, + 0xdf,0xb0,0x5e,0x6e,0xb1,0x31,0x0c,0xde,0x94,0x8b,0x59,0xee, + 0xf0,0x75,0x53,0x65,0xc0,0x6a,0x33,0x92,0x66,0xaf,0xe5,0x94, + 0x94,0x8c,0x56,0xa5,0x38,0xd9,0x8a,0x65,0x76,0x71,0x13,0x93, + 0x8a,0x9a,0x78,0xd8, + }; + const unsigned char tc_sid_out_ir[] = { + 0x00,0xa2,0x33,0x3a,0x79,0x48,0x1a,0xbe,0x71,0xef,0xd6,0x59, + 0x4d,0x7b,0xba,0xac,0x55,0xc8,0x08,0x48,0x2e,0x86,0x9c,0x9b, + 0x65,0xc4,0xb5,0x3d,0x71,0x00,0xd3,0xda,0x8f,0x3c,0xab,0xd5, + 0x9f,0xa0,0xc1,0xf2,0x2d,0x6d,0x2f,0x9a,0xc0,0xc0,0x93,0x96, + 0x22,0x92,0x79,0x8f,0xca,0x2c,0x0b,0x93,0x26,0x89,0x74,0xca, + 0xd7,0x5d,0x57,0x5a, + }; + const unsigned char tc_sid_out_oc[] = { + 0xa1,0xce,0x90,0x53,0x7a,0x8d,0x53,0xb0,0x6d,0x77,0xe7,0x9f, + 0xe7,0x19,0x46,0x1c,0xc5,0xed,0x83,0x00,0xd2,0x1d,0x18,0x66, + 0xa5,0x9f,0x96,0x38,0x60,0x18,0x33,0xf5,0x7a,0x8b,0x5e,0x88, + 0xdb,0x9a,0x52,0xab,0xfa,0x1b,0x4e,0x8a,0x65,0x1a,0x40,0x0b, + 0xc9,0x20,0x50,0x82,0xaa,0xd8,0x1e,0xb3,0x11,0xc4,0x43,0x73, + 0xb9,0xa1,0x9e,0xff, + }; + +B.2.9. Testvectors as JSON file encoded as BASE64 + + #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT + #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI1 + #MjIzRTBDREM0NUQ2NTc1NjY4RDY0QzU1MjAwNDEyNCIsICJnIjogIkUyOTNCN0NDRj + #YxQ0E3RUI5MjhBMjYzOTFDRjM4QjY2MEY4NzRBMDAxRkRGMEJGM0E5MUZEMTgyRjJC + #NkQ4M0U2MUE5Mzc3RURFMTI3RUJBN0UwRDRDMDg1OTJFQUZGMzNENEFBNzA1RDZDRT + #U0QkIiLCAieWEiOiAiMjFCNEY0QkQ5RTY0RUQzNTVDM0VCNjc2QTI4RUJFREFGNkQ4 + #RjE3QkRDMzY1OTk1QjMxOTA5NzE1MzA0NDA4MDUxNkJEMDgzQkZDQ0U2NjEyMUEzMD + #cyNjQ2OTk0Qzg0MzBDQzM4MkI4REM1NDNFOCIsICJBRGEiOiAiNDE0NDYxIiwgIllh + #IjogIjdGNjQ1NzcyQ0MyMDlCRjlGRDlENzZEQkIxMDI4M0JFQTcxQjEyMjM1RTNCQj + #IxODc4RDVFNTZBNzA1MDZFMTY1NzQzQTYzMkRFOThFQ0E5OTMyQzVEMkVGRTM2NTAw + #QTU5QjJGREFFRDBEOEExNDgiLCAieWIiOiAiODQ4QjA3NzlGRjQxNUYwQUY0RUExNE + #RGOUREMUQzQzI5QUM0MUQ4MzZDNzgwODg5NkM0RUJBMTlDNTFBQzQwQTQzOUNBRjVF + #NjFFQzg4QzMwN0M3RDYxOTE5NTIyOTQxMkVBQTczRkIyQTVFQTIwRCIsICJBRGIiOi + #AiNDE0NDYyIiwgIlliIjogIkE0NjkwQTA3NTBDNDJCMjg4REREMEJBMDhFM0Y0OTAy + #REZFNzBCQUU1QzlFMkM2RUU5NTg0NERFRjI2OTJCRTc3NjQ2QjIwRDNCNDI5RjhEQT + #AwRDIxNDMzRUUwODkxQzY2NzY1OEQ4RDBDNDhFMzgiLCAiSyI6ICJEQjNGRkY5REE1 + #OTU3NjcxNUIwNEQ0REY4REM4RDE4REIyNDMwRTU3QkJFRDMzN0RCRUVFNUJCMkQ2QU + #I2Q0VEREM5Qzc1QzVDMEIxN0ZBRDdFQjcyNERBQTEyRjhGMTkwM0RENkMyQ0VERTYx + #MzVBIiwgIklTS19JUiI6ICI1OTk4OTJBMjA3OEE4Qzk4ODE4MTYyNUUxRTVFNUY3QT + #YxNjNGN0Q3MkYyMUI5M0VCRUZCQTBGMTdGRjdFQTNBQTA1OTRCRDU2OUNGNzQyNjQx + #NTdCM0MwMDg3QkRDQ0YyRjU5Qzc3MTU2NjI4NDg3RjVDQTE2NDVCOEU5RDA1QiIsIC + #JJU0tfU1kiOiAiM0FDNzNGMDMwMzAyOTZBQTU5MUYwMTMyNkIxOEFGQTQ3RTExODkx + #MjlDRDA2QUU4REZCMDVFNkVCMTMxMENERTk0OEI1OUVFRjA3NTUzNjVDMDZBMzM5Mj + #Y2QUZFNTk0OTQ4QzU2QTUzOEQ5OEE2NTc2NzExMzkzOEE5QTc4RDgiLCAic2lkX291 + #dHB1dF9pciI6ICIwMEEyMzMzQTc5NDgxQUJFNzFFRkQ2NTk0RDdCQkFBQzU1QzgwOD + #Q4MkU4NjlDOUI2NUM0QjUzRDcxMDBEM0RBOEYzQ0FCRDU5RkEwQzFGMjJENkQyRjlB + #QzBDMDkzOTYyMjkyNzk4RkNBMkMwQjkzMjY4OTc0Q0FENzVENTc1QSIsICJzaWRfb3 + #V0cHV0X29jIjogIkExQ0U5MDUzN0E4RDUzQjA2RDc3RTc5RkU3MTk0NjFDQzVFRDgz + #MDBEMjFEMTg2NkE1OUY5NjM4NjAxODMzRjU3QThCNUU4OERCOUE1MkFCRkExQjRFOE + #E2NTFBNDAwQkM5MjA1MDgyQUFEODFFQjMxMUM0NDM3M0I5QTE5RUZGIn0= + +B.2.10. Test vectors for G_X448.scalar_mult_vfy: low order points + + Test vectors for which G_X448.scalar_mult_vfy(s_in,ux) must return + the neutral element. This includes points that are non-canonicaly + encoded, i.e. have coordinate values larger than the field prime. + + Weak points for X448 smaller than the field prime (canonical) + + u0: (length: 56 bytes) + 0000000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000000000000000000000000000 + u1: (length: 56 bytes) + 0100000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000000000000000000000000000 + u2: (length: 56 bytes) + fefffffffffffffffffffffffffffffffffffffffffffffffffffffffe + ffffffffffffffffffffffffffffffffffffffffffffffffffffff + + Weak points for X448 larger or equal to the field prime (non- + canonical) + + u3: (length: 56 bytes) + fffffffffffffffffffffffffffffffffffffffffffffffffffffffffe + ffffffffffffffffffffffffffffffffffffffffffffffffffffff + u4: (length: 56 bytes) + 00000000000000000000000000000000000000000000000000000000ff + ffffffffffffffffffffffffffffffffffffffffffffffffffffff + + All of the above points u0 ... u4 MUST trigger the abort case + when included in the protocol messages from A or B. + + Expected results for X448 resp. G_X448.scalar_mult_vfy + + scalar s: (length: 56 bytes) + af8a14218bf2a2062926d2ea9b8fe4e8b6817349b6ed2feb1e5d64d7a4 + 523f15fceec70fb111e870dc58d191e66a14d3e9d482d04432cadd + G_X448.scalar_mult_vfy(s,u0): (length: 56 bytes) + 0000000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000000000000000000000000000 + G_X448.scalar_mult_vfy(s,u1): (length: 56 bytes) + 0000000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000000000000000000000000000 + G_X448.scalar_mult_vfy(s,u2): (length: 56 bytes) + 0000000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000000000000000000000000000 + G_X448.scalar_mult_vfy(s,u3): (length: 56 bytes) + 0000000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000000000000000000000000000 + G_X448.scalar_mult_vfy(s,u4): (length: 56 bytes) + 0000000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000000000000000000000000000 + + Test vectors for scalar_mult with nonzero outputs + + scalar s: (length: 56 bytes) + af8a14218bf2a2062926d2ea9b8fe4e8b6817349b6ed2feb1e5d64d7a4 + 523f15fceec70fb111e870dc58d191e66a14d3e9d482d04432cadd + point coordinate u_curve on the curve: (length: 56 bytes) + ab0c68d772ec2eb9de25c49700e46d6325e66d6aa39d7b65eb84a68c55 + 69d47bd71b41f3e0d210f44e146dec8926b174acb3f940a0b82cab + G_X448.scalar_mult_vfy(s,u_curve): (length: 56 bytes) + 3b0fa9bc40a6fdc78c9e06ff7a54c143c5d52f365607053bf0656f5142 + 0496295f910a101b38edc1acd3bd240fd55dcb7a360553b8a7627e + + point coordinate u_twist on the twist: (length: 56 bytes) + c981cd1e1f72d9c35c7d7cf6be426757c0dc8206a2fcfa564a8e7618c0 + 3c0e61f9a2eb1c3e0dd97d6e9b1010f5edd03397a83f5a914cb3ff + G_X448.scalar_mult_vfy(s,u_twist): (length: 56 bytes) + d0a2bb7e9c5c2c627793d8342f23b759fe7d9e3320a85ca4fd61376331 + 50ffd9a9148a9b75c349fac43d64bec49a6e126cc92cbfbf353961 + +B.2.10.1. Testvectors as JSON file encoded as BASE64 + + #eyJJbnZhbGlkIFkxIjogIjAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAiLCAiSW52YWxpZCBZMiI6ICIwMT + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwIiwgIkludmFsaWQgWTMiOiAiRkVGRkZGRkZGRkZGRkZGRkZGRkZG + #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRUZGRkZGRkZGRkZGRk + #ZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRiIsICJJbnZh + #bGlkIFk0IjogIkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRk + #ZGRkZGRkZGRkZGRkZGRkZGRkVGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZG + #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkYiLCAiSW52YWxpZCBZNSI6ICIwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMEZG + #RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRk + #ZGRkZGIiwgIlZhbGlkIChvbiBjdXJ2ZSkiOiB7InMiOiAiQUY4QTE0MjE4QkYyQTIw + #NjI5MjZEMkVBOUI4RkU0RThCNjgxNzM0OUI2RUQyRkVCMUU1RDY0RDdBNDUyM0YxNU + #ZDRUVDNzBGQjExMUU4NzBEQzU4RDE5MUU2NkExNEQzRTlENDgyRDA0NDMyQ0FERCIs + #ICJ1X2N1cnZlIjogIkFCMEM2OEQ3NzJFQzJFQjlERTI1QzQ5NzAwRTQ2RDYzMjVFNj + #ZENkFBMzlEN0I2NUVCODRBNjhDNTU2OUQ0N0JENzFCNDFGM0UwRDIxMEY0NEUxNDZE + #RUM4OTI2QjE3NEFDQjNGOTQwQTBCODJDQUIiLCAicmVzX2N1cnZlIjogIjNCMEZBOU + #JDNDBBNkZEQzc4QzlFMDZGRjdBNTRDMTQzQzVENTJGMzY1NjA3MDUzQkYwNjU2RjUx + #NDIwNDk2Mjk1RjkxMEExMDFCMzhFREMxQUNEM0JEMjQwRkQ1NURDQjdBMzYwNTUzQj + #hBNzYyN0UifSwgIlZhbGlkIChvbiB0d2lzdCkiOiB7InMiOiAiQUY4QTE0MjE4QkYy + #QTIwNjI5MjZEMkVBOUI4RkU0RThCNjgxNzM0OUI2RUQyRkVCMUU1RDY0RDdBNDUyM0 + #YxNUZDRUVDNzBGQjExMUU4NzBEQzU4RDE5MUU2NkExNEQzRTlENDgyRDA0NDMyQ0FE + #RCIsICJ1X3R3aXN0IjogIkM5ODFDRDFFMUY3MkQ5QzM1QzdEN0NGNkJFNDI2NzU3Qz + #BEQzgyMDZBMkZDRkE1NjRBOEU3NjE4QzAzQzBFNjFGOUEyRUIxQzNFMEREOTdENkU5 + #QjEwMTBGNUVERDAzMzk3QTgzRjVBOTE0Q0IzRkYiLCAicmVzX3R3aXN0IjogIkQwQT + #JCQjdFOUM1QzJDNjI3NzkzRDgzNDJGMjNCNzU5RkU3RDlFMzMyMEE4NUNBNEZENjEz + #NzYzMzE1MEZGRDlBOTE0OEE5Qjc1QzM0OUZBQzQzRDY0QkVDNDlBNkUxMjZDQzkyQ0 + #JGQkYzNTM5NjEifX0= + +B.3. Test vector for CPace using group ristretto255 and hash SHA-512 + +B.3.1. Test vectors for calculate_generator with group ristretto255 + + Inputs + H = SHA-512 with input block size 128 bytes. + PRS = b'Password' ; ZPAD length: 100 ; + DSI = b'CPaceRistretto255' + CI = b'oc\x0bB_responder\x0bA_initiator' + CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72 + sid = 7e4b4791d6a8ef019b936c79fb7f2c57 + Outputs + generator_string(G.DSI,PRS,CI,sid,H.s_in_bytes): + (length: 172 bytes) + 11435061636552697374726574746f3235350850617373776f726464 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000001a6f630b425f726573706f6e + 6465720b415f696e69746961746f72107e4b4791d6a8ef019b936c79 + fb7f2c57 + hash result: (length: 64 bytes) + c63a5750e2439c17ccd8213be14fde2f87e1bc637001a97f5929c77b + 30ea0e08afbc75ace5d3d73b2842a79d01488c5fd7ea30d475ee6095 + 45af1bfd1ff77c8e + encoded generator g: (length: 32 bytes) + a6fc82c3b8968fbb2e06fee81ca858586dea50d248f0c7ca6a18b090 + 2a30b36b + +B.3.1.1. Testvectors as JSON file encoded as BASE64 + + #eyJIIjogIlNIQS01MTIiLCAiSC5zX2luX2J5dGVzIjogMTI4LCAiUFJTIjogIjUwNj + #E3MzczNzc2RjcyNjQiLCAiWlBBRCBsZW5ndGgiOiAxMDAsICJEU0kiOiAiNDM1MDYx + #NjM2NTUyNjk3Mzc0NzI2NTc0NzQ2RjMyMzUzNSIsICJDSSI6ICI2RjYzMEI0MjVGNz + #I2NTczNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6 + #ICI3RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJnZW5lcmF0b3Jfc3 + #RyaW5nKEcuRFNJLFBSUyxDSSxzaWQsSC5zX2luX2J5dGVzKSI6ICIxMTQzNTA2MTYz + #NjU1MjY5NzM3NDcyNjU3NDc0NkYzMjM1MzUwODUwNjE3MzczNzc2RjcyNjQ2NDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMU + #E2RjYzMEI0MjVGNzI2NTczNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2 + #RjcyMTA3RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJoYXNoIHJlc3 + #VsdCI6ICJDNjNBNTc1MEUyNDM5QzE3Q0NEODIxM0JFMTRGREUyRjg3RTFCQzYzNzAw + #MUE5N0Y1OTI5Qzc3QjMwRUEwRTA4QUZCQzc1QUNFNUQzRDczQjI4NDJBNzlEMDE0OD + #hDNUZEN0VBMzBENDc1RUU2MDk1NDVBRjFCRkQxRkY3N0M4RSIsICJlbmNvZGVkIGdl + #bmVyYXRvciBnIjogIkE2RkM4MkMzQjg5NjhGQkIyRTA2RkVFODFDQTg1ODU4NkRFQT + #UwRDI0OEYwQzdDQTZBMThCMDkwMkEzMEIzNkIifQ== + +B.3.2. Test vector for message from A + + Inputs + ADa = b'ADa' + ya (little endian): (length: 32 bytes) + da3d23700a9e5699258aef94dc060dfda5ebb61f02a5ea77fad53f4f + f0976d08 + Outputs + Ya: (length: 32 bytes) + d40fb265a7abeaee7939d91a585fe59f7053f982c296ec413c624c66 + 9308f87a + +B.3.3. Test vector for message from B + + Inputs + ADb = b'ADb' + yb (little endian): (length: 32 bytes) + d2316b454718c35362d83d69df6320f38578ed5984651435e2949762 + d900b80d + Outputs + Yb: (length: 32 bytes) + 08bcf6e9777a9c313a3db6daa510f2d398403319c2341bd506a92e67 + 2eb7e307 + +B.3.4. Test vector for secret points K + + scalar_mult_vfy(ya,Yb): (length: 32 bytes) + e22b1ef7788f661478f3cddd4c600774fc0f41e6b711569190ff88fa + 0e607e09 + scalar_mult_vfy(yb,Ya): (length: 32 bytes) + e22b1ef7788f661478f3cddd4c600774fc0f41e6b711569190ff88fa + 0e607e09 + +B.3.5. Test vector for ISK calculation initiator/responder + + transcript_ir(Ya,ADa,Yb,ADb): (length: 74 bytes) + 20d40fb265a7abeaee7939d91a585fe59f7053f982c296ec413c624c + 669308f87a034144612008bcf6e9777a9c313a3db6daa510f2d39840 + 3319c2341bd506a92e672eb7e30703414462 + DSI = G.DSI_ISK, b'CPaceRistretto255_ISK': + (length: 21 bytes) + 435061636552697374726574746f3235355f49534b + lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb): + (length: 146 bytes) + 15435061636552697374726574746f3235355f49534b107e4b4791d6 + a8ef019b936c79fb7f2c5720e22b1ef7788f661478f3cddd4c600774 + fc0f41e6b711569190ff88fa0e607e0920d40fb265a7abeaee7939d9 + 1a585fe59f7053f982c296ec413c624c669308f87a034144612008bc + f6e9777a9c313a3db6daa510f2d398403319c2341bd506a92e672eb7 + e30703414462 + ISK result: (length: 64 bytes) + 4c5469a16b2364c4b944ebc1a79e51d1674ad47db26e8718154f59fa + ebfaa52d8346f30aa58377117eb20d527f2cbc5c76381f7fd372e89d + f8239f87f2e02ed1 + +B.3.6. Test vector for ISK calculation parallel execution + + transcript_oc(Ya,ADa,Yb,ADb): (length: 76 bytes) + 6f6320d40fb265a7abeaee7939d91a585fe59f7053f982c296ec413c + 624c669308f87a034144612008bcf6e9777a9c313a3db6daa510f2d3 + 98403319c2341bd506a92e672eb7e30703414462 + DSI = G.DSI_ISK, b'CPaceRistretto255_ISK': + (length: 21 bytes) + 435061636552697374726574746f3235355f49534b + lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb): + (length: 148 bytes) + 15435061636552697374726574746f3235355f49534b107e4b4791d6 + a8ef019b936c79fb7f2c5720e22b1ef7788f661478f3cddd4c600774 + fc0f41e6b711569190ff88fa0e607e096f6320d40fb265a7abeaee79 + 39d91a585fe59f7053f982c296ec413c624c669308f87a0341446120 + 08bcf6e9777a9c313a3db6daa510f2d398403319c2341bd506a92e67 + 2eb7e30703414462 + ISK result: (length: 64 bytes) + 980dcc5a1c52ceea031e75f38ed266586616488c5c5780285fcbcf79 + 087c7bcdbd993502eee606b718ba31e840a000a7b7befe15ea427c5c + fe88344fa1237f35 + +B.3.7. Test vector for optional output of session id + + H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + 2a76d3bbc499dfdc4dcacc9ff042f4e1a54e3843258e100ccd7c60f0 + a541f9d3ebf025e68a460dde218bd39f0711bc6fa11409c9d7b69d8c + cf6b32fc51ddb699 + H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + ca4b50700c46203ccd10bc0e9f31095e508189cb59857537be561048 + d34b9ed9a9697af11c998f484c3d783b0b531434caa6835d4c32344f + cd17160c9c348fc7 + +B.3.8. Corresponding C programming language initializers + + const unsigned char tc_PRS[] = { + 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64, + }; + const unsigned char tc_CI[] = { + 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64, + 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74, + 0x6f,0x72, + }; + const unsigned char tc_sid[] = { + 0x7e,0x4b,0x47,0x91,0xd6,0xa8,0xef,0x01,0x9b,0x93,0x6c,0x79, + 0xfb,0x7f,0x2c,0x57, + }; + const unsigned char tc_g[] = { + 0xa6,0xfc,0x82,0xc3,0xb8,0x96,0x8f,0xbb,0x2e,0x06,0xfe,0xe8, + 0x1c,0xa8,0x58,0x58,0x6d,0xea,0x50,0xd2,0x48,0xf0,0xc7,0xca, + 0x6a,0x18,0xb0,0x90,0x2a,0x30,0xb3,0x6b, + }; + const unsigned char tc_ya[] = { + 0xda,0x3d,0x23,0x70,0x0a,0x9e,0x56,0x99,0x25,0x8a,0xef,0x94, + 0xdc,0x06,0x0d,0xfd,0xa5,0xeb,0xb6,0x1f,0x02,0xa5,0xea,0x77, + 0xfa,0xd5,0x3f,0x4f,0xf0,0x97,0x6d,0x08, + }; + const unsigned char tc_ADa[] = { + 0x41,0x44,0x61, + }; + const unsigned char tc_Ya[] = { + 0xd4,0x0f,0xb2,0x65,0xa7,0xab,0xea,0xee,0x79,0x39,0xd9,0x1a, + 0x58,0x5f,0xe5,0x9f,0x70,0x53,0xf9,0x82,0xc2,0x96,0xec,0x41, + 0x3c,0x62,0x4c,0x66,0x93,0x08,0xf8,0x7a, + }; + const unsigned char tc_yb[] = { + 0xd2,0x31,0x6b,0x45,0x47,0x18,0xc3,0x53,0x62,0xd8,0x3d,0x69, + 0xdf,0x63,0x20,0xf3,0x85,0x78,0xed,0x59,0x84,0x65,0x14,0x35, + 0xe2,0x94,0x97,0x62,0xd9,0x00,0xb8,0x0d, + }; + const unsigned char tc_ADb[] = { + 0x41,0x44,0x62, + }; + const unsigned char tc_Yb[] = { + 0x08,0xbc,0xf6,0xe9,0x77,0x7a,0x9c,0x31,0x3a,0x3d,0xb6,0xda, + 0xa5,0x10,0xf2,0xd3,0x98,0x40,0x33,0x19,0xc2,0x34,0x1b,0xd5, + 0x06,0xa9,0x2e,0x67,0x2e,0xb7,0xe3,0x07, + }; + const unsigned char tc_K[] = { + 0xe2,0x2b,0x1e,0xf7,0x78,0x8f,0x66,0x14,0x78,0xf3,0xcd,0xdd, + 0x4c,0x60,0x07,0x74,0xfc,0x0f,0x41,0xe6,0xb7,0x11,0x56,0x91, + 0x90,0xff,0x88,0xfa,0x0e,0x60,0x7e,0x09, + }; + const unsigned char tc_ISK_IR[] = { + 0x4c,0x54,0x69,0xa1,0x6b,0x23,0x64,0xc4,0xb9,0x44,0xeb,0xc1, + 0xa7,0x9e,0x51,0xd1,0x67,0x4a,0xd4,0x7d,0xb2,0x6e,0x87,0x18, + 0x15,0x4f,0x59,0xfa,0xeb,0xfa,0xa5,0x2d,0x83,0x46,0xf3,0x0a, + 0xa5,0x83,0x77,0x11,0x7e,0xb2,0x0d,0x52,0x7f,0x2c,0xbc,0x5c, + 0x76,0x38,0x1f,0x7f,0xd3,0x72,0xe8,0x9d,0xf8,0x23,0x9f,0x87, + 0xf2,0xe0,0x2e,0xd1, + }; + const unsigned char tc_ISK_SY[] = { + 0x98,0x0d,0xcc,0x5a,0x1c,0x52,0xce,0xea,0x03,0x1e,0x75,0xf3, + 0x8e,0xd2,0x66,0x58,0x66,0x16,0x48,0x8c,0x5c,0x57,0x80,0x28, + 0x5f,0xcb,0xcf,0x79,0x08,0x7c,0x7b,0xcd,0xbd,0x99,0x35,0x02, + 0xee,0xe6,0x06,0xb7,0x18,0xba,0x31,0xe8,0x40,0xa0,0x00,0xa7, + 0xb7,0xbe,0xfe,0x15,0xea,0x42,0x7c,0x5c,0xfe,0x88,0x34,0x4f, + 0xa1,0x23,0x7f,0x35, + }; + const unsigned char tc_ISK_SY[] = { + 0x98,0x0d,0xcc,0x5a,0x1c,0x52,0xce,0xea,0x03,0x1e,0x75,0xf3, + 0x8e,0xd2,0x66,0x58,0x66,0x16,0x48,0x8c,0x5c,0x57,0x80,0x28, + 0x5f,0xcb,0xcf,0x79,0x08,0x7c,0x7b,0xcd,0xbd,0x99,0x35,0x02, + 0xee,0xe6,0x06,0xb7,0x18,0xba,0x31,0xe8,0x40,0xa0,0x00,0xa7, + 0xb7,0xbe,0xfe,0x15,0xea,0x42,0x7c,0x5c,0xfe,0x88,0x34,0x4f, + 0xa1,0x23,0x7f,0x35, + }; + const unsigned char tc_sid_out_ir[] = { + 0x2a,0x76,0xd3,0xbb,0xc4,0x99,0xdf,0xdc,0x4d,0xca,0xcc,0x9f, + 0xf0,0x42,0xf4,0xe1,0xa5,0x4e,0x38,0x43,0x25,0x8e,0x10,0x0c, + 0xcd,0x7c,0x60,0xf0,0xa5,0x41,0xf9,0xd3,0xeb,0xf0,0x25,0xe6, + 0x8a,0x46,0x0d,0xde,0x21,0x8b,0xd3,0x9f,0x07,0x11,0xbc,0x6f, + 0xa1,0x14,0x09,0xc9,0xd7,0xb6,0x9d,0x8c,0xcf,0x6b,0x32,0xfc, + 0x51,0xdd,0xb6,0x99, + }; + const unsigned char tc_sid_out_oc[] = { + 0xca,0x4b,0x50,0x70,0x0c,0x46,0x20,0x3c,0xcd,0x10,0xbc,0x0e, + 0x9f,0x31,0x09,0x5e,0x50,0x81,0x89,0xcb,0x59,0x85,0x75,0x37, + 0xbe,0x56,0x10,0x48,0xd3,0x4b,0x9e,0xd9,0xa9,0x69,0x7a,0xf1, + 0x1c,0x99,0x8f,0x48,0x4c,0x3d,0x78,0x3b,0x0b,0x53,0x14,0x34, + 0xca,0xa6,0x83,0x5d,0x4c,0x32,0x34,0x4f,0xcd,0x17,0x16,0x0c, + 0x9c,0x34,0x8f,0xc7, + }; + +B.3.9. Testvectors as JSON file encoded as BASE64 + + #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT + #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI3 + #RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJnIjogIkE2RkM4MkMzQj + #g5NjhGQkIyRTA2RkVFODFDQTg1ODU4NkRFQTUwRDI0OEYwQzdDQTZBMThCMDkwMkEz + #MEIzNkIiLCAieWEiOiAiREEzRDIzNzAwQTlFNTY5OTI1OEFFRjk0REMwNjBERkRBNU + #VCQjYxRjAyQTVFQTc3RkFENTNGNEZGMDk3NkQwOCIsICJBRGEiOiAiNDE0NDYxIiwg + #IllhIjogIkQ0MEZCMjY1QTdBQkVBRUU3OTM5RDkxQTU4NUZFNTlGNzA1M0Y5ODJDMj + #k2RUM0MTNDNjI0QzY2OTMwOEY4N0EiLCAieWIiOiAiRDIzMTZCNDU0NzE4QzM1MzYy + #RDgzRDY5REY2MzIwRjM4NTc4RUQ1OTg0NjUxNDM1RTI5NDk3NjJEOTAwQjgwRCIsIC + #JBRGIiOiAiNDE0NDYyIiwgIlliIjogIjA4QkNGNkU5Nzc3QTlDMzEzQTNEQjZEQUE1 + #MTBGMkQzOTg0MDMzMTlDMjM0MUJENTA2QTkyRTY3MkVCN0UzMDciLCAiSyI6ICJFMj + #JCMUVGNzc4OEY2NjE0NzhGM0NEREQ0QzYwMDc3NEZDMEY0MUU2QjcxMTU2OTE5MEZG + #ODhGQTBFNjA3RTA5IiwgIklTS19JUiI6ICI0QzU0NjlBMTZCMjM2NEM0Qjk0NEVCQz + #FBNzlFNTFEMTY3NEFENDdEQjI2RTg3MTgxNTRGNTlGQUVCRkFBNTJEODM0NkYzMEFB + #NTgzNzcxMTdFQjIwRDUyN0YyQ0JDNUM3NjM4MUY3RkQzNzJFODlERjgyMzlGODdGMk + #UwMkVEMSIsICJJU0tfU1kiOiAiOTgwRENDNUExQzUyQ0VFQTAzMUU3NUYzOEVEMjY2 + #NTg2NjE2NDg4QzVDNTc4MDI4NUZDQkNGNzkwODdDN0JDREJEOTkzNTAyRUVFNjA2Qj + #cxOEJBMzFFODQwQTAwMEE3QjdCRUZFMTVFQTQyN0M1Q0ZFODgzNDRGQTEyMzdGMzUi + #LCAic2lkX291dHB1dF9pciI6ICIyQTc2RDNCQkM0OTlERkRDNERDQUNDOUZGMDQyRj + #RFMUE1NEUzODQzMjU4RTEwMENDRDdDNjBGMEE1NDFGOUQzRUJGMDI1RTY4QTQ2MERE + #RTIxOEJEMzlGMDcxMUJDNkZBMTE0MDlDOUQ3QjY5RDhDQ0Y2QjMyRkM1MUREQjY5OS + #IsICJzaWRfb3V0cHV0X29jIjogIkNBNEI1MDcwMEM0NjIwM0NDRDEwQkMwRTlGMzEw + #OTVFNTA4MTg5Q0I1OTg1NzUzN0JFNTYxMDQ4RDM0QjlFRDlBOTY5N0FGMTFDOTk4Rj + #Q4NEMzRDc4M0IwQjUzMTQzNENBQTY4MzVENEMzMjM0NEZDRDE3MTYwQzlDMzQ4RkM3 + #In0= + +B.3.10. Test case for scalar_mult with valid inputs + + s: (length: 32 bytes) + 7cd0e075fa7955ba52c02759a6c90dbbfc10e6d40aea8d283e407d88 + cf538a05 + X: (length: 32 bytes) + 2c3c6b8c4f3800e7aef6864025b4ed79bd599117e427c41bd47d93d6 + 54b4a51c + G.scalar_mult(s,decode(X)): (length: 32 bytes) + 7c13645fe790a468f62c39beb7388e541d8405d1ade69d1778c5fe3e + 7f6b600e + G.scalar_mult_vfy(s,X): (length: 32 bytes) + 7c13645fe790a468f62c39beb7388e541d8405d1ade69d1778c5fe3e + 7f6b600e + +B.3.11. Invalid inputs for scalar_mult_vfy + + For these test cases scalar_mult_vfy(y,.) MUST return the + representation of the neutral element G.I. When points Y_i1 or Y_i2 + are included in message of A or B the protocol MUST abort. + + s: (length: 32 bytes) + 7cd0e075fa7955ba52c02759a6c90dbbfc10e6d40aea8d283e407d88 + cf538a05 + Y_i1: (length: 32 bytes) + 2b3c6b8c4f3800e7aef6864025b4ed79bd599117e427c41bd47d93d6 + 54b4a51c + Y_i2 == G.I: (length: 32 bytes) + 00000000000000000000000000000000000000000000000000000000 + 00000000 + G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I + +B.3.11.1. Testvectors as JSON file encoded as BASE64 + + #eyJWYWxpZCI6IHsicyI6ICI3Q0QwRTA3NUZBNzk1NUJBNTJDMDI3NTlBNkM5MERCQk + #ZDMTBFNkQ0MEFFQThEMjgzRTQwN0Q4OENGNTM4QTA1IiwgIlgiOiAiMkMzQzZCOEM0 + #RjM4MDBFN0FFRjY4NjQwMjVCNEVENzlCRDU5OTExN0U0MjdDNDFCRDQ3RDkzRDY1NE + #I0QTUxQyIsICJHLnNjYWxhcl9tdWx0KHMsZGVjb2RlKFgpKSI6ICI3QzEzNjQ1RkU3 + #OTBBNDY4RjYyQzM5QkVCNzM4OEU1NDFEODQwNUQxQURFNjlEMTc3OEM1RkUzRTdGNk + #I2MDBFIiwgIkcuc2NhbGFyX211bHRfdmZ5KHMsWCkiOiAiN0MxMzY0NUZFNzkwQTQ2 + #OEY2MkMzOUJFQjczODhFNTQxRDg0MDVEMUFERTY5RDE3NzhDNUZFM0U3RjZCNjAwRS + #J9LCAiSW52YWxpZCBZMSI6ICIyQjNDNkI4QzRGMzgwMEU3QUVGNjg2NDAyNUI0RUQ3 + #OUJENTk5MTE3RTQyN0M0MUJENDdEOTNENjU0QjRBNTFDIiwgIkludmFsaWQgWTIiOi + #AiMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMCJ9 + +B.4. Test vector for CPace using group decaf448 and hash SHAKE-256 + +B.4.1. Test vectors for calculate_generator with group decaf448 + + Inputs + H = SHAKE-256 with input block size 136 bytes. + PRS = b'Password' ; ZPAD length: 112 ; + DSI = b'CPaceDecaf448' + CI = b'oc\x0bB_responder\x0bA_initiator' + CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72 + sid = 5223e0cdc45d6575668d64c552004124 + Outputs + generator_string(G.DSI,PRS,CI,sid,H.s_in_bytes): + (length: 180 bytes) + 0d435061636544656361663434380850617373776f72647000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 0000000000000000000000000000000000000000000000001a6f630b + 425f726573706f6e6465720b415f696e69746961746f72105223e0cd + c45d6575668d64c552004124 + hash result: (length: 112 bytes) + 7148f4d60587aaafa64d2fd6bcfe45ee71e8b971d1d5ff3bbf8c1451 + 797c62a1af22ab25638749f97f9b15fedcf4aeee87282cf667594ab0 + 92b6023c8f8d3a61c38b0af791c9271137df01b57d63b79734bbce69 + 91e3e2e10fdc805abc9e6e6f3daeff6fd34093d26de240b326764252 + encoded generator g: (length: 56 bytes) + 9a700ecc378eb98e57387df456d5b4b4f1dceebbb1371527eeb7e1bf + bab64ecc9c9303396145ba04f5b5aea5baedfa61f31f00fbc5fd5606 + +B.4.1.1. Testvectors as JSON file encoded as BASE64 + + #eyJIIjogIlNIQUtFLTI1NiIsICJILnNfaW5fYnl0ZXMiOiAxMzYsICJQUlMiOiAiNT + #A2MTczNzM3NzZGNzI2NCIsICJaUEFEIGxlbmd0aCI6IDExMiwgIkRTSSI6ICI0MzUw + #NjE2MzY1NDQ2NTYzNjE2NjM0MzQzOCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NTczNz + #A2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI1MjIz + #RTBDREM0NUQ2NTc1NjY4RDY0QzU1MjAwNDEyNCIsICJnZW5lcmF0b3Jfc3RyaW5nKE + #cuRFNJLFBSUyxDSSxzaWQsSC5zX2luX2J5dGVzKSI6ICIwRDQzNTA2MTYzNjU0NDY1 + #NjM2MTY2MzQzNDM4MDg1MDYxNzM3Mzc3NkY3MjY0NzAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDFBNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0NjU3MjBCNDE1RjY5NkU2 + #OTc0Njk2MTc0NkY3MjEwNTIyM0UwQ0RDNDVENjU3NTY2OEQ2NEM1NTIwMDQxMjQiLC + #AiaGFzaCByZXN1bHQiOiAiNzE0OEY0RDYwNTg3QUFBRkE2NEQyRkQ2QkNGRTQ1RUU3 + #MUU4Qjk3MUQxRDVGRjNCQkY4QzE0NTE3OTdDNjJBMUFGMjJBQjI1NjM4NzQ5Rjk3Rj + #lCMTVGRURDRjRBRUVFODcyODJDRjY2NzU5NEFCMDkyQjYwMjNDOEY4RDNBNjFDMzhC + #MEFGNzkxQzkyNzExMzdERjAxQjU3RDYzQjc5NzM0QkJDRTY5OTFFM0UyRTEwRkRDOD + #A1QUJDOUU2RTZGM0RBRUZGNkZEMzQwOTNEMjZERTI0MEIzMjY3NjQyNTIiLCAiZW5j + #b2RlZCBnZW5lcmF0b3IgZyI6ICI5QTcwMEVDQzM3OEVCOThFNTczODdERjQ1NkQ1Qj + #RCNEYxRENFRUJCQjEzNzE1MjdFRUI3RTFCRkJBQjY0RUNDOUM5MzAzMzk2MTQ1QkEw + #NEY1QjVBRUE1QkFFREZBNjFGMzFGMDBGQkM1RkQ1NjA2In0= + +B.4.2. Test vector for message from A + + Inputs + ADa = b'ADa' + ya (little endian): (length: 56 bytes) + 33d561f13cfc0dca279c30e8cde895175dc25483892819eba132d58c + 13c0462a8eb0d73fda941950594bef5191d8394691f86edffcad6c1e + Outputs + Ya: (length: 56 bytes) + 627f8bb2ae945e2a518967df9b00aff19253d3086398f2ec18be846c + c0d1f286c2ce3caf1da639859ccd2a6a01a9372a17e66bb7006e571b + +B.4.3. Test vector for message from B + + Inputs + ADb = b'ADb' + yb (little endian): (length: 56 bytes) + 2523c969f68fa2b2aea294c2539ef36eb1e0558abd14712a7828f16a + 85ed2c7e77e2bdd418994405fb1b57b6bbaadd66849892aac9d81402 + Outputs + Yb: (length: 56 bytes) + 8e9811e4402fac098743ca7b2b509b91b38c8cf1360cc6cab3011871 + 7019782b7f58a591c63d9c9247b774e6b0e0b826ff4f8399f94772db + +B.4.4. Test vector for secret points K + + scalar_mult_vfy(ya,Yb): (length: 56 bytes) + 94f4ae494f4e8b07ade3354726eee49c5518b363cda544f5b4541b97 + 32830be37ea0e63fc83f54be280dea0747a043c76d473e01689af77f + scalar_mult_vfy(yb,Ya): (length: 56 bytes) + 94f4ae494f4e8b07ade3354726eee49c5518b363cda544f5b4541b97 + 32830be37ea0e63fc83f54be280dea0747a043c76d473e01689af77f + +B.4.5. Test vector for ISK calculation initiator/responder + + transcript_ir(Ya,ADa,Yb,ADb): (length: 122 bytes) + 38627f8bb2ae945e2a518967df9b00aff19253d3086398f2ec18be84 + 6cc0d1f286c2ce3caf1da639859ccd2a6a01a9372a17e66bb7006e57 + 1b03414461388e9811e4402fac098743ca7b2b509b91b38c8cf1360c + c6cab30118717019782b7f58a591c63d9c9247b774e6b0e0b826ff4f + 8399f94772db03414462 + DSI = G.DSI_ISK, b'CPaceDecaf448_ISK': (length: 17 bytes) + 435061636544656361663434385f49534b + lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb): + (length: 214 bytes) + 11435061636544656361663434385f49534b105223e0cdc45d657566 + 8d64c5520041243894f4ae494f4e8b07ade3354726eee49c5518b363 + cda544f5b4541b9732830be37ea0e63fc83f54be280dea0747a043c7 + 6d473e01689af77f38627f8bb2ae945e2a518967df9b00aff19253d3 + 086398f2ec18be846cc0d1f286c2ce3caf1da639859ccd2a6a01a937 + 2a17e66bb7006e571b03414461388e9811e4402fac098743ca7b2b50 + 9b91b38c8cf1360cc6cab30118717019782b7f58a591c63d9c9247b7 + 74e6b0e0b826ff4f8399f94772db03414462 + ISK result: (length: 64 bytes) + 9c2726a6cda1179349cbc38f31765eab646a2a5f176f3019fab4a0aa + bd9d17c2ba895998cff698d801761a003512c1cf67d144b21e1cb6d6 + b82da71d0da76cad + +B.4.6. Test vector for ISK calculation parallel execution + + transcript_oc(Ya,ADa,Yb,ADb): (length: 124 bytes) + 6f63388e9811e4402fac098743ca7b2b509b91b38c8cf1360cc6cab3 + 0118717019782b7f58a591c63d9c9247b774e6b0e0b826ff4f8399f9 + 4772db0341446238627f8bb2ae945e2a518967df9b00aff19253d308 + 6398f2ec18be846cc0d1f286c2ce3caf1da639859ccd2a6a01a9372a + 17e66bb7006e571b03414461 + DSI = G.DSI_ISK, b'CPaceDecaf448_ISK': (length: 17 bytes) + 435061636544656361663434385f49534b + lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb): + (length: 216 bytes) + 11435061636544656361663434385f49534b105223e0cdc45d657566 + 8d64c5520041243894f4ae494f4e8b07ade3354726eee49c5518b363 + cda544f5b4541b9732830be37ea0e63fc83f54be280dea0747a043c7 + 6d473e01689af77f6f63388e9811e4402fac098743ca7b2b509b91b3 + 8c8cf1360cc6cab30118717019782b7f58a591c63d9c9247b774e6b0 + e0b826ff4f8399f94772db0341446238627f8bb2ae945e2a518967df + 9b00aff19253d3086398f2ec18be846cc0d1f286c2ce3caf1da63985 + 9ccd2a6a01a9372a17e66bb7006e571b03414461 + ISK result: (length: 64 bytes) + 6d2178ed3048703025b9007ec84c4d969e8d8135df455e608c16aa15 + 2e1219c86cea563254428a9d969903ae3649d1050da1e6e0c1c060e1 + ebf7316a7e993389 + +B.4.7. Test vector for optional output of session id + + H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + 65bffde17b7acf07cfd437bdb973a8f7340bf911d393a61498c0a50e + f0d68bca103fbdb0f5b799505562e59811df1bc5d9b4f5f0f7c57c22 + cd7ed6db4d153e3a + H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + 7ce27043d1b1d0d0e02e16979637e2a00547ed6e15ea988f7d3c9b3c + 2159b26ab3834bff7ff86240323e25216ba2ee6ea6e1582502017f8e + 6d65f8c4a5e65543 + +B.4.8. Corresponding C programming language initializers + + const unsigned char tc_PRS[] = { + 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64, + }; + const unsigned char tc_CI[] = { + 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64, + 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74, + 0x6f,0x72, + }; + const unsigned char tc_sid[] = { + 0x52,0x23,0xe0,0xcd,0xc4,0x5d,0x65,0x75,0x66,0x8d,0x64,0xc5, + 0x52,0x00,0x41,0x24, + }; + const unsigned char tc_g[] = { + 0x9a,0x70,0x0e,0xcc,0x37,0x8e,0xb9,0x8e,0x57,0x38,0x7d,0xf4, + 0x56,0xd5,0xb4,0xb4,0xf1,0xdc,0xee,0xbb,0xb1,0x37,0x15,0x27, + 0xee,0xb7,0xe1,0xbf,0xba,0xb6,0x4e,0xcc,0x9c,0x93,0x03,0x39, + 0x61,0x45,0xba,0x04,0xf5,0xb5,0xae,0xa5,0xba,0xed,0xfa,0x61, + 0xf3,0x1f,0x00,0xfb,0xc5,0xfd,0x56,0x06, + }; + const unsigned char tc_ya[] = { + 0x33,0xd5,0x61,0xf1,0x3c,0xfc,0x0d,0xca,0x27,0x9c,0x30,0xe8, + 0xcd,0xe8,0x95,0x17,0x5d,0xc2,0x54,0x83,0x89,0x28,0x19,0xeb, + 0xa1,0x32,0xd5,0x8c,0x13,0xc0,0x46,0x2a,0x8e,0xb0,0xd7,0x3f, + 0xda,0x94,0x19,0x50,0x59,0x4b,0xef,0x51,0x91,0xd8,0x39,0x46, + 0x91,0xf8,0x6e,0xdf,0xfc,0xad,0x6c,0x1e, + }; + const unsigned char tc_ADa[] = { + 0x41,0x44,0x61, + }; + const unsigned char tc_Ya[] = { + 0x62,0x7f,0x8b,0xb2,0xae,0x94,0x5e,0x2a,0x51,0x89,0x67,0xdf, + 0x9b,0x00,0xaf,0xf1,0x92,0x53,0xd3,0x08,0x63,0x98,0xf2,0xec, + 0x18,0xbe,0x84,0x6c,0xc0,0xd1,0xf2,0x86,0xc2,0xce,0x3c,0xaf, + 0x1d,0xa6,0x39,0x85,0x9c,0xcd,0x2a,0x6a,0x01,0xa9,0x37,0x2a, + 0x17,0xe6,0x6b,0xb7,0x00,0x6e,0x57,0x1b, + }; + const unsigned char tc_yb[] = { + 0x25,0x23,0xc9,0x69,0xf6,0x8f,0xa2,0xb2,0xae,0xa2,0x94,0xc2, + 0x53,0x9e,0xf3,0x6e,0xb1,0xe0,0x55,0x8a,0xbd,0x14,0x71,0x2a, + 0x78,0x28,0xf1,0x6a,0x85,0xed,0x2c,0x7e,0x77,0xe2,0xbd,0xd4, + 0x18,0x99,0x44,0x05,0xfb,0x1b,0x57,0xb6,0xbb,0xaa,0xdd,0x66, + 0x84,0x98,0x92,0xaa,0xc9,0xd8,0x14,0x02, + }; + const unsigned char tc_ADb[] = { + 0x41,0x44,0x62, + }; + const unsigned char tc_Yb[] = { + 0x8e,0x98,0x11,0xe4,0x40,0x2f,0xac,0x09,0x87,0x43,0xca,0x7b, + 0x2b,0x50,0x9b,0x91,0xb3,0x8c,0x8c,0xf1,0x36,0x0c,0xc6,0xca, + 0xb3,0x01,0x18,0x71,0x70,0x19,0x78,0x2b,0x7f,0x58,0xa5,0x91, + 0xc6,0x3d,0x9c,0x92,0x47,0xb7,0x74,0xe6,0xb0,0xe0,0xb8,0x26, + 0xff,0x4f,0x83,0x99,0xf9,0x47,0x72,0xdb, + }; + const unsigned char tc_K[] = { + 0x94,0xf4,0xae,0x49,0x4f,0x4e,0x8b,0x07,0xad,0xe3,0x35,0x47, + 0x26,0xee,0xe4,0x9c,0x55,0x18,0xb3,0x63,0xcd,0xa5,0x44,0xf5, + 0xb4,0x54,0x1b,0x97,0x32,0x83,0x0b,0xe3,0x7e,0xa0,0xe6,0x3f, + 0xc8,0x3f,0x54,0xbe,0x28,0x0d,0xea,0x07,0x47,0xa0,0x43,0xc7, + 0x6d,0x47,0x3e,0x01,0x68,0x9a,0xf7,0x7f, + }; + const unsigned char tc_ISK_IR[] = { + 0x9c,0x27,0x26,0xa6,0xcd,0xa1,0x17,0x93,0x49,0xcb,0xc3,0x8f, + 0x31,0x76,0x5e,0xab,0x64,0x6a,0x2a,0x5f,0x17,0x6f,0x30,0x19, + 0xfa,0xb4,0xa0,0xaa,0xbd,0x9d,0x17,0xc2,0xba,0x89,0x59,0x98, + 0xcf,0xf6,0x98,0xd8,0x01,0x76,0x1a,0x00,0x35,0x12,0xc1,0xcf, + 0x67,0xd1,0x44,0xb2,0x1e,0x1c,0xb6,0xd6,0xb8,0x2d,0xa7,0x1d, + 0x0d,0xa7,0x6c,0xad, + }; + const unsigned char tc_ISK_SY[] = { + 0x6d,0x21,0x78,0xed,0x30,0x48,0x70,0x30,0x25,0xb9,0x00,0x7e, + 0xc8,0x4c,0x4d,0x96,0x9e,0x8d,0x81,0x35,0xdf,0x45,0x5e,0x60, + 0x8c,0x16,0xaa,0x15,0x2e,0x12,0x19,0xc8,0x6c,0xea,0x56,0x32, + 0x54,0x42,0x8a,0x9d,0x96,0x99,0x03,0xae,0x36,0x49,0xd1,0x05, + 0x0d,0xa1,0xe6,0xe0,0xc1,0xc0,0x60,0xe1,0xeb,0xf7,0x31,0x6a, + 0x7e,0x99,0x33,0x89, + }; + const unsigned char tc_ISK_SY[] = { + 0x6d,0x21,0x78,0xed,0x30,0x48,0x70,0x30,0x25,0xb9,0x00,0x7e, + 0xc8,0x4c,0x4d,0x96,0x9e,0x8d,0x81,0x35,0xdf,0x45,0x5e,0x60, + 0x8c,0x16,0xaa,0x15,0x2e,0x12,0x19,0xc8,0x6c,0xea,0x56,0x32, + 0x54,0x42,0x8a,0x9d,0x96,0x99,0x03,0xae,0x36,0x49,0xd1,0x05, + 0x0d,0xa1,0xe6,0xe0,0xc1,0xc0,0x60,0xe1,0xeb,0xf7,0x31,0x6a, + 0x7e,0x99,0x33,0x89, + }; + const unsigned char tc_sid_out_ir[] = { + 0x65,0xbf,0xfd,0xe1,0x7b,0x7a,0xcf,0x07,0xcf,0xd4,0x37,0xbd, + 0xb9,0x73,0xa8,0xf7,0x34,0x0b,0xf9,0x11,0xd3,0x93,0xa6,0x14, + 0x98,0xc0,0xa5,0x0e,0xf0,0xd6,0x8b,0xca,0x10,0x3f,0xbd,0xb0, + 0xf5,0xb7,0x99,0x50,0x55,0x62,0xe5,0x98,0x11,0xdf,0x1b,0xc5, + 0xd9,0xb4,0xf5,0xf0,0xf7,0xc5,0x7c,0x22,0xcd,0x7e,0xd6,0xdb, + 0x4d,0x15,0x3e,0x3a, + }; + const unsigned char tc_sid_out_oc[] = { + 0x7c,0xe2,0x70,0x43,0xd1,0xb1,0xd0,0xd0,0xe0,0x2e,0x16,0x97, + 0x96,0x37,0xe2,0xa0,0x05,0x47,0xed,0x6e,0x15,0xea,0x98,0x8f, + 0x7d,0x3c,0x9b,0x3c,0x21,0x59,0xb2,0x6a,0xb3,0x83,0x4b,0xff, + 0x7f,0xf8,0x62,0x40,0x32,0x3e,0x25,0x21,0x6b,0xa2,0xee,0x6e, + 0xa6,0xe1,0x58,0x25,0x02,0x01,0x7f,0x8e,0x6d,0x65,0xf8,0xc4, + 0xa5,0xe6,0x55,0x43, + }; + +B.4.9. Testvectors as JSON file encoded as BASE64 + + #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT + #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI1 + #MjIzRTBDREM0NUQ2NTc1NjY4RDY0QzU1MjAwNDEyNCIsICJnIjogIjlBNzAwRUNDMz + #c4RUI5OEU1NzM4N0RGNDU2RDVCNEI0RjFEQ0VFQkJCMTM3MTUyN0VFQjdFMUJGQkFC + #NjRFQ0M5QzkzMDMzOTYxNDVCQTA0RjVCNUFFQTVCQUVERkE2MUYzMUYwMEZCQzVGRD + #U2MDYiLCAieWEiOiAiMzNENTYxRjEzQ0ZDMERDQTI3OUMzMEU4Q0RFODk1MTc1REMy + #NTQ4Mzg5MjgxOUVCQTEzMkQ1OEMxM0MwNDYyQThFQjBENzNGREE5NDE5NTA1OTRCRU + #Y1MTkxRDgzOTQ2OTFGODZFREZGQ0FENkMxRSIsICJBRGEiOiAiNDE0NDYxIiwgIllh + #IjogIjYyN0Y4QkIyQUU5NDVFMkE1MTg5NjdERjlCMDBBRkYxOTI1M0QzMDg2Mzk4Rj + #JFQzE4QkU4NDZDQzBEMUYyODZDMkNFM0NBRjFEQTYzOTg1OUNDRDJBNkEwMUE5Mzcy + #QTE3RTY2QkI3MDA2RTU3MUIiLCAieWIiOiAiMjUyM0M5NjlGNjhGQTJCMkFFQTI5NE + #MyNTM5RUYzNkVCMUUwNTU4QUJEMTQ3MTJBNzgyOEYxNkE4NUVEMkM3RTc3RTJCREQ0 + #MTg5OTQ0MDVGQjFCNTdCNkJCQUFERDY2ODQ5ODkyQUFDOUQ4MTQwMiIsICJBRGIiOi + #AiNDE0NDYyIiwgIlliIjogIjhFOTgxMUU0NDAyRkFDMDk4NzQzQ0E3QjJCNTA5Qjkx + #QjM4QzhDRjEzNjBDQzZDQUIzMDExODcxNzAxOTc4MkI3RjU4QTU5MUM2M0Q5QzkyND + #dCNzc0RTZCMEUwQjgyNkZGNEY4Mzk5Rjk0NzcyREIiLCAiSyI6ICI5NEY0QUU0OTRG + #NEU4QjA3QURFMzM1NDcyNkVFRTQ5QzU1MThCMzYzQ0RBNTQ0RjVCNDU0MUI5NzMyOD + #MwQkUzN0VBMEU2M0ZDODNGNTRCRTI4MERFQTA3NDdBMDQzQzc2RDQ3M0UwMTY4OUFG + #NzdGIiwgIklTS19JUiI6ICI5QzI3MjZBNkNEQTExNzkzNDlDQkMzOEYzMTc2NUVBQj + #Y0NkEyQTVGMTc2RjMwMTlGQUI0QTBBQUJEOUQxN0MyQkE4OTU5OThDRkY2OThEODAx + #NzYxQTAwMzUxMkMxQ0Y2N0QxNDRCMjFFMUNCNkQ2QjgyREE3MUQwREE3NkNBRCIsIC + #JJU0tfU1kiOiAiNkQyMTc4RUQzMDQ4NzAzMDI1QjkwMDdFQzg0QzREOTY5RThEODEz + #NURGNDU1RTYwOEMxNkFBMTUyRTEyMTlDODZDRUE1NjMyNTQ0MjhBOUQ5Njk5MDNBRT + #M2NDlEMTA1MERBMUU2RTBDMUMwNjBFMUVCRjczMTZBN0U5OTMzODkiLCAic2lkX291 + #dHB1dF9pciI6ICI2NUJGRkRFMTdCN0FDRjA3Q0ZENDM3QkRCOTczQThGNzM0MEJGOT + #ExRDM5M0E2MTQ5OEMwQTUwRUYwRDY4QkNBMTAzRkJEQjBGNUI3OTk1MDU1NjJFNTk4 + #MTFERjFCQzVEOUI0RjVGMEY3QzU3QzIyQ0Q3RUQ2REI0RDE1M0UzQSIsICJzaWRfb3 + #V0cHV0X29jIjogIjdDRTI3MDQzRDFCMUQwRDBFMDJFMTY5Nzk2MzdFMkEwMDU0N0VE + #NkUxNUVBOTg4RjdEM0M5QjNDMjE1OUIyNkFCMzgzNEJGRjdGRjg2MjQwMzIzRTI1Mj + #E2QkEyRUU2RUE2RTE1ODI1MDIwMTdGOEU2RDY1RjhDNEE1RTY1NTQzIn0= + +B.4.10. Test case for scalar_mult with valid inputs + + s: (length: 56 bytes) + dd1bc7015daabb7672129cc35a3ba815486b139deff9bdeca7a4fc61 + 34323d34658761e90ff079972a7ca8aa5606498f4f4f0ebc0933a819 + X: (length: 56 bytes) + 601431d5e51f43d422a92d3fb2373bde28217aab42524c341aa404ea + ba5aa5541f7042dbb3253ce4c90f772b038a413dcb3a0f6bf3ae9e21 + G.scalar_mult(s,decode(X)): (length: 56 bytes) + 388b35c60eb41b66085a2118316218681d78979d667702de105fdc1f + 21ffe884a577d795f45691781390a229a3bd7b527e831380f2f585a4 + G.scalar_mult_vfy(s,X): (length: 56 bytes) + 388b35c60eb41b66085a2118316218681d78979d667702de105fdc1f + 21ffe884a577d795f45691781390a229a3bd7b527e831380f2f585a4 + +B.4.11. Invalid inputs for scalar_mult_vfy + + For these test cases scalar_mult_vfy(y,.) MUST return the + representation of the neutral element G.I. When points Y_i1 or Y_i2 + are included in message of A or B the protocol MUST abort. + + s: (length: 56 bytes) + dd1bc7015daabb7672129cc35a3ba815486b139deff9bdeca7a4fc61 + 34323d34658761e90ff079972a7ca8aa5606498f4f4f0ebc0933a819 + Y_i1: (length: 56 bytes) + 5f1431d5e51f43d422a92d3fb2373bde28217aab42524c341aa404ea + ba5aa5541f7042dbb3253ce4c90f772b038a413dcb3a0f6bf3ae9e21 + Y_i2 == G.I: (length: 56 bytes) + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I + +B.4.11.1. Testvectors as JSON file encoded as BASE64 + + #eyJWYWxpZCI6IHsicyI6ICJERDFCQzcwMTVEQUFCQjc2NzIxMjlDQzM1QTNCQTgxNT + #Q4NkIxMzlERUZGOUJERUNBN0E0RkM2MTM0MzIzRDM0NjU4NzYxRTkwRkYwNzk5NzJB + #N0NBOEFBNTYwNjQ5OEY0RjRGMEVCQzA5MzNBODE5IiwgIlgiOiAiNjAxNDMxRDVFNT + #FGNDNENDIyQTkyRDNGQjIzNzNCREUyODIxN0FBQjQyNTI0QzM0MUFBNDA0RUFCQTVB + #QTU1NDFGNzA0MkRCQjMyNTNDRTRDOTBGNzcyQjAzOEE0MTNEQ0IzQTBGNkJGM0FFOU + #UyMSIsICJHLnNjYWxhcl9tdWx0KHMsZGVjb2RlKFgpKSI6ICIzODhCMzVDNjBFQjQx + #QjY2MDg1QTIxMTgzMTYyMTg2ODFENzg5NzlENjY3NzAyREUxMDVGREMxRjIxRkZFOD + #g0QTU3N0Q3OTVGNDU2OTE3ODEzOTBBMjI5QTNCRDdCNTI3RTgzMTM4MEYyRjU4NUE0 + #IiwgIkcuc2NhbGFyX211bHRfdmZ5KHMsWCkiOiAiMzg4QjM1QzYwRUI0MUI2NjA4NU + #EyMTE4MzE2MjE4NjgxRDc4OTc5RDY2NzcwMkRFMTA1RkRDMUYyMUZGRTg4NEE1NzdE + #Nzk1RjQ1NjkxNzgxMzkwQTIyOUEzQkQ3QjUyN0U4MzEzODBGMkY1ODVBNCJ9LCAiSW + #52YWxpZCBZMSI6ICI1RjE0MzFENUU1MUY0M0Q0MjJBOTJEM0ZCMjM3M0JERTI4MjE3 + #QUFCNDI1MjRDMzQxQUE0MDRFQUJBNUFBNTU0MUY3MDQyREJCMzI1M0NFNEM5MEY3Nz + #JCMDM4QTQxM0RDQjNBMEY2QkYzQUU5RTIxIiwgIkludmFsaWQgWTIiOiAiMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMCJ9 + +B.5. Test vector for CPace using group NIST P-256 and hash SHA-256 + +B.5.1. Test vectors for calculate_generator with group NIST P-256 + + Inputs + H = SHA-256 with input block size 64 bytes. + PRS = b'Password' ; ZPAD length: 23 ; + DSI = b'CPaceP256_XMD:SHA-256_SSWU_NU_' + DST = b'CPaceP256_XMD:SHA-256_SSWU_NU__DST' + CI = b'oc\x0bB_responder\x0bA_initiator' + CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72 + sid = 34b36454cab2e7842c389f7d88ecb7df + Outputs + generator_string(PRS,G.DSI,CI,sid,H.s_in_bytes): + (length: 108 bytes) + 1e4350616365503235365f584d443a5348412d3235365f535357555f + 4e555f0850617373776f726417000000000000000000000000000000 + 00000000000000001a6f630b425f726573706f6e6465720b415f696e + 69746961746f721034b36454cab2e7842c389f7d88ecb7df + generator g: (length: 65 bytes) + 04eee577320b1c241a79419fcde5718c2b63f81ef8717d56a57d2fb2 + 6b65a8beb63573b52605efb32ff4cf31aaef9a92df84e4e8408cc6c7 + cf27a535aad2b38a56 + +B.5.1.1. Testvectors as JSON file encoded as BASE64 + + #eyJIIjogIlNIQS0yNTYiLCAiSC5zX2luX2J5dGVzIjogNjQsICJQUlMiOiAiNTA2MT + #czNzM3NzZGNzI2NCIsICJaUEFEIGxlbmd0aCI6IDIzLCAiRFNJIjogIjQzNTA2MTYz + #NjU1MDMyMzUzNjVGNTg0RDQ0M0E1MzQ4NDEyRDMyMzUzNjVGNTM1MzU3NTU1RjRFNT + #U1RiIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NTczNzA2RjZFNjQ2NTcyMEI0MTVGNjk2 + #RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICIzNEIzNjQ1NENBQjJFNzg0MkMzODlGN0 + #Q4OEVDQjdERiIsICJnZW5lcmF0b3Jfc3RyaW5nKEcuRFNJLFBSUyxDSSxzaWQsSC5z + #X2luX2J5dGVzKSI6ICIxRTQzNTA2MTYzNjU1MDMyMzUzNjVGNTg0RDQ0M0E1MzQ4ND + #EyRDMyMzUzNjVGNTM1MzU3NTU1RjRFNTU1RjA4NTA2MTczNzM3NzZGNzI2NDE3MDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDFBNkY2Mz + #BCNDI1RjcyNjU3MzcwNkY2RTY0NjU3MjBCNDE1RjY5NkU2OTc0Njk2MTc0NkY3MjEw + #MzRCMzY0NTRDQUIyRTc4NDJDMzg5RjdEODhFQ0I3REYiLCAiZ2VuZXJhdG9yIGciOi + #AiMDRFRUU1NzczMjBCMUMyNDFBNzk0MTlGQ0RFNTcxOEMyQjYzRjgxRUY4NzE3RDU2 + #QTU3RDJGQjI2QjY1QThCRUI2MzU3M0I1MjYwNUVGQjMyRkY0Q0YzMUFBRUY5QTkyRE + #Y4NEU0RTg0MDhDQzZDN0NGMjdBNTM1QUFEMkIzOEE1NiJ9 + +B.5.2. Test vector for message from A + + Inputs + ADa = b'ADa' + ya (big endian): (length: 32 bytes) + 37574cfbf1b95ff6a8e2d7be462d4d01e6dde2618f34f4de9df869b2 + 4f532c5d + Outputs + Ya: (length: 65 bytes) + 041f12ad5fc65010a24fc04c86197109a36df0e9ce85a7479e1e1364 + 692fdace17ea5a634e19c207a5d52ead6c6817a163cf2f2fe3406c5d + fdfc2ecdf8e42c5e16 + Alternative correct value for Ya: (-ya)*g: + (length: 65 bytes) + 041f12ad5fc65010a24fc04c86197109a36df0e9ce85a7479e1e1364 + 692fdace1715a59cb0e63df85b2ad1529397e85e9c30d0d01dbf93a2 + 0203d132071bd3a1e9 + +B.5.3. Test vector for message from B + + Inputs + ADb = b'ADb' + yb (big endian): (length: 32 bytes) + e5672fc9eb4e721f41d80181ec4c9fd9886668acc48024d33c82bb10 + 2aecba52 + Outputs + Yb: (length: 65 bytes) + 046a51180b6ebabaf5ed0af8cd786886d93342bcae4c158ce1617a0a + cc8ec354486f9ed2e9210913206d1e3f5e463d2d320c4f1f5ce8b677 + a7e38a26f752bf8f84 + Alternative correct value for Yb: (-yb)*g: + (length: 65 bytes) + 046a51180b6ebabaf5ed0af8cd786886d93342bcae4c158ce1617a0a + cc8ec3544890612d15def6ece092e1c0a1b9c2d2cdf3b0e0a4174988 + 581c75d908ad40707b + +B.5.4. Test vector for secret points K + + scalar_mult_vfy(ya,Yb): (length: 32 bytes) + 3e0e2f8976fb8d0deee30aef4b5cd3631eed249af32f53d0dd009b5d + 7b8f6b6c + scalar_mult_vfy(yb,Ya): (length: 32 bytes) + 3e0e2f8976fb8d0deee30aef4b5cd3631eed249af32f53d0dd009b5d + 7b8f6b6c + +B.5.5. Test vector for ISK calculation initiator/responder + + transcript_ir(Ya,ADa,Yb,ADb): (length: 140 bytes) + 41041f12ad5fc65010a24fc04c86197109a36df0e9ce85a7479e1e13 + 64692fdace17ea5a634e19c207a5d52ead6c6817a163cf2f2fe3406c + 5dfdfc2ecdf8e42c5e160341446141046a51180b6ebabaf5ed0af8cd + 786886d93342bcae4c158ce1617a0acc8ec354486f9ed2e921091320 + 6d1e3f5e463d2d320c4f1f5ce8b677a7e38a26f752bf8f8403414462 + DSI = G.DSI_ISK, b'CPaceP256_XMD:SHA-256_SSWU_NU__ISK': + (length: 34 bytes) + 4350616365503235365f584d443a5348412d3235365f535357555f4e + 555f5f49534b + lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb): + (length: 225 bytes) + 224350616365503235365f584d443a5348412d3235365f535357555f + 4e555f5f49534b1034b36454cab2e7842c389f7d88ecb7df203e0e2f + 8976fb8d0deee30aef4b5cd3631eed249af32f53d0dd009b5d7b8f6b + 6c41041f12ad5fc65010a24fc04c86197109a36df0e9ce85a7479e1e + 1364692fdace17ea5a634e19c207a5d52ead6c6817a163cf2f2fe340 + 6c5dfdfc2ecdf8e42c5e160341446141046a51180b6ebabaf5ed0af8 + cd786886d93342bcae4c158ce1617a0acc8ec354486f9ed2e9210913 + 206d1e3f5e463d2d320c4f1f5ce8b677a7e38a26f752bf8f84034144 + 62 + ISK result: (length: 32 bytes) + 9565ed286b6e3cf1f943fd31746f9a22935537025a1328d4980005ba + 984f0c39 + +B.5.6. Test vector for ISK calculation parallel execution + + transcript_oc(Ya,ADa,Yb,ADb): (length: 142 bytes) + 6f6341046a51180b6ebabaf5ed0af8cd786886d93342bcae4c158ce1 + 617a0acc8ec354486f9ed2e9210913206d1e3f5e463d2d320c4f1f5c + e8b677a7e38a26f752bf8f840341446241041f12ad5fc65010a24fc0 + 4c86197109a36df0e9ce85a7479e1e1364692fdace17ea5a634e19c2 + 07a5d52ead6c6817a163cf2f2fe3406c5dfdfc2ecdf8e42c5e160341 + 4461 + DSI = G.DSI_ISK, b'CPaceP256_XMD:SHA-256_SSWU_NU__ISK': + (length: 34 bytes) + 4350616365503235365f584d443a5348412d3235365f535357555f4e + 555f5f49534b + lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb): + (length: 227 bytes) + 224350616365503235365f584d443a5348412d3235365f535357555f + 4e555f5f49534b1034b36454cab2e7842c389f7d88ecb7df203e0e2f + 8976fb8d0deee30aef4b5cd3631eed249af32f53d0dd009b5d7b8f6b + 6c6f6341046a51180b6ebabaf5ed0af8cd786886d93342bcae4c158c + e1617a0acc8ec354486f9ed2e9210913206d1e3f5e463d2d320c4f1f + 5ce8b677a7e38a26f752bf8f840341446241041f12ad5fc65010a24f + c04c86197109a36df0e9ce85a7479e1e1364692fdace17ea5a634e19 + c207a5d52ead6c6817a163cf2f2fe3406c5dfdfc2ecdf8e42c5e1603 + 414461 + ISK result: (length: 32 bytes) + 62a445a4daa3546dd031c66ead2e4e015abbcc83bde31c90f841149f + d441c58a + +B.5.7. Test vector for optional output of session id + + H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)): + (length: 32 bytes) + a7386d1c2eb06e8056d7fecbcf691e08d189d96236020ef31b414069 + 8a4b99f9 + H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)): + (length: 32 bytes) + d337dbc0dd797b4e6f2f14ea4925c58e5d5523871e8cb43a3c1b0f2b + 1a1ffde3 + +B.5.8. Corresponding C programming language initializers + + const unsigned char tc_PRS[] = { + 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64, + }; + const unsigned char tc_CI[] = { + 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64, + 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74, + 0x6f,0x72, + }; + const unsigned char tc_sid[] = { + 0x34,0xb3,0x64,0x54,0xca,0xb2,0xe7,0x84,0x2c,0x38,0x9f,0x7d, + 0x88,0xec,0xb7,0xdf, + }; + const unsigned char tc_g[] = { + 0x04,0xee,0xe5,0x77,0x32,0x0b,0x1c,0x24,0x1a,0x79,0x41,0x9f, + 0xcd,0xe5,0x71,0x8c,0x2b,0x63,0xf8,0x1e,0xf8,0x71,0x7d,0x56, + 0xa5,0x7d,0x2f,0xb2,0x6b,0x65,0xa8,0xbe,0xb6,0x35,0x73,0xb5, + 0x26,0x05,0xef,0xb3,0x2f,0xf4,0xcf,0x31,0xaa,0xef,0x9a,0x92, + 0xdf,0x84,0xe4,0xe8,0x40,0x8c,0xc6,0xc7,0xcf,0x27,0xa5,0x35, + 0xaa,0xd2,0xb3,0x8a,0x56, + }; + const unsigned char tc_ya[] = { + 0x37,0x57,0x4c,0xfb,0xf1,0xb9,0x5f,0xf6,0xa8,0xe2,0xd7,0xbe, + 0x46,0x2d,0x4d,0x01,0xe6,0xdd,0xe2,0x61,0x8f,0x34,0xf4,0xde, + 0x9d,0xf8,0x69,0xb2,0x4f,0x53,0x2c,0x5d, + }; + const unsigned char tc_ADa[] = { + 0x41,0x44,0x61, + }; + const unsigned char tc_Ya[] = { + 0x04,0x1f,0x12,0xad,0x5f,0xc6,0x50,0x10,0xa2,0x4f,0xc0,0x4c, + 0x86,0x19,0x71,0x09,0xa3,0x6d,0xf0,0xe9,0xce,0x85,0xa7,0x47, + 0x9e,0x1e,0x13,0x64,0x69,0x2f,0xda,0xce,0x17,0xea,0x5a,0x63, + 0x4e,0x19,0xc2,0x07,0xa5,0xd5,0x2e,0xad,0x6c,0x68,0x17,0xa1, + 0x63,0xcf,0x2f,0x2f,0xe3,0x40,0x6c,0x5d,0xfd,0xfc,0x2e,0xcd, + 0xf8,0xe4,0x2c,0x5e,0x16, + }; + const unsigned char tc_yb[] = { + 0xe5,0x67,0x2f,0xc9,0xeb,0x4e,0x72,0x1f,0x41,0xd8,0x01,0x81, + 0xec,0x4c,0x9f,0xd9,0x88,0x66,0x68,0xac,0xc4,0x80,0x24,0xd3, + 0x3c,0x82,0xbb,0x10,0x2a,0xec,0xba,0x52, + }; + const unsigned char tc_ADb[] = { + 0x41,0x44,0x62, + }; + const unsigned char tc_Yb[] = { + 0x04,0x6a,0x51,0x18,0x0b,0x6e,0xba,0xba,0xf5,0xed,0x0a,0xf8, + 0xcd,0x78,0x68,0x86,0xd9,0x33,0x42,0xbc,0xae,0x4c,0x15,0x8c, + 0xe1,0x61,0x7a,0x0a,0xcc,0x8e,0xc3,0x54,0x48,0x6f,0x9e,0xd2, + 0xe9,0x21,0x09,0x13,0x20,0x6d,0x1e,0x3f,0x5e,0x46,0x3d,0x2d, + 0x32,0x0c,0x4f,0x1f,0x5c,0xe8,0xb6,0x77,0xa7,0xe3,0x8a,0x26, + 0xf7,0x52,0xbf,0x8f,0x84, + }; + const unsigned char tc_K[] = { + 0x3e,0x0e,0x2f,0x89,0x76,0xfb,0x8d,0x0d,0xee,0xe3,0x0a,0xef, + 0x4b,0x5c,0xd3,0x63,0x1e,0xed,0x24,0x9a,0xf3,0x2f,0x53,0xd0, + 0xdd,0x00,0x9b,0x5d,0x7b,0x8f,0x6b,0x6c, + }; + const unsigned char tc_ISK_IR[] = { + 0x95,0x65,0xed,0x28,0x6b,0x6e,0x3c,0xf1,0xf9,0x43,0xfd,0x31, + 0x74,0x6f,0x9a,0x22,0x93,0x55,0x37,0x02,0x5a,0x13,0x28,0xd4, + 0x98,0x00,0x05,0xba,0x98,0x4f,0x0c,0x39, + }; + const unsigned char tc_ISK_SY[] = { + 0x62,0xa4,0x45,0xa4,0xda,0xa3,0x54,0x6d,0xd0,0x31,0xc6,0x6e, + 0xad,0x2e,0x4e,0x01,0x5a,0xbb,0xcc,0x83,0xbd,0xe3,0x1c,0x90, + 0xf8,0x41,0x14,0x9f,0xd4,0x41,0xc5,0x8a, + }; + const unsigned char tc_ISK_SY[] = { + 0x62,0xa4,0x45,0xa4,0xda,0xa3,0x54,0x6d,0xd0,0x31,0xc6,0x6e, + 0xad,0x2e,0x4e,0x01,0x5a,0xbb,0xcc,0x83,0xbd,0xe3,0x1c,0x90, + 0xf8,0x41,0x14,0x9f,0xd4,0x41,0xc5,0x8a, + }; + const unsigned char tc_sid_out_ir[] = { + 0xa7,0x38,0x6d,0x1c,0x2e,0xb0,0x6e,0x80,0x56,0xd7,0xfe,0xcb, + 0xcf,0x69,0x1e,0x08,0xd1,0x89,0xd9,0x62,0x36,0x02,0x0e,0xf3, + 0x1b,0x41,0x40,0x69,0x8a,0x4b,0x99,0xf9, + }; + const unsigned char tc_sid_out_oc[] = { + 0xd3,0x37,0xdb,0xc0,0xdd,0x79,0x7b,0x4e,0x6f,0x2f,0x14,0xea, + 0x49,0x25,0xc5,0x8e,0x5d,0x55,0x23,0x87,0x1e,0x8c,0xb4,0x3a, + 0x3c,0x1b,0x0f,0x2b,0x1a,0x1f,0xfd,0xe3, + }; + +B.5.9. Testvectors as JSON file encoded as BASE64 + + #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT + #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICIz + #NEIzNjQ1NENBQjJFNzg0MkMzODlGN0Q4OEVDQjdERiIsICJnIjogIjA0RUVFNTc3Mz + #IwQjFDMjQxQTc5NDE5RkNERTU3MThDMkI2M0Y4MUVGODcxN0Q1NkE1N0QyRkIyNkI2 + #NUE4QkVCNjM1NzNCNTI2MDVFRkIzMkZGNENGMzFBQUVGOUE5MkRGODRFNEU4NDA4Q0 + #M2QzdDRjI3QTUzNUFBRDJCMzhBNTYiLCAieWEiOiAiMzc1NzRDRkJGMUI5NUZGNkE4 + #RTJEN0JFNDYyRDREMDFFNkRERTI2MThGMzRGNERFOURGODY5QjI0RjUzMkM1RCIsIC + #JBRGEiOiAiNDE0NDYxIiwgIllhIjogIjA0MUYxMkFENUZDNjUwMTBBMjRGQzA0Qzg2 + #MTk3MTA5QTM2REYwRTlDRTg1QTc0NzlFMUUxMzY0NjkyRkRBQ0UxN0VBNUE2MzRFMT + #lDMjA3QTVENTJFQUQ2QzY4MTdBMTYzQ0YyRjJGRTM0MDZDNURGREZDMkVDREY4RTQy + #QzVFMTYiLCAieWIiOiAiRTU2NzJGQzlFQjRFNzIxRjQxRDgwMTgxRUM0QzlGRDk4OD + #Y2NjhBQ0M0ODAyNEQzM0M4MkJCMTAyQUVDQkE1MiIsICJBRGIiOiAiNDE0NDYyIiwg + #IlliIjogIjA0NkE1MTE4MEI2RUJBQkFGNUVEMEFGOENENzg2ODg2RDkzMzQyQkNBRT + #RDMTU4Q0UxNjE3QTBBQ0M4RUMzNTQ0ODZGOUVEMkU5MjEwOTEzMjA2RDFFM0Y1RTQ2 + #M0QyRDMyMEM0RjFGNUNFOEI2NzdBN0UzOEEyNkY3NTJCRjhGODQiLCAiSyI6ICIzRT + #BFMkY4OTc2RkI4RDBERUVFMzBBRUY0QjVDRDM2MzFFRUQyNDlBRjMyRjUzRDBERDAw + #OUI1RDdCOEY2QjZDIiwgIklTS19JUiI6ICI5NTY1RUQyODZCNkUzQ0YxRjk0M0ZEMz + #E3NDZGOUEyMjkzNTUzNzAyNUExMzI4RDQ5ODAwMDVCQTk4NEYwQzM5IiwgIklTS19T + #WSI6ICI2MkE0NDVBNERBQTM1NDZERDAzMUM2NkVBRDJFNEUwMTVBQkJDQzgzQkRFMz + #FDOTBGODQxMTQ5RkQ0NDFDNThBIiwgInNpZF9vdXRwdXRfaXIiOiAiQTczODZEMUMy + #RUIwNkU4MDU2RDdGRUNCQ0Y2OTFFMDhEMTg5RDk2MjM2MDIwRUYzMUI0MTQwNjk4QT + #RCOTlGOSIsICJzaWRfb3V0cHV0X29jIjogIkQzMzdEQkMwREQ3OTdCNEU2RjJGMTRF + #QTQ5MjVDNThFNUQ1NTIzODcxRThDQjQzQTNDMUIwRjJCMUExRkZERTMifQ== + +B.5.10. Test case for scalar_mult_vfy with correct inputs + + s: (length: 32 bytes) + f012501c091ff9b99a123fffe571d8bc01e8077ee581362e1bd21399 + 0835643b + X: (length: 65 bytes) + 0424648eb986c2be0af636455cef0550671d6bcd8aa26e0d72ffa1b1 + fd12ba4e0f78da2b6d2184f31af39e566aef127014b6936c9a37346d + 10a4ab2514faef5831 + G.scalar_mult(s,X) (full coordinates): (length: 65 bytes) + 04f5a191f078c87c36633b78c701751159d56c59f3fe9105b5720673 + 470f303ab925b6a7fd1cdd8f649a21cf36b68d9e9c4a11919a951892 + 519786104b27033757 + G.scalar_mult_vfy(s,X) (only X-coordinate): + (length: 32 bytes) + f5a191f078c87c36633b78c701751159d56c59f3fe9105b572067347 + 0f303ab9 + +B.5.11. Invalid inputs for scalar_mult_vfy + + For these test cases scalar_mult_vfy(y,.) MUST return the + representation of the neutral element G.I. When including Y_i1 or + Y_i2 in messages of A or B the protocol MUST abort. + + s: (length: 32 bytes) + f012501c091ff9b99a123fffe571d8bc01e8077ee581362e1bd21399 + 0835643b + Y_i1: (length: 65 bytes) + 0424648eb986c2be0af636455cef0550671d6bcd8aa26e0d72ffa1b1 + fd12ba4e0f78da2b6d2184f31af39e566aef127014b6936c9a37346d + 10a4ab2514faef5857 + Y_i2: (length: 1 bytes) + 00 + G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I + +B.5.11.1. Testvectors as JSON file encoded as BASE64 + + #eyJWYWxpZCI6IHsicyI6ICJGMDEyNTAxQzA5MUZGOUI5OUExMjNGRkZFNTcxRDhCQz + #AxRTgwNzdFRTU4MTM2MkUxQkQyMTM5OTA4MzU2NDNCIiwgIlgiOiAiMDQyNDY0OEVC + #OTg2QzJCRTBBRjYzNjQ1NUNFRjA1NTA2NzFENkJDRDhBQTI2RTBENzJGRkExQjFGRD + #EyQkE0RTBGNzhEQTJCNkQyMTg0RjMxQUYzOUU1NjZBRUYxMjcwMTRCNjkzNkM5QTM3 + #MzQ2RDEwQTRBQjI1MTRGQUVGNTgzMSIsICJHLnNjYWxhcl9tdWx0KHMsWCkgKGZ1bG + #wgY29vcmRpbmF0ZXMpIjogIjA0RjVBMTkxRjA3OEM4N0MzNjYzM0I3OEM3MDE3NTEx + #NTlENTZDNTlGM0ZFOTEwNUI1NzIwNjczNDcwRjMwM0FCOTI1QjZBN0ZEMUNERDhGNj + #Q5QTIxQ0YzNkI2OEQ5RTlDNEExMTkxOUE5NTE4OTI1MTk3ODYxMDRCMjcwMzM3NTci + #LCAiRy5zY2FsYXJfbXVsdF92ZnkocyxYKSAob25seSBYLWNvb3JkaW5hdGUpIjogIk + #Y1QTE5MUYwNzhDODdDMzY2MzNCNzhDNzAxNzUxMTU5RDU2QzU5RjNGRTkxMDVCNTcy + #MDY3MzQ3MEYzMDNBQjkifSwgIkludmFsaWQgWTEiOiAiMDQyNDY0OEVCOTg2QzJCRT + #BBRjYzNjQ1NUNFRjA1NTA2NzFENkJDRDhBQTI2RTBENzJGRkExQjFGRDEyQkE0RTBG + #NzhEQTJCNkQyMTg0RjMxQUYzOUU1NjZBRUYxMjcwMTRCNjkzNkM5QTM3MzQ2RDEwQT + #RBQjI1MTRGQUVGNTg1NyIsICJJbnZhbGlkIFkyIjogIjAwIn0= + +B.6. Test vector for CPace using group NIST P-384 and hash SHA-384 + +B.6.1. Test vectors for calculate_generator with group NIST P-384 + + Inputs + H = SHA-384 with input block size 128 bytes. + PRS = b'Password' ; ZPAD length: 87 ; + DSI = b'CPaceP384_XMD:SHA-384_SSWU_NU_' + DST = b'CPaceP384_XMD:SHA-384_SSWU_NU__DST' + CI = b'oc\x0bB_responder\x0bA_initiator' + CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72 + sid = 5b3773aa90e8f23c61563a4b645b276c + Outputs + generator_string(PRS,G.DSI,CI,sid,H.s_in_bytes): + (length: 172 bytes) + 1e4350616365503338345f584d443a5348412d3338345f535357555f + 4e555f0850617373776f726457000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000001a6f630b425f726573706f6e + 6465720b415f696e69746961746f72105b3773aa90e8f23c61563a4b + 645b276c + generator g: (length: 97 bytes) + 04ffe1bdc3293fdbe31b2959916e52c018e923eac99836bd9a1cbeec + 794a8d4d78baa32cdafc9685bc1067a780f4ad9c8a6c6e164aa42906 + d1e27f782581adc8e0109219626a2b8fbdc34602e4084554bdd6c0c6 + 98dd657ac8e31b2bcce1c7b0d8 + +B.6.1.1. Testvectors as JSON file encoded as BASE64 + + #eyJIIjogIlNIQS0zODQiLCAiSC5zX2luX2J5dGVzIjogMTI4LCAiUFJTIjogIjUwNj + #E3MzczNzc2RjcyNjQiLCAiWlBBRCBsZW5ndGgiOiA4NywgIkRTSSI6ICI0MzUwNjE2 + #MzY1NTAzMzM4MzQ1RjU4NEQ0NDNBNTM0ODQxMkQzMzM4MzQ1RjUzNTM1NzU1NUY0RT + #U1NUYiLCAiQ0kiOiAiNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0NjU3MjBCNDE1RjY5 + #NkU2OTc0Njk2MTc0NkY3MiIsICJzaWQiOiAiNUIzNzczQUE5MEU4RjIzQzYxNTYzQT + #RCNjQ1QjI3NkMiLCAiZ2VuZXJhdG9yX3N0cmluZyhHLkRTSSxQUlMsQ0ksc2lkLEgu + #c19pbl9ieXRlcykiOiAiMUU0MzUwNjE2MzY1NTAzMzM4MzQ1RjU4NEQ0NDNBNTM0OD + #QxMkQzMzM4MzQ1RjUzNTM1NzU1NUY0RTU1NUYwODUwNjE3MzczNzc2RjcyNjQ1NzAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDFBNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0 + #NjU3MjBCNDE1RjY5NkU2OTc0Njk2MTc0NkY3MjEwNUIzNzczQUE5MEU4RjIzQzYxNT + #YzQTRCNjQ1QjI3NkMiLCAiZ2VuZXJhdG9yIGciOiAiMDRGRkUxQkRDMzI5M0ZEQkUz + #MUIyOTU5OTE2RTUyQzAxOEU5MjNFQUM5OTgzNkJEOUExQ0JFRUM3OTRBOEQ0RDc4Qk + #FBMzJDREFGQzk2ODVCQzEwNjdBNzgwRjRBRDlDOEE2QzZFMTY0QUE0MjkwNkQxRTI3 + #Rjc4MjU4MUFEQzhFMDEwOTIxOTYyNkEyQjhGQkRDMzQ2MDJFNDA4NDU1NEJERDZDME + #M2OThERDY1N0FDOEUzMUIyQkNDRTFDN0IwRDgifQ== + +B.6.2. Test vector for message from A + + Inputs + ADa = b'ADa' + ya (big endian): (length: 48 bytes) + ef433dd5ad142c860e7cb6400dd315d388d5ec5420c550e9d6f0907f + 375d988bc4d704837e43561c497e7dd93edcdb9d + Outputs + Ya: (length: 97 bytes) + 0434a04da121995d81d7c5ded02cf2e70954dca49059485ea38310b7 + 3b96fa1ec78619c5a1e524472778331fbe009fa1564a3203e42993a3 + 6285fa54e6c24184fd227458c87781be16fff46dbc970cc1b1770050 + a94d6826d52f211b234792e66d + Alternative correct value for Ya: (-ya)*g: + (length: 97 bytes) + 0434a04da121995d81d7c5ded02cf2e70954dca49059485ea38310b7 + 3b96fa1ec78619c5a1e524472778331fbe009fa156b5cdfc1bd66c5c + 9d7a05ab193dbe7b02dd8ba737887e41e9000b924368f33e4d88ffaf + 55b297d92ad0dee4ddb86d1992 + +B.6.3. Test vector for message from B + + Inputs + ADb = b'ADb' + yb (big endian): (length: 48 bytes) + 50b0e36b95a2edfaa8342b843dddc90b175330f2399c1b36586dedda + 3c255975f30be6a750f9404fccc62a6323b5e471 + Outputs + Yb: (length: 97 bytes) + 040a6559147fd492ad74ab1f4def6196fd6399540e84706227a1f90d + 104cdaeb630b7c5c18748deb25653ad2a4cb5e6274841cad328bb031 + 2628b9b1f51bea72b8c610999a6730f752649205ae85c452ef83f98b + e715cd0103186874b07cf02074 + Alternative correct value for Yb: (-yb)*g: + (length: 97 bytes) + 040a6559147fd492ad74ab1f4def6196fd6399540e84706227a1f90d + 104cdaeb630b7c5c18748deb25653ad2a4cb5e62747be352cd744fce + d9d7464e0ae4158d4739ef666598cf08ad9b6dfa517a3bad0f7c0674 + 17ea32fefce7978b50830fdf8b + +B.6.4. Test vector for secret points K + + scalar_mult_vfy(ya,Yb): (length: 48 bytes) + a9acaea95692a64462067fe8e4321f2fca9793a8a0420f0e253ed0d6 + db858fe161de7576206a8a35bd4a60e00724fd3e + scalar_mult_vfy(yb,Ya): (length: 48 bytes) + a9acaea95692a64462067fe8e4321f2fca9793a8a0420f0e253ed0d6 + db858fe161de7576206a8a35bd4a60e00724fd3e + +B.6.5. Test vector for ISK calculation initiator/responder + + transcript_ir(Ya,ADa,Yb,ADb): (length: 204 bytes) + 610434a04da121995d81d7c5ded02cf2e70954dca49059485ea38310 + b73b96fa1ec78619c5a1e524472778331fbe009fa1564a3203e42993 + a36285fa54e6c24184fd227458c87781be16fff46dbc970cc1b17700 + 50a94d6826d52f211b234792e66d0341446161040a6559147fd492ad + 74ab1f4def6196fd6399540e84706227a1f90d104cdaeb630b7c5c18 + 748deb25653ad2a4cb5e6274841cad328bb0312628b9b1f51bea72b8 + c610999a6730f752649205ae85c452ef83f98be715cd0103186874b0 + 7cf0207403414462 + DSI = G.DSI_ISK, b'CPaceP384_XMD:SHA-384_SSWU_NU__ISK': + (length: 34 bytes) + 4350616365503338345f584d443a5348412d3338345f535357555f4e + 555f5f49534b + lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb): + (length: 305 bytes) + 224350616365503338345f584d443a5348412d3338345f535357555f + 4e555f5f49534b105b3773aa90e8f23c61563a4b645b276c30a9acae + a95692a64462067fe8e4321f2fca9793a8a0420f0e253ed0d6db858f + e161de7576206a8a35bd4a60e00724fd3e610434a04da121995d81d7 + c5ded02cf2e70954dca49059485ea38310b73b96fa1ec78619c5a1e5 + 24472778331fbe009fa1564a3203e42993a36285fa54e6c24184fd22 + 7458c87781be16fff46dbc970cc1b1770050a94d6826d52f211b2347 + 92e66d0341446161040a6559147fd492ad74ab1f4def6196fd639954 + 0e84706227a1f90d104cdaeb630b7c5c18748deb25653ad2a4cb5e62 + 74841cad328bb0312628b9b1f51bea72b8c610999a6730f752649205 + ae85c452ef83f98be715cd0103186874b07cf0207403414462 + ISK result: (length: 48 bytes) + d1b74375c7d63d7de246cbf3fc2b3092645c73a0aa816989c0de6048 + ed4ece6a54df82d05d2be3498cb9288be7bdbdb9 + +B.6.6. Test vector for ISK calculation parallel execution + + transcript_oc(Ya,ADa,Yb,ADb): (length: 206 bytes) + 6f63610434a04da121995d81d7c5ded02cf2e70954dca49059485ea3 + 8310b73b96fa1ec78619c5a1e524472778331fbe009fa1564a3203e4 + 2993a36285fa54e6c24184fd227458c87781be16fff46dbc970cc1b1 + 770050a94d6826d52f211b234792e66d0341446161040a6559147fd4 + 92ad74ab1f4def6196fd6399540e84706227a1f90d104cdaeb630b7c + 5c18748deb25653ad2a4cb5e6274841cad328bb0312628b9b1f51bea + 72b8c610999a6730f752649205ae85c452ef83f98be715cd01031868 + 74b07cf0207403414462 + DSI = G.DSI_ISK, b'CPaceP384_XMD:SHA-384_SSWU_NU__ISK': + (length: 34 bytes) + 4350616365503338345f584d443a5348412d3338345f535357555f4e + 555f5f49534b + lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb): + (length: 307 bytes) + 224350616365503338345f584d443a5348412d3338345f535357555f + 4e555f5f49534b105b3773aa90e8f23c61563a4b645b276c30a9acae + a95692a64462067fe8e4321f2fca9793a8a0420f0e253ed0d6db858f + e161de7576206a8a35bd4a60e00724fd3e6f63610434a04da121995d + 81d7c5ded02cf2e70954dca49059485ea38310b73b96fa1ec78619c5 + a1e524472778331fbe009fa1564a3203e42993a36285fa54e6c24184 + fd227458c87781be16fff46dbc970cc1b1770050a94d6826d52f211b + 234792e66d0341446161040a6559147fd492ad74ab1f4def6196fd63 + 99540e84706227a1f90d104cdaeb630b7c5c18748deb25653ad2a4cb + 5e6274841cad328bb0312628b9b1f51bea72b8c610999a6730f75264 + 9205ae85c452ef83f98be715cd0103186874b07cf0207403414462 + ISK result: (length: 48 bytes) + a051d4532ca9fb6774e097ebac69c1d6a18144a15421dc155d0b1e8a + ef9f9d8c0fe86e85d3cbee7796ff50171f42801b + +B.6.7. Test vector for optional output of session id + + H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)): + (length: 48 bytes) + 8d5a03946a69ffa12cd6efd469fe8671bbc25fad6db2656f3963c94e + 9c940bdecc2bd555474c211817787d5cf7870ed1 + H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)): + (length: 48 bytes) + c0729db25db40c48a35f787d5410b2cb9a2d9f5e9cf1cf159ed2f63c + 6b2185e597e176cc221422e9496eeda2bf123c8b + +B.6.8. Corresponding C programming language initializers + + const unsigned char tc_PRS[] = { + 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64, + }; + const unsigned char tc_CI[] = { + 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64, + 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74, + 0x6f,0x72, + }; + const unsigned char tc_sid[] = { + 0x5b,0x37,0x73,0xaa,0x90,0xe8,0xf2,0x3c,0x61,0x56,0x3a,0x4b, + 0x64,0x5b,0x27,0x6c, + }; + const unsigned char tc_g[] = { + 0x04,0xff,0xe1,0xbd,0xc3,0x29,0x3f,0xdb,0xe3,0x1b,0x29,0x59, + 0x91,0x6e,0x52,0xc0,0x18,0xe9,0x23,0xea,0xc9,0x98,0x36,0xbd, + 0x9a,0x1c,0xbe,0xec,0x79,0x4a,0x8d,0x4d,0x78,0xba,0xa3,0x2c, + 0xda,0xfc,0x96,0x85,0xbc,0x10,0x67,0xa7,0x80,0xf4,0xad,0x9c, + 0x8a,0x6c,0x6e,0x16,0x4a,0xa4,0x29,0x06,0xd1,0xe2,0x7f,0x78, + 0x25,0x81,0xad,0xc8,0xe0,0x10,0x92,0x19,0x62,0x6a,0x2b,0x8f, + 0xbd,0xc3,0x46,0x02,0xe4,0x08,0x45,0x54,0xbd,0xd6,0xc0,0xc6, + 0x98,0xdd,0x65,0x7a,0xc8,0xe3,0x1b,0x2b,0xcc,0xe1,0xc7,0xb0, + 0xd8, + }; + const unsigned char tc_ya[] = { + 0xef,0x43,0x3d,0xd5,0xad,0x14,0x2c,0x86,0x0e,0x7c,0xb6,0x40, + 0x0d,0xd3,0x15,0xd3,0x88,0xd5,0xec,0x54,0x20,0xc5,0x50,0xe9, + 0xd6,0xf0,0x90,0x7f,0x37,0x5d,0x98,0x8b,0xc4,0xd7,0x04,0x83, + 0x7e,0x43,0x56,0x1c,0x49,0x7e,0x7d,0xd9,0x3e,0xdc,0xdb,0x9d, + }; + const unsigned char tc_ADa[] = { + 0x41,0x44,0x61, + }; + const unsigned char tc_Ya[] = { + 0x04,0x34,0xa0,0x4d,0xa1,0x21,0x99,0x5d,0x81,0xd7,0xc5,0xde, + 0xd0,0x2c,0xf2,0xe7,0x09,0x54,0xdc,0xa4,0x90,0x59,0x48,0x5e, + 0xa3,0x83,0x10,0xb7,0x3b,0x96,0xfa,0x1e,0xc7,0x86,0x19,0xc5, + 0xa1,0xe5,0x24,0x47,0x27,0x78,0x33,0x1f,0xbe,0x00,0x9f,0xa1, + 0x56,0x4a,0x32,0x03,0xe4,0x29,0x93,0xa3,0x62,0x85,0xfa,0x54, + 0xe6,0xc2,0x41,0x84,0xfd,0x22,0x74,0x58,0xc8,0x77,0x81,0xbe, + 0x16,0xff,0xf4,0x6d,0xbc,0x97,0x0c,0xc1,0xb1,0x77,0x00,0x50, + 0xa9,0x4d,0x68,0x26,0xd5,0x2f,0x21,0x1b,0x23,0x47,0x92,0xe6, + 0x6d, + }; + const unsigned char tc_yb[] = { + 0x50,0xb0,0xe3,0x6b,0x95,0xa2,0xed,0xfa,0xa8,0x34,0x2b,0x84, + 0x3d,0xdd,0xc9,0x0b,0x17,0x53,0x30,0xf2,0x39,0x9c,0x1b,0x36, + 0x58,0x6d,0xed,0xda,0x3c,0x25,0x59,0x75,0xf3,0x0b,0xe6,0xa7, + 0x50,0xf9,0x40,0x4f,0xcc,0xc6,0x2a,0x63,0x23,0xb5,0xe4,0x71, + }; + const unsigned char tc_ADb[] = { + 0x41,0x44,0x62, + }; + const unsigned char tc_Yb[] = { + 0x04,0x0a,0x65,0x59,0x14,0x7f,0xd4,0x92,0xad,0x74,0xab,0x1f, + 0x4d,0xef,0x61,0x96,0xfd,0x63,0x99,0x54,0x0e,0x84,0x70,0x62, + 0x27,0xa1,0xf9,0x0d,0x10,0x4c,0xda,0xeb,0x63,0x0b,0x7c,0x5c, + 0x18,0x74,0x8d,0xeb,0x25,0x65,0x3a,0xd2,0xa4,0xcb,0x5e,0x62, + 0x74,0x84,0x1c,0xad,0x32,0x8b,0xb0,0x31,0x26,0x28,0xb9,0xb1, + 0xf5,0x1b,0xea,0x72,0xb8,0xc6,0x10,0x99,0x9a,0x67,0x30,0xf7, + 0x52,0x64,0x92,0x05,0xae,0x85,0xc4,0x52,0xef,0x83,0xf9,0x8b, + 0xe7,0x15,0xcd,0x01,0x03,0x18,0x68,0x74,0xb0,0x7c,0xf0,0x20, + 0x74, + }; + const unsigned char tc_K[] = { + 0xa9,0xac,0xae,0xa9,0x56,0x92,0xa6,0x44,0x62,0x06,0x7f,0xe8, + 0xe4,0x32,0x1f,0x2f,0xca,0x97,0x93,0xa8,0xa0,0x42,0x0f,0x0e, + 0x25,0x3e,0xd0,0xd6,0xdb,0x85,0x8f,0xe1,0x61,0xde,0x75,0x76, + 0x20,0x6a,0x8a,0x35,0xbd,0x4a,0x60,0xe0,0x07,0x24,0xfd,0x3e, + }; + const unsigned char tc_ISK_IR[] = { + 0xd1,0xb7,0x43,0x75,0xc7,0xd6,0x3d,0x7d,0xe2,0x46,0xcb,0xf3, + 0xfc,0x2b,0x30,0x92,0x64,0x5c,0x73,0xa0,0xaa,0x81,0x69,0x89, + 0xc0,0xde,0x60,0x48,0xed,0x4e,0xce,0x6a,0x54,0xdf,0x82,0xd0, + 0x5d,0x2b,0xe3,0x49,0x8c,0xb9,0x28,0x8b,0xe7,0xbd,0xbd,0xb9, + }; + const unsigned char tc_ISK_SY[] = { + 0xa0,0x51,0xd4,0x53,0x2c,0xa9,0xfb,0x67,0x74,0xe0,0x97,0xeb, + 0xac,0x69,0xc1,0xd6,0xa1,0x81,0x44,0xa1,0x54,0x21,0xdc,0x15, + 0x5d,0x0b,0x1e,0x8a,0xef,0x9f,0x9d,0x8c,0x0f,0xe8,0x6e,0x85, + 0xd3,0xcb,0xee,0x77,0x96,0xff,0x50,0x17,0x1f,0x42,0x80,0x1b, + }; + const unsigned char tc_ISK_SY[] = { + 0xa0,0x51,0xd4,0x53,0x2c,0xa9,0xfb,0x67,0x74,0xe0,0x97,0xeb, + 0xac,0x69,0xc1,0xd6,0xa1,0x81,0x44,0xa1,0x54,0x21,0xdc,0x15, + 0x5d,0x0b,0x1e,0x8a,0xef,0x9f,0x9d,0x8c,0x0f,0xe8,0x6e,0x85, + 0xd3,0xcb,0xee,0x77,0x96,0xff,0x50,0x17,0x1f,0x42,0x80,0x1b, + }; + const unsigned char tc_sid_out_ir[] = { + 0x8d,0x5a,0x03,0x94,0x6a,0x69,0xff,0xa1,0x2c,0xd6,0xef,0xd4, + 0x69,0xfe,0x86,0x71,0xbb,0xc2,0x5f,0xad,0x6d,0xb2,0x65,0x6f, + 0x39,0x63,0xc9,0x4e,0x9c,0x94,0x0b,0xde,0xcc,0x2b,0xd5,0x55, + 0x47,0x4c,0x21,0x18,0x17,0x78,0x7d,0x5c,0xf7,0x87,0x0e,0xd1, + }; + const unsigned char tc_sid_out_oc[] = { + 0xc0,0x72,0x9d,0xb2,0x5d,0xb4,0x0c,0x48,0xa3,0x5f,0x78,0x7d, + 0x54,0x10,0xb2,0xcb,0x9a,0x2d,0x9f,0x5e,0x9c,0xf1,0xcf,0x15, + 0x9e,0xd2,0xf6,0x3c,0x6b,0x21,0x85,0xe5,0x97,0xe1,0x76,0xcc, + 0x22,0x14,0x22,0xe9,0x49,0x6e,0xed,0xa2,0xbf,0x12,0x3c,0x8b, + }; + +B.6.9. Testvectors as JSON file encoded as BASE64 + + #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT + #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI1 + #QjM3NzNBQTkwRThGMjNDNjE1NjNBNEI2NDVCMjc2QyIsICJnIjogIjA0RkZFMUJEQz + #MyOTNGREJFMzFCMjk1OTkxNkU1MkMwMThFOTIzRUFDOTk4MzZCRDlBMUNCRUVDNzk0 + #QThENEQ3OEJBQTMyQ0RBRkM5Njg1QkMxMDY3QTc4MEY0QUQ5QzhBNkM2RTE2NEFBND + #I5MDZEMUUyN0Y3ODI1ODFBREM4RTAxMDkyMTk2MjZBMkI4RkJEQzM0NjAyRTQwODQ1 + #NTRCREQ2QzBDNjk4REQ2NTdBQzhFMzFCMkJDQ0UxQzdCMEQ4IiwgInlhIjogIkVGND + #MzREQ1QUQxNDJDODYwRTdDQjY0MDBERDMxNUQzODhENUVDNTQyMEM1NTBFOUQ2RjA5 + #MDdGMzc1RDk4OEJDNEQ3MDQ4MzdFNDM1NjFDNDk3RTdERDkzRURDREI5RCIsICJBRG + #EiOiAiNDE0NDYxIiwgIllhIjogIjA0MzRBMDREQTEyMTk5NUQ4MUQ3QzVERUQwMkNG + #MkU3MDk1NERDQTQ5MDU5NDg1RUEzODMxMEI3M0I5NkZBMUVDNzg2MTlDNUExRTUyND + #Q3Mjc3ODMzMUZCRTAwOUZBMTU2NEEzMjAzRTQyOTkzQTM2Mjg1RkE1NEU2QzI0MTg0 + #RkQyMjc0NThDODc3ODFCRTE2RkZGNDZEQkM5NzBDQzFCMTc3MDA1MEE5NEQ2ODI2RD + #UyRjIxMUIyMzQ3OTJFNjZEIiwgInliIjogIjUwQjBFMzZCOTVBMkVERkFBODM0MkI4 + #NDNERERDOTBCMTc1MzMwRjIzOTlDMUIzNjU4NkRFRERBM0MyNTU5NzVGMzBCRTZBNz + #UwRjk0MDRGQ0NDNjJBNjMyM0I1RTQ3MSIsICJBRGIiOiAiNDE0NDYyIiwgIlliIjog + #IjA0MEE2NTU5MTQ3RkQ0OTJBRDc0QUIxRjRERUY2MTk2RkQ2Mzk5NTQwRTg0NzA2Mj + #I3QTFGOTBEMTA0Q0RBRUI2MzBCN0M1QzE4NzQ4REVCMjU2NTNBRDJBNENCNUU2Mjc0 + #ODQxQ0FEMzI4QkIwMzEyNjI4QjlCMUY1MUJFQTcyQjhDNjEwOTk5QTY3MzBGNzUyNj + #Q5MjA1QUU4NUM0NTJFRjgzRjk4QkU3MTVDRDAxMDMxODY4NzRCMDdDRjAyMDc0Iiwg + #IksiOiAiQTlBQ0FFQTk1NjkyQTY0NDYyMDY3RkU4RTQzMjFGMkZDQTk3OTNBOEEwND + #IwRjBFMjUzRUQwRDZEQjg1OEZFMTYxREU3NTc2MjA2QThBMzVCRDRBNjBFMDA3MjRG + #RDNFIiwgIklTS19JUiI6ICJEMUI3NDM3NUM3RDYzRDdERTI0NkNCRjNGQzJCMzA5Mj + #Y0NUM3M0EwQUE4MTY5ODlDMERFNjA0OEVENEVDRTZBNTRERjgyRDA1RDJCRTM0OThD + #QjkyODhCRTdCREJEQjkiLCAiSVNLX1NZIjogIkEwNTFENDUzMkNBOUZCNjc3NEUwOT + #dFQkFDNjlDMUQ2QTE4MTQ0QTE1NDIxREMxNTVEMEIxRThBRUY5RjlEOEMwRkU4NkU4 + #NUQzQ0JFRTc3OTZGRjUwMTcxRjQyODAxQiIsICJzaWRfb3V0cHV0X2lyIjogIjhENU + #EwMzk0NkE2OUZGQTEyQ0Q2RUZENDY5RkU4NjcxQkJDMjVGQUQ2REIyNjU2RjM5NjND + #OTRFOUM5NDBCREVDQzJCRDU1NTQ3NEMyMTE4MTc3ODdENUNGNzg3MEVEMSIsICJzaW + #Rfb3V0cHV0X29jIjogIkMwNzI5REIyNURCNDBDNDhBMzVGNzg3RDU0MTBCMkNCOUEy + #RDlGNUU5Q0YxQ0YxNTlFRDJGNjNDNkIyMTg1RTU5N0UxNzZDQzIyMTQyMkU5NDk2RU + #VEQTJCRjEyM0M4QiJ9 + +B.6.10. Test case for scalar_mult_vfy with correct inputs + + s: (length: 48 bytes) + 6e8a99a5cdd408eae98e1b8aed286e7b12adbbdac7f2c628d9060ce9 + 2ae0d90bd57a564fd3500fbcce3425dc94ba0ade + X: (length: 97 bytes) + 045b4cd53c4506cc04ba4c44f2762d5d32c3e55df25b8baa5571b165 + 7ad9576efea8259f0684de065a470585b4be876748c7797054f3defe + f21b77f83d53bac57c89d52aa4d6dd5872bd281989b138359698009f + 8ac1f301538badcce9d9f4036e + G.scalar_mult(s,X) (full coordinates): (length: 97 bytes) + 0465c28db05fd9f9a93651c5cc31eae49c4e5246b46489b8f6105873 + 3173a033cda76c3e3ea5352b804e67fdbe2e334be8245dad5c8c993e + 63bacf0456478f29b71b6c859f13676f84ff150d2741f028f560584a + 0bdba19a63df62c08949c2fd6d + G.scalar_mult_vfy(s,X) (only X-coordinate): + (length: 48 bytes) + 65c28db05fd9f9a93651c5cc31eae49c4e5246b46489b8f610587331 + 73a033cda76c3e3ea5352b804e67fdbe2e334be8 + +B.6.11. Invalid inputs for scalar_mult_vfy + + For these test cases scalar_mult_vfy(y,.) MUST return the + representation of the neutral element G.I. When including Y_i1 or + Y_i2 in messages of A or B the protocol MUST abort. + + s: (length: 48 bytes) + 6e8a99a5cdd408eae98e1b8aed286e7b12adbbdac7f2c628d9060ce9 + 2ae0d90bd57a564fd3500fbcce3425dc94ba0ade + Y_i1: (length: 97 bytes) + 045b4cd53c4506cc04ba4c44f2762d5d32c3e55df25b8baa5571b165 + 7ad9576efea8259f0684de065a470585b4be876748c7797054f3defe + f21b77f83d53bac57c89d52aa4d6dd5872bd281989b138359698009f + 8ac1f301538badcce9d9f40302 + Y_i2: (length: 1 bytes) + 00 + G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I + +B.6.11.1. Testvectors as JSON file encoded as BASE64 + + #eyJWYWxpZCI6IHsicyI6ICI2RThBOTlBNUNERDQwOEVBRTk4RTFCOEFFRDI4NkU3Qj + #EyQURCQkRBQzdGMkM2MjhEOTA2MENFOTJBRTBEOTBCRDU3QTU2NEZEMzUwMEZCQ0NF + #MzQyNURDOTRCQTBBREUiLCAiWCI6ICIwNDVCNENENTNDNDUwNkNDMDRCQTRDNDRGMj + #c2MkQ1RDMyQzNFNTVERjI1QjhCQUE1NTcxQjE2NTdBRDk1NzZFRkVBODI1OUYwNjg0 + #REUwNjVBNDcwNTg1QjRCRTg3Njc0OEM3Nzk3MDU0RjNERUZFRjIxQjc3RjgzRDUzQk + #FDNTdDODlENTJBQTRENkRENTg3MkJEMjgxOTg5QjEzODM1OTY5ODAwOUY4QUMxRjMw + #MTUzOEJBRENDRTlEOUY0MDM2RSIsICJHLnNjYWxhcl9tdWx0KHMsWCkgKGZ1bGwgY2 + #9vcmRpbmF0ZXMpIjogIjA0NjVDMjhEQjA1RkQ5RjlBOTM2NTFDNUNDMzFFQUU0OUM0 + #RTUyNDZCNDY0ODlCOEY2MTA1ODczMzE3M0EwMzNDREE3NkMzRTNFQTUzNTJCODA0RT + #Y3RkRCRTJFMzM0QkU4MjQ1REFENUM4Qzk5M0U2M0JBQ0YwNDU2NDc4RjI5QjcxQjZD + #ODU5RjEzNjc2Rjg0RkYxNTBEMjc0MUYwMjhGNTYwNTg0QTBCREJBMTlBNjNERjYyQz + #A4OTQ5QzJGRDZEIiwgIkcuc2NhbGFyX211bHRfdmZ5KHMsWCkgKG9ubHkgWC1jb29y + #ZGluYXRlKSI6ICI2NUMyOERCMDVGRDlGOUE5MzY1MUM1Q0MzMUVBRTQ5QzRFNTI0Nk + #I0NjQ4OUI4RjYxMDU4NzMzMTczQTAzM0NEQTc2QzNFM0VBNTM1MkI4MDRFNjdGREJF + #MkUzMzRCRTgifSwgIkludmFsaWQgWTEiOiAiMDQ1QjRDRDUzQzQ1MDZDQzA0QkE0Qz + #Q0RjI3NjJENUQzMkMzRTU1REYyNUI4QkFBNTU3MUIxNjU3QUQ5NTc2RUZFQTgyNTlG + #MDY4NERFMDY1QTQ3MDU4NUI0QkU4NzY3NDhDNzc5NzA1NEYzREVGRUYyMUI3N0Y4M0 + #Q1M0JBQzU3Qzg5RDUyQUE0RDZERDU4NzJCRDI4MTk4OUIxMzgzNTk2OTgwMDlGOEFD + #MUYzMDE1MzhCQURDQ0U5RDlGNDAzMDIiLCAiSW52YWxpZCBZMiI6ICIwMCJ9 + +B.7. Test vector for CPace using group NIST P-521 and hash SHA-512 + +B.7.1. Test vectors for calculate_generator with group NIST P-521 + + Inputs + H = SHA-512 with input block size 128 bytes. + PRS = b'Password' ; ZPAD length: 87 ; + DSI = b'CPaceP521_XMD:SHA-512_SSWU_NU_' + DST = b'CPaceP521_XMD:SHA-512_SSWU_NU__DST' + CI = b'oc\x0bB_responder\x0bA_initiator' + CI = 6f630b425f726573706f6e6465720b415f696e69746961746f72 + sid = 7e4b4791d6a8ef019b936c79fb7f2c57 + Outputs + generator_string(PRS,G.DSI,CI,sid,H.s_in_bytes): + (length: 172 bytes) + 1e4350616365503532315f584d443a5348412d3531325f535357555f + 4e555f0850617373776f726457000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 00000000000000000000000000000000000000000000000000000000 + 000000000000000000000000000000001a6f630b425f726573706f6e + 6465720b415f696e69746961746f72107e4b4791d6a8ef019b936c79 + fb7f2c57 + generator g: (length: 133 bytes) + 0400e58a8fbf08b38e34a3676f6d690bed58aa4115ff32a57ec87172 + fc2a1fb89d03258c6429c464981b3284b5fedbd1244bf27432008868 + 7065b9075dd558e14ed69901d2162db1ba3a49c97dca7c902cb1b96b + abe21a31942114c860665b35c46b8213f6de17194de54c441083dd11 + 63d5907adad8824bb1307dcf6a55c11a8f01d9789b + +B.7.1.1. Testvectors as JSON file encoded as BASE64 + + #eyJIIjogIlNIQS01MTIiLCAiSC5zX2luX2J5dGVzIjogMTI4LCAiUFJTIjogIjUwNj + #E3MzczNzc2RjcyNjQiLCAiWlBBRCBsZW5ndGgiOiA4NywgIkRTSSI6ICI0MzUwNjE2 + #MzY1NTAzNTMyMzE1RjU4NEQ0NDNBNTM0ODQxMkQzNTMxMzI1RjUzNTM1NzU1NUY0RT + #U1NUYiLCAiQ0kiOiAiNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0NjU3MjBCNDE1RjY5 + #NkU2OTc0Njk2MTc0NkY3MiIsICJzaWQiOiAiN0U0QjQ3OTFENkE4RUYwMTlCOTM2Qz + #c5RkI3RjJDNTciLCAiZ2VuZXJhdG9yX3N0cmluZyhHLkRTSSxQUlMsQ0ksc2lkLEgu + #c19pbl9ieXRlcykiOiAiMUU0MzUwNjE2MzY1NTAzNTMyMzE1RjU4NEQ0NDNBNTM0OD + #QxMkQzNTMxMzI1RjUzNTM1NzU1NUY0RTU1NUYwODUwNjE3MzczNzc2RjcyNjQ1NzAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAw + #MDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMD + #AwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDFBNkY2MzBCNDI1RjcyNjU3MzcwNkY2RTY0 + #NjU3MjBCNDE1RjY5NkU2OTc0Njk2MTc0NkY3MjEwN0U0QjQ3OTFENkE4RUYwMTlCOT + #M2Qzc5RkI3RjJDNTciLCAiZ2VuZXJhdG9yIGciOiAiMDQwMEU1OEE4RkJGMDhCMzhF + #MzRBMzY3NkY2RDY5MEJFRDU4QUE0MTE1RkYzMkE1N0VDODcxNzJGQzJBMUZCODlEMD + #MyNThDNjQyOUM0NjQ5ODFCMzI4NEI1RkVEQkQxMjQ0QkYyNzQzMjAwODg2ODcwNjVC + #OTA3NURENTU4RTE0RUQ2OTkwMUQyMTYyREIxQkEzQTQ5Qzk3RENBN0M5MDJDQjFCOT + #ZCQUJFMjFBMzE5NDIxMTRDODYwNjY1QjM1QzQ2QjgyMTNGNkRFMTcxOTRERTU0QzQ0 + #MTA4M0REMTE2M0Q1OTA3QURBRDg4MjRCQjEzMDdEQ0Y2QTU1QzExQThGMDFEOTc4OU + #IifQ== + +B.7.2. Test vector for message from A + + Inputs + ADa = b'ADa' + ya (big endian): (length: 66 bytes) + 006367e9c2aeff9f1db19af600cca73343d47cbe446cebbd1ccd783f + 82755a872da86fd0707eb3767c6114f1803deb62d63bdd1e613f67e6 + 3e8c141ee5310e3ee819 + Outputs + Ya: (length: 133 bytes) + 0400c2bfd794467f4438277e85a42e101fa4061e1ef6e05f81e5381f + 30e73b341dd726089cb6a6bbe5a509fad009857488db7130ff768090 + 7312eb724cddb4dcce675b0098ad400fef80e1deb4bc1756c43961ef + 60b85f2d62ed458454e11616a5d1df1e5809636821a73662f9f12254 + e6f9950dd01fa8e26a8b20736fb63c63c81094f681 + Alternative correct value for Ya: (-ya)*g: + (length: 133 bytes) + 0400c2bfd794467f4438277e85a42e101fa4061e1ef6e05f81e5381f + 30e73b341dd726089cb6a6bbe5a509fad009857488db7130ff768090 + 7312eb724cddb4dcce675b016752bff0107f1e214b43e8a93bc69e10 + 9f47a0d29d12ba7bab1ee9e95a2e20e1a7f69c97de58c99d060eddab + 19066af22fe0571d9574df8c9049c39c37ef6b097e + +B.7.3. Test vector for message from B + + Inputs + ADb = b'ADb' + yb (big endian): (length: 66 bytes) + 009227bf8dc741dacc9422f8bf3c0e96fce9587bc562eaafe0dc5f6f + 82f28594e4a6f98553560c62b75fa4abb198cecbbb86ebd41b0ea025 + 4cde78ac68d39a240ae7 + Outputs + Yb: (length: 133 bytes) + 0400706ea69b2b7167773248ea6e69a574e9dd2ff8a3d04a6e07f70c + 709869ca486827d59f9290599d1cf94e1a03fc242e2b1316afe2fa21 + 8bfaeb3e1ffd9f19bf062d01f6b15c9c3651be4c08baf01eec25c818 + ee12c6edc4620644b1d97cf24f868732d56fe45ce78e302c221c92f4 + 03e0fa3207de8bb41b388d81046a298ed8ddac9b2a + Alternative correct value for Yb: (-yb)*g: + (length: 133 bytes) + 0400706ea69b2b7167773248ea6e69a574e9dd2ff8a3d04a6e07f70c + 709869ca486827d59f9290599d1cf94e1a03fc242e2b1316afe2fa21 + 8bfaeb3e1ffd9f19bf062d00094ea363c9ae41b3f7450fe113da37e7 + 11ed39123b9df9bb4e26830db07978cd2a901ba31871cfd3dde36d0b + fc1f05cdf821744be4c7727efb95d67127225364d5 + +B.7.4. Test vector for secret points K + + scalar_mult_vfy(ya,Yb): (length: 66 bytes) + 018e0e7e9ade74917c11c0f6b52f95ed871eab235437cbee8b5c2509 + 516e787a80e825ed5d539fa6a0ec32c48fa8fabe85809d000d0cfd30 + 832c23d477c991bea8e5 + scalar_mult_vfy(yb,Ya): (length: 66 bytes) + 018e0e7e9ade74917c11c0f6b52f95ed871eab235437cbee8b5c2509 + 516e787a80e825ed5d539fa6a0ec32c48fa8fabe85809d000d0cfd30 + 832c23d477c991bea8e5 + +B.7.5. Test vector for ISK calculation initiator/responder + + transcript_ir(Ya,ADa,Yb,ADb): (length: 278 bytes) + 85010400c2bfd794467f4438277e85a42e101fa4061e1ef6e05f81e5 + 381f30e73b341dd726089cb6a6bbe5a509fad009857488db7130ff76 + 80907312eb724cddb4dcce675b0098ad400fef80e1deb4bc1756c439 + 61ef60b85f2d62ed458454e11616a5d1df1e5809636821a73662f9f1 + 2254e6f9950dd01fa8e26a8b20736fb63c63c81094f6810341446185 + 010400706ea69b2b7167773248ea6e69a574e9dd2ff8a3d04a6e07f7 + 0c709869ca486827d59f9290599d1cf94e1a03fc242e2b1316afe2fa + 218bfaeb3e1ffd9f19bf062d01f6b15c9c3651be4c08baf01eec25c8 + 18ee12c6edc4620644b1d97cf24f868732d56fe45ce78e302c221c92 + f403e0fa3207de8bb41b388d81046a298ed8ddac9b2a03414462 + DSI = G.DSI_ISK, b'CPaceP521_XMD:SHA-512_SSWU_NU__ISK': + (length: 34 bytes) + 4350616365503532315f584d443a5348412d3531325f535357555f4e + 555f5f49534b + lv_cat(DSI,sid,K)||transcript_ir(Ya,ADa,Yb,ADb): + (length: 397 bytes) + 224350616365503532315f584d443a5348412d3531325f535357555f + 4e555f5f49534b107e4b4791d6a8ef019b936c79fb7f2c5742018e0e + 7e9ade74917c11c0f6b52f95ed871eab235437cbee8b5c2509516e78 + 7a80e825ed5d539fa6a0ec32c48fa8fabe85809d000d0cfd30832c23 + d477c991bea8e585010400c2bfd794467f4438277e85a42e101fa406 + 1e1ef6e05f81e5381f30e73b341dd726089cb6a6bbe5a509fad00985 + 7488db7130ff7680907312eb724cddb4dcce675b0098ad400fef80e1 + deb4bc1756c43961ef60b85f2d62ed458454e11616a5d1df1e580963 + 6821a73662f9f12254e6f9950dd01fa8e26a8b20736fb63c63c81094 + f6810341446185010400706ea69b2b7167773248ea6e69a574e9dd2f + f8a3d04a6e07f70c709869ca486827d59f9290599d1cf94e1a03fc24 + 2e2b1316afe2fa218bfaeb3e1ffd9f19bf062d01f6b15c9c3651be4c + 08baf01eec25c818ee12c6edc4620644b1d97cf24f868732d56fe45c + e78e302c221c92f403e0fa3207de8bb41b388d81046a298ed8ddac9b + 2a03414462 + ISK result: (length: 64 bytes) + 1669a0a29726adc7eea2510d6f7e004a135fa63ac3c9f9e6ce53cba5 + d5e3781aced515956041e43358409a13ef90ddc3c36fd8d7d81424c8 + e94592e21854260a + +B.7.6. Test vector for ISK calculation parallel execution + + transcript_oc(Ya,ADa,Yb,ADb): (length: 280 bytes) + 6f6385010400c2bfd794467f4438277e85a42e101fa4061e1ef6e05f + 81e5381f30e73b341dd726089cb6a6bbe5a509fad009857488db7130 + ff7680907312eb724cddb4dcce675b0098ad400fef80e1deb4bc1756 + c43961ef60b85f2d62ed458454e11616a5d1df1e5809636821a73662 + f9f12254e6f9950dd01fa8e26a8b20736fb63c63c81094f681034144 + 6185010400706ea69b2b7167773248ea6e69a574e9dd2ff8a3d04a6e + 07f70c709869ca486827d59f9290599d1cf94e1a03fc242e2b1316af + e2fa218bfaeb3e1ffd9f19bf062d01f6b15c9c3651be4c08baf01eec + 25c818ee12c6edc4620644b1d97cf24f868732d56fe45ce78e302c22 + 1c92f403e0fa3207de8bb41b388d81046a298ed8ddac9b2a03414462 + DSI = G.DSI_ISK, b'CPaceP521_XMD:SHA-512_SSWU_NU__ISK': + (length: 34 bytes) + 4350616365503532315f584d443a5348412d3531325f535357555f4e + 555f5f49534b + lv_cat(DSI,sid,K)||transcript_oc(Ya,ADa,Yb,ADb): + (length: 399 bytes) + 224350616365503532315f584d443a5348412d3531325f535357555f + 4e555f5f49534b107e4b4791d6a8ef019b936c79fb7f2c5742018e0e + 7e9ade74917c11c0f6b52f95ed871eab235437cbee8b5c2509516e78 + 7a80e825ed5d539fa6a0ec32c48fa8fabe85809d000d0cfd30832c23 + d477c991bea8e56f6385010400c2bfd794467f4438277e85a42e101f + a4061e1ef6e05f81e5381f30e73b341dd726089cb6a6bbe5a509fad0 + 09857488db7130ff7680907312eb724cddb4dcce675b0098ad400fef + 80e1deb4bc1756c43961ef60b85f2d62ed458454e11616a5d1df1e58 + 09636821a73662f9f12254e6f9950dd01fa8e26a8b20736fb63c63c8 + 1094f6810341446185010400706ea69b2b7167773248ea6e69a574e9 + dd2ff8a3d04a6e07f70c709869ca486827d59f9290599d1cf94e1a03 + fc242e2b1316afe2fa218bfaeb3e1ffd9f19bf062d01f6b15c9c3651 + be4c08baf01eec25c818ee12c6edc4620644b1d97cf24f868732d56f + e45ce78e302c221c92f403e0fa3207de8bb41b388d81046a298ed8dd + ac9b2a03414462 + ISK result: (length: 64 bytes) + f2f3bd8cd442a4e16659b47a7b7a84f29be75893ed2e5f772d7a3c8b + 779eb0df937a4ec50a4f1ff01ebbaa97d80e090ea69b00a95200ed25 + 8e48c6f7e9d8fbc2 + +B.7.7. Test vector for optional output of session id + + H.hash(b"CPaceSidOut" + transcript_ir(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + 56cc3cd8be77cdc84c0d1906de1ffc8ef7cbb326a3f05267b6e8c634 + 4e2781eb20ef725e84cb1bb45927435051b4e0fae78e975bf15099f9 + e38d755413eee2fd + H.hash(b"CPaceSidOut" + transcript_oc(Ya,ADa, Yb,ADb)): + (length: 64 bytes) + a46c7189ba6a36c4447741e057da39c885b7d59e08bd2df1852a5271 + f2a8a2e9b187ccd07325a3eede646adee0c06fe58da77f74177896b2 + 1053c5d107de006d + +B.7.8. Corresponding C programming language initializers + + const unsigned char tc_PRS[] = { + 0x50,0x61,0x73,0x73,0x77,0x6f,0x72,0x64, + }; + const unsigned char tc_CI[] = { + 0x6f,0x63,0x0b,0x42,0x5f,0x72,0x65,0x73,0x70,0x6f,0x6e,0x64, + 0x65,0x72,0x0b,0x41,0x5f,0x69,0x6e,0x69,0x74,0x69,0x61,0x74, + 0x6f,0x72, + }; + const unsigned char tc_sid[] = { + 0x7e,0x4b,0x47,0x91,0xd6,0xa8,0xef,0x01,0x9b,0x93,0x6c,0x79, + 0xfb,0x7f,0x2c,0x57, + }; + const unsigned char tc_g[] = { + 0x04,0x00,0xe5,0x8a,0x8f,0xbf,0x08,0xb3,0x8e,0x34,0xa3,0x67, + 0x6f,0x6d,0x69,0x0b,0xed,0x58,0xaa,0x41,0x15,0xff,0x32,0xa5, + 0x7e,0xc8,0x71,0x72,0xfc,0x2a,0x1f,0xb8,0x9d,0x03,0x25,0x8c, + 0x64,0x29,0xc4,0x64,0x98,0x1b,0x32,0x84,0xb5,0xfe,0xdb,0xd1, + 0x24,0x4b,0xf2,0x74,0x32,0x00,0x88,0x68,0x70,0x65,0xb9,0x07, + 0x5d,0xd5,0x58,0xe1,0x4e,0xd6,0x99,0x01,0xd2,0x16,0x2d,0xb1, + 0xba,0x3a,0x49,0xc9,0x7d,0xca,0x7c,0x90,0x2c,0xb1,0xb9,0x6b, + 0xab,0xe2,0x1a,0x31,0x94,0x21,0x14,0xc8,0x60,0x66,0x5b,0x35, + 0xc4,0x6b,0x82,0x13,0xf6,0xde,0x17,0x19,0x4d,0xe5,0x4c,0x44, + 0x10,0x83,0xdd,0x11,0x63,0xd5,0x90,0x7a,0xda,0xd8,0x82,0x4b, + 0xb1,0x30,0x7d,0xcf,0x6a,0x55,0xc1,0x1a,0x8f,0x01,0xd9,0x78, + 0x9b, + }; + const unsigned char tc_ya[] = { + 0x00,0x63,0x67,0xe9,0xc2,0xae,0xff,0x9f,0x1d,0xb1,0x9a,0xf6, + 0x00,0xcc,0xa7,0x33,0x43,0xd4,0x7c,0xbe,0x44,0x6c,0xeb,0xbd, + 0x1c,0xcd,0x78,0x3f,0x82,0x75,0x5a,0x87,0x2d,0xa8,0x6f,0xd0, + 0x70,0x7e,0xb3,0x76,0x7c,0x61,0x14,0xf1,0x80,0x3d,0xeb,0x62, + 0xd6,0x3b,0xdd,0x1e,0x61,0x3f,0x67,0xe6,0x3e,0x8c,0x14,0x1e, + 0xe5,0x31,0x0e,0x3e,0xe8,0x19, + }; + const unsigned char tc_ADa[] = { + 0x41,0x44,0x61, + }; + const unsigned char tc_Ya[] = { + 0x04,0x00,0xc2,0xbf,0xd7,0x94,0x46,0x7f,0x44,0x38,0x27,0x7e, + 0x85,0xa4,0x2e,0x10,0x1f,0xa4,0x06,0x1e,0x1e,0xf6,0xe0,0x5f, + 0x81,0xe5,0x38,0x1f,0x30,0xe7,0x3b,0x34,0x1d,0xd7,0x26,0x08, + 0x9c,0xb6,0xa6,0xbb,0xe5,0xa5,0x09,0xfa,0xd0,0x09,0x85,0x74, + 0x88,0xdb,0x71,0x30,0xff,0x76,0x80,0x90,0x73,0x12,0xeb,0x72, + 0x4c,0xdd,0xb4,0xdc,0xce,0x67,0x5b,0x00,0x98,0xad,0x40,0x0f, + 0xef,0x80,0xe1,0xde,0xb4,0xbc,0x17,0x56,0xc4,0x39,0x61,0xef, + 0x60,0xb8,0x5f,0x2d,0x62,0xed,0x45,0x84,0x54,0xe1,0x16,0x16, + 0xa5,0xd1,0xdf,0x1e,0x58,0x09,0x63,0x68,0x21,0xa7,0x36,0x62, + 0xf9,0xf1,0x22,0x54,0xe6,0xf9,0x95,0x0d,0xd0,0x1f,0xa8,0xe2, + 0x6a,0x8b,0x20,0x73,0x6f,0xb6,0x3c,0x63,0xc8,0x10,0x94,0xf6, + 0x81, + }; + const unsigned char tc_yb[] = { + 0x00,0x92,0x27,0xbf,0x8d,0xc7,0x41,0xda,0xcc,0x94,0x22,0xf8, + 0xbf,0x3c,0x0e,0x96,0xfc,0xe9,0x58,0x7b,0xc5,0x62,0xea,0xaf, + 0xe0,0xdc,0x5f,0x6f,0x82,0xf2,0x85,0x94,0xe4,0xa6,0xf9,0x85, + 0x53,0x56,0x0c,0x62,0xb7,0x5f,0xa4,0xab,0xb1,0x98,0xce,0xcb, + 0xbb,0x86,0xeb,0xd4,0x1b,0x0e,0xa0,0x25,0x4c,0xde,0x78,0xac, + 0x68,0xd3,0x9a,0x24,0x0a,0xe7, + }; + const unsigned char tc_ADb[] = { + 0x41,0x44,0x62, + }; + const unsigned char tc_Yb[] = { + 0x04,0x00,0x70,0x6e,0xa6,0x9b,0x2b,0x71,0x67,0x77,0x32,0x48, + 0xea,0x6e,0x69,0xa5,0x74,0xe9,0xdd,0x2f,0xf8,0xa3,0xd0,0x4a, + 0x6e,0x07,0xf7,0x0c,0x70,0x98,0x69,0xca,0x48,0x68,0x27,0xd5, + 0x9f,0x92,0x90,0x59,0x9d,0x1c,0xf9,0x4e,0x1a,0x03,0xfc,0x24, + 0x2e,0x2b,0x13,0x16,0xaf,0xe2,0xfa,0x21,0x8b,0xfa,0xeb,0x3e, + 0x1f,0xfd,0x9f,0x19,0xbf,0x06,0x2d,0x01,0xf6,0xb1,0x5c,0x9c, + 0x36,0x51,0xbe,0x4c,0x08,0xba,0xf0,0x1e,0xec,0x25,0xc8,0x18, + 0xee,0x12,0xc6,0xed,0xc4,0x62,0x06,0x44,0xb1,0xd9,0x7c,0xf2, + 0x4f,0x86,0x87,0x32,0xd5,0x6f,0xe4,0x5c,0xe7,0x8e,0x30,0x2c, + 0x22,0x1c,0x92,0xf4,0x03,0xe0,0xfa,0x32,0x07,0xde,0x8b,0xb4, + 0x1b,0x38,0x8d,0x81,0x04,0x6a,0x29,0x8e,0xd8,0xdd,0xac,0x9b, + 0x2a, + }; + const unsigned char tc_K[] = { + 0x01,0x8e,0x0e,0x7e,0x9a,0xde,0x74,0x91,0x7c,0x11,0xc0,0xf6, + 0xb5,0x2f,0x95,0xed,0x87,0x1e,0xab,0x23,0x54,0x37,0xcb,0xee, + 0x8b,0x5c,0x25,0x09,0x51,0x6e,0x78,0x7a,0x80,0xe8,0x25,0xed, + 0x5d,0x53,0x9f,0xa6,0xa0,0xec,0x32,0xc4,0x8f,0xa8,0xfa,0xbe, + 0x85,0x80,0x9d,0x00,0x0d,0x0c,0xfd,0x30,0x83,0x2c,0x23,0xd4, + 0x77,0xc9,0x91,0xbe,0xa8,0xe5, + }; + const unsigned char tc_ISK_IR[] = { + 0x16,0x69,0xa0,0xa2,0x97,0x26,0xad,0xc7,0xee,0xa2,0x51,0x0d, + 0x6f,0x7e,0x00,0x4a,0x13,0x5f,0xa6,0x3a,0xc3,0xc9,0xf9,0xe6, + 0xce,0x53,0xcb,0xa5,0xd5,0xe3,0x78,0x1a,0xce,0xd5,0x15,0x95, + 0x60,0x41,0xe4,0x33,0x58,0x40,0x9a,0x13,0xef,0x90,0xdd,0xc3, + 0xc3,0x6f,0xd8,0xd7,0xd8,0x14,0x24,0xc8,0xe9,0x45,0x92,0xe2, + 0x18,0x54,0x26,0x0a, + }; + const unsigned char tc_ISK_SY[] = { + 0xf2,0xf3,0xbd,0x8c,0xd4,0x42,0xa4,0xe1,0x66,0x59,0xb4,0x7a, + 0x7b,0x7a,0x84,0xf2,0x9b,0xe7,0x58,0x93,0xed,0x2e,0x5f,0x77, + 0x2d,0x7a,0x3c,0x8b,0x77,0x9e,0xb0,0xdf,0x93,0x7a,0x4e,0xc5, + 0x0a,0x4f,0x1f,0xf0,0x1e,0xbb,0xaa,0x97,0xd8,0x0e,0x09,0x0e, + 0xa6,0x9b,0x00,0xa9,0x52,0x00,0xed,0x25,0x8e,0x48,0xc6,0xf7, + 0xe9,0xd8,0xfb,0xc2, + }; + const unsigned char tc_ISK_SY[] = { + 0xf2,0xf3,0xbd,0x8c,0xd4,0x42,0xa4,0xe1,0x66,0x59,0xb4,0x7a, + 0x7b,0x7a,0x84,0xf2,0x9b,0xe7,0x58,0x93,0xed,0x2e,0x5f,0x77, + 0x2d,0x7a,0x3c,0x8b,0x77,0x9e,0xb0,0xdf,0x93,0x7a,0x4e,0xc5, + 0x0a,0x4f,0x1f,0xf0,0x1e,0xbb,0xaa,0x97,0xd8,0x0e,0x09,0x0e, + 0xa6,0x9b,0x00,0xa9,0x52,0x00,0xed,0x25,0x8e,0x48,0xc6,0xf7, + 0xe9,0xd8,0xfb,0xc2, + }; + const unsigned char tc_sid_out_ir[] = { + 0x56,0xcc,0x3c,0xd8,0xbe,0x77,0xcd,0xc8,0x4c,0x0d,0x19,0x06, + 0xde,0x1f,0xfc,0x8e,0xf7,0xcb,0xb3,0x26,0xa3,0xf0,0x52,0x67, + 0xb6,0xe8,0xc6,0x34,0x4e,0x27,0x81,0xeb,0x20,0xef,0x72,0x5e, + 0x84,0xcb,0x1b,0xb4,0x59,0x27,0x43,0x50,0x51,0xb4,0xe0,0xfa, + 0xe7,0x8e,0x97,0x5b,0xf1,0x50,0x99,0xf9,0xe3,0x8d,0x75,0x54, + 0x13,0xee,0xe2,0xfd, + }; + const unsigned char tc_sid_out_oc[] = { + 0xa4,0x6c,0x71,0x89,0xba,0x6a,0x36,0xc4,0x44,0x77,0x41,0xe0, + 0x57,0xda,0x39,0xc8,0x85,0xb7,0xd5,0x9e,0x08,0xbd,0x2d,0xf1, + 0x85,0x2a,0x52,0x71,0xf2,0xa8,0xa2,0xe9,0xb1,0x87,0xcc,0xd0, + 0x73,0x25,0xa3,0xee,0xde,0x64,0x6a,0xde,0xe0,0xc0,0x6f,0xe5, + 0x8d,0xa7,0x7f,0x74,0x17,0x78,0x96,0xb2,0x10,0x53,0xc5,0xd1, + 0x07,0xde,0x00,0x6d, + }; + +B.7.9. Testvectors as JSON file encoded as BASE64 + + #eyJQUlMiOiAiNTA2MTczNzM3NzZGNzI2NCIsICJDSSI6ICI2RjYzMEI0MjVGNzI2NT + #czNzA2RjZFNjQ2NTcyMEI0MTVGNjk2RTY5NzQ2OTYxNzQ2RjcyIiwgInNpZCI6ICI3 + #RTRCNDc5MUQ2QThFRjAxOUI5MzZDNzlGQjdGMkM1NyIsICJnIjogIjA0MDBFNThBOE + #ZCRjA4QjM4RTM0QTM2NzZGNkQ2OTBCRUQ1OEFBNDExNUZGMzJBNTdFQzg3MTcyRkMy + #QTFGQjg5RDAzMjU4QzY0MjlDNDY0OTgxQjMyODRCNUZFREJEMTI0NEJGMjc0MzIwMD + #g4Njg3MDY1QjkwNzVERDU1OEUxNEVENjk5MDFEMjE2MkRCMUJBM0E0OUM5N0RDQTdD + #OTAyQ0IxQjk2QkFCRTIxQTMxOTQyMTE0Qzg2MDY2NUIzNUM0NkI4MjEzRjZERTE3MT + #k0REU1NEM0NDEwODNERDExNjNENTkwN0FEQUQ4ODI0QkIxMzA3RENGNkE1NUMxMUE4 + #RjAxRDk3ODlCIiwgInlhIjogIjAwNjM2N0U5QzJBRUZGOUYxREIxOUFGNjAwQ0NBNz + #MzNDNENDdDQkU0NDZDRUJCRDFDQ0Q3ODNGODI3NTVBODcyREE4NkZEMDcwN0VCMzc2 + #N0M2MTE0RjE4MDNERUI2MkQ2M0JERDFFNjEzRjY3RTYzRThDMTQxRUU1MzEwRTNFRT + #gxOSIsICJBRGEiOiAiNDE0NDYxIiwgIllhIjogIjA0MDBDMkJGRDc5NDQ2N0Y0NDM4 + #Mjc3RTg1QTQyRTEwMUZBNDA2MUUxRUY2RTA1RjgxRTUzODFGMzBFNzNCMzQxREQ3Mj + #YwODlDQjZBNkJCRTVBNTA5RkFEMDA5ODU3NDg4REI3MTMwRkY3NjgwOTA3MzEyRUI3 + #MjRDRERCNERDQ0U2NzVCMDA5OEFENDAwRkVGODBFMURFQjRCQzE3NTZDNDM5NjFFRj + #YwQjg1RjJENjJFRDQ1ODQ1NEUxMTYxNkE1RDFERjFFNTgwOTYzNjgyMUE3MzY2MkY5 + #RjEyMjU0RTZGOTk1MEREMDFGQThFMjZBOEIyMDczNkZCNjNDNjNDODEwOTRGNjgxIi + #wgInliIjogIjAwOTIyN0JGOERDNzQxREFDQzk0MjJGOEJGM0MwRTk2RkNFOTU4N0JD + #NTYyRUFBRkUwREM1RjZGODJGMjg1OTRFNEE2Rjk4NTUzNTYwQzYyQjc1RkE0QUJCMT + #k4Q0VDQkJCODZFQkQ0MUIwRUEwMjU0Q0RFNzhBQzY4RDM5QTI0MEFFNyIsICJBRGIi + #OiAiNDE0NDYyIiwgIlliIjogIjA0MDA3MDZFQTY5QjJCNzE2Nzc3MzI0OEVBNkU2OU + #E1NzRFOUREMkZGOEEzRDA0QTZFMDdGNzBDNzA5ODY5Q0E0ODY4MjdENTlGOTI5MDU5 + #OUQxQ0Y5NEUxQTAzRkMyNDJFMkIxMzE2QUZFMkZBMjE4QkZBRUIzRTFGRkQ5RjE5Qk + #YwNjJEMDFGNkIxNUM5QzM2NTFCRTRDMDhCQUYwMUVFQzI1QzgxOEVFMTJDNkVEQzQ2 + #MjA2NDRCMUQ5N0NGMjRGODY4NzMyRDU2RkU0NUNFNzhFMzAyQzIyMUM5MkY0MDNFME + #ZBMzIwN0RFOEJCNDFCMzg4RDgxMDQ2QTI5OEVEOEREQUM5QjJBIiwgIksiOiAiMDE4 + #RTBFN0U5QURFNzQ5MTdDMTFDMEY2QjUyRjk1RUQ4NzFFQUIyMzU0MzdDQkVFOEI1Qz + #I1MDk1MTZFNzg3QTgwRTgyNUVENUQ1MzlGQTZBMEVDMzJDNDhGQThGQUJFODU4MDlE + #MDAwRDBDRkQzMDgzMkMyM0Q0NzdDOTkxQkVBOEU1IiwgIklTS19JUiI6ICIxNjY5QT + #BBMjk3MjZBREM3RUVBMjUxMEQ2RjdFMDA0QTEzNUZBNjNBQzNDOUY5RTZDRTUzQ0JB + #NUQ1RTM3ODFBQ0VENTE1OTU2MDQxRTQzMzU4NDA5QTEzRUY5MEREQzNDMzZGRDhEN0 + #Q4MTQyNEM4RTk0NTkyRTIxODU0MjYwQSIsICJJU0tfU1kiOiAiRjJGM0JEOENENDQy + #QTRFMTY2NTlCNDdBN0I3QTg0RjI5QkU3NTg5M0VEMkU1Rjc3MkQ3QTNDOEI3NzlFQj + #BERjkzN0E0RUM1MEE0RjFGRjAxRUJCQUE5N0Q4MEUwOTBFQTY5QjAwQTk1MjAwRUQy + #NThFNDhDNkY3RTlEOEZCQzIiLCAic2lkX291dHB1dF9pciI6ICI1NkNDM0NEOEJFNz + #dDREM4NEMwRDE5MDZERTFGRkM4RUY3Q0JCMzI2QTNGMDUyNjdCNkU4QzYzNDRFMjc4 + #MUVCMjBFRjcyNUU4NENCMUJCNDU5Mjc0MzUwNTFCNEUwRkFFNzhFOTc1QkYxNTA5OU + #Y5RTM4RDc1NTQxM0VFRTJGRCIsICJzaWRfb3V0cHV0X29jIjogIkE0NkM3MTg5QkE2 + #QTM2QzQ0NDc3NDFFMDU3REEzOUM4ODVCN0Q1OUUwOEJEMkRGMTg1MkE1MjcxRjJBOE + #EyRTlCMTg3Q0NEMDczMjVBM0VFREU2NDZBREVFMEMwNkZFNThEQTc3Rjc0MTc3ODk2 + #QjIxMDUzQzVEMTA3REUwMDZEIn0= + +B.7.10. Test case for scalar_mult_vfy with correct inputs + + s: (length: 66 bytes) + 0182dd7925f1753419e4bf83429763acd37d64000cd5a175edf53a15 + 87dd986bc95acc1506991702b6ba1a9ee2458fee8efc00198cf0088c + 480965ef65ff2048b856 + X: (length: 133 bytes) + 0400dc5078b24c4af1620cc10fbecc6cd8cf1cab0b011efb73c782f2 + 26dc21c7ca7eb406be74a69ecba5b4a87c07cfc6e687b4beca9a6eda + c95940a3b4120573b26a80005e697833b0ba285fce7b3f1f25243008 + 860b8f1de710a0dcc05b0d20341efe90eb2bcca26797c2d85ae6ca74 + c00696cb1b13e40bda15b27964d7670576647bfab9 + G.scalar_mult(s,X) (full coordinates): (length: 133 bytes) + 040122f88ce73ec5aa2d1c8c5d04148760c3d97ba87daa10d8cb8bb7 + c73cf6e951fc922721bf1437995cfb13e132a78beb86389e60d3517c + df6d99a8a2d6db19ef27bd0055af9e8ddcf337ce0a7c22a9c8099bc4 + a44faeded1eb72effd26e4f322217b67d60b944b267b3df5046078fd + 577f1785728f49b241fd5e8c83223a994a2d219281 + G.scalar_mult_vfy(s,X) (only X-coordinate): + (length: 66 bytes) + 0122f88ce73ec5aa2d1c8c5d04148760c3d97ba87daa10d8cb8bb7c7 + 3cf6e951fc922721bf1437995cfb13e132a78beb86389e60d3517cdf + 6d99a8a2d6db19ef27bd + +B.7.11. Invalid inputs for scalar_mult_vfy + + For these test cases scalar_mult_vfy(y,.) MUST return the + representation of the neutral element G.I. When including Y_i1 or + Y_i2 in messages of A or B the protocol MUST abort. + + s: (length: 66 bytes) + 0182dd7925f1753419e4bf83429763acd37d64000cd5a175edf53a15 + 87dd986bc95acc1506991702b6ba1a9ee2458fee8efc00198cf0088c + 480965ef65ff2048b856 + Y_i1: (length: 133 bytes) + 0400dc5078b24c4af1620cc10fbecc6cd8cf1cab0b011efb73c782f2 + 26dc21c7ca7eb406be74a69ecba5b4a87c07cfc6e687b4beca9a6eda + c95940a3b4120573b26a80005e697833b0ba285fce7b3f1f25243008 + 860b8f1de710a0dcc05b0d20341efe90eb2bcca26797c2d85ae6ca74 + c00696cb1b13e40bda15b27964d7670576647bfaf9 + Y_i2: (length: 1 bytes) + 00 + G.scalar_mult_vfy(s,Y_i1) = G.scalar_mult_vfy(s,Y_i2) = G.I + +B.7.11.1. Testvectors as JSON file encoded as BASE64 + + #eyJWYWxpZCI6IHsicyI6ICIwMTgyREQ3OTI1RjE3NTM0MTlFNEJGODM0Mjk3NjNBQ0 + #QzN0Q2NDAwMENENUExNzVFREY1M0ExNTg3REQ5ODZCQzk1QUNDMTUwNjk5MTcwMkI2 + #QkExQTlFRTI0NThGRUU4RUZDMDAxOThDRjAwODhDNDgwOTY1RUY2NUZGMjA0OEI4NT + #YiLCAiWCI6ICIwNDAwREM1MDc4QjI0QzRBRjE2MjBDQzEwRkJFQ0M2Q0Q4Q0YxQ0FC + #MEIwMTFFRkI3M0M3ODJGMjI2REMyMUM3Q0E3RUI0MDZCRTc0QTY5RUNCQTVCNEE4N0 + #MwN0NGQzZFNjg3QjRCRUNBOUE2RURBQzk1OTQwQTNCNDEyMDU3M0IyNkE4MDAwNUU2 + #OTc4MzNCMEJBMjg1RkNFN0IzRjFGMjUyNDMwMDg4NjBCOEYxREU3MTBBMERDQzA1Qj + #BEMjAzNDFFRkU5MEVCMkJDQ0EyNjc5N0MyRDg1QUU2Q0E3NEMwMDY5NkNCMUIxM0U0 + #MEJEQTE1QjI3OTY0RDc2NzA1NzY2NDdCRkFCOSIsICJHLnNjYWxhcl9tdWx0KHMsWC + #kgKGZ1bGwgY29vcmRpbmF0ZXMpIjogIjA0MDEyMkY4OENFNzNFQzVBQTJEMUM4QzVE + #MDQxNDg3NjBDM0Q5N0JBODdEQUExMEQ4Q0I4QkI3QzczQ0Y2RTk1MUZDOTIyNzIxQk + #YxNDM3OTk1Q0ZCMTNFMTMyQTc4QkVCODYzODlFNjBEMzUxN0NERjZEOTlBOEEyRDZE + #QjE5RUYyN0JEMDA1NUFGOUU4RERDRjMzN0NFMEE3QzIyQTlDODA5OUJDNEE0NEZBRU + #RFRDFFQjcyRUZGRDI2RTRGMzIyMjE3QjY3RDYwQjk0NEIyNjdCM0RGNTA0NjA3OEZE + #NTc3RjE3ODU3MjhGNDlCMjQxRkQ1RThDODMyMjNBOTk0QTJEMjE5MjgxIiwgIkcuc2 + #NhbGFyX211bHRfdmZ5KHMsWCkgKG9ubHkgWC1jb29yZGluYXRlKSI6ICIwMTIyRjg4 + #Q0U3M0VDNUFBMkQxQzhDNUQwNDE0ODc2MEMzRDk3QkE4N0RBQTEwRDhDQjhCQjdDNz + #NDRjZFOTUxRkM5MjI3MjFCRjE0Mzc5OTVDRkIxM0UxMzJBNzhCRUI4NjM4OUU2MEQz + #NTE3Q0RGNkQ5OUE4QTJENkRCMTlFRjI3QkQifSwgIkludmFsaWQgWTEiOiAiMDQwME + #RDNTA3OEIyNEM0QUYxNjIwQ0MxMEZCRUNDNkNEOENGMUNBQjBCMDExRUZCNzNDNzgy + #RjIyNkRDMjFDN0NBN0VCNDA2QkU3NEE2OUVDQkE1QjRBODdDMDdDRkM2RTY4N0I0Qk + #VDQTlBNkVEQUM5NTk0MEEzQjQxMjA1NzNCMjZBODAwMDVFNjk3ODMzQjBCQTI4NUZD + #RTdCM0YxRjI1MjQzMDA4ODYwQjhGMURFNzEwQTBEQ0MwNUIwRDIwMzQxRUZFOTBFQj + #JCQ0NBMjY3OTdDMkQ4NUFFNkNBNzRDMDA2OTZDQjFCMTNFNDBCREExNUIyNzk2NEQ3 + #NjcwNTc2NjQ3QkZBRjkiLCAiSW52YWxpZCBZMiI6ICIwMCJ9 + +Authors' Addresses + + Michel Abdalla + Nexus - San Francisco + Email: michel.abdalla@gmail.com + + + Bjoern Haase + Endress + Hauser Liquid Analysis - Gerlingen + Email: bjoern.m.haase@web.de + + + Julia Hesse + IBM Research Europe - Zurich + Email: juliahesse2@gmail.com diff --git a/draft-irtf-cfrg-cpace-13/index.html b/draft-irtf-cfrg-cpace-13/index.html new file mode 100644 index 0000000..06103a7 --- /dev/null +++ b/draft-irtf-cfrg-cpace-13/index.html @@ -0,0 +1,45 @@ + + + + cfrg/draft-irtf-cfrg-cpace draft-irtf-cfrg-cpace-13 preview + + + + +

Editor's drafts for draft-irtf-cfrg-cpace-13 branch of cfrg/draft-irtf-cfrg-cpace

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+ + + diff --git a/index.html b/index.html index 6f75bf9..6a0b2ec 100644 --- a/index.html +++ b/index.html @@ -32,6 +32,14 @@

Preview for branch draft-irtf-cfrg-cpace- diff with master +

Preview for branch draft-irtf-cfrg-cpace-13

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