This Rust library provides an implementation of Schnorr signatures based on the curve25519_dalek library.
Schnorr signatures are a cryptographic primitive that provides a secure and efficient way to prove the authenticity of a message or transaction. They offer several advantages over other signature schemes, including compactness, resistance to side-channel attacks, and simplicity.
- Key Pair Generation: To create a Schnorr signature, user generates key pair consisting of a private key (xi) and a corresponding public key (Xi), where Xi = xi * G and G is a known generator point on the elliptic curve.
- Signing: The signing process involves user combining his private key, public key, nonce and the message to create a signature.
- Verification: The signature can be verified using the public key, public nonce and the message. If the verification equation holds, the signature is considered valid.
The simple Schnorr signature algorithm involves the following components:
- Private keys: x1, x2, …, with corresponding public keys X1, X2, … (where Xi = xi * G, and G is the generator point).
- Message: m
- L = H(X1, X2, …) (where H() denotes a hash function)
The equations relevant for Schnorr signatures:
- Signing: (R,s) = (rG, r + H(X,R,m)x) where r is a random nonce chosen by the signer
- Verification: sG = R + H(X,R,m)X
The MuSig algorithm is a variant of the Schnorr signature scheme designed for multi-party signing. It ensures that all participants agree on the final signature without revealing individual private keys.
In the MuSig algorithm:
- n participants have private keys x1, x2, …, xn with corresponding public keys X1, X2, …, Xn.
- A message m is to be signed.
- L is calculated as L = H(X1, X2, …, Xn).
- H() represents a hash function.
The algorithm proceeds in the following steps:
- Participants send their public keys (Xi) to the leader. The leader then calculates the aggregated public key (X) as the sum of (H(L, Xi) * Xi) for all participants.
- Each participant generates a new key pair (Ri = ri * G) and sends it to the leader. The leader accumulates these values to compute the common value R = sum(Ri) and shares it with all participants, along with the computed X.
- Each signer computes their partial signature (si) as follows: si = ri + H(X, R, m) * H(L, Xi) * xi and sends it to the leader. The leader aggregates these partial signatures to form the final signature (R, s), where s is the sum of all si values. Verification of the signature is performed using the equation s * G = R + H(X, R, m) * X.
To use this library in your Rust project, simply include it as a dependency and refer to the provided functions and types in your code.
Contributions to this library are welcome! Feel free to open issues or pull requests for bug fixes, improvements, or new features.
This library builds upon the curve25519_dalek library and is inspired by the Schnorr signature and MuSig algorithms. Thanks to the open-source community for their contributions and support.