ZIP: 221 Title: FlyClient - Consensus-Layer Changes Owners: Jack Grigg <[email protected]> Original-Authors: Ying Tong Lai James Prestwich Georgios Konstantopoulos Status: Proposed Category: Consensus Created: 2019-03-30 License: MIT
The key words "MUST", "MUST NOT", "SHOULD", and "MAY" in this document are to be interpreted as described in RFC 2119. [1]
The terms "consensus branch", "epoch", and "network upgrade" in this document are to be interpreted as described in ZIP 200. [8]
- Light client
- A client that is not a full participant in the network of Zcash peers. It can send and receive payments, but does not store or validate a copy of the block chain.
- High probability
- An event occurs with high probability if it occurs with probability 1-O(1/2^\lambda ), where \lambda is a security parameter.
- Negligible probability
- An event occurs with negligible probability if it occurs with probability O(1/2^\lambda ), where \lambda is the security parameter.
- Merkle mountain range (MMR)
- A Merkle mountain range (MMR) is a binary hash tree that allows for efficient appends of new leaves without changing the value of existing nodes.
This ZIP specifies modifications to the Zcash block header semantics and consensus rules
in order to support the probabilistic verification FlyClient protocol [2]. The
hashFinalSaplingRoot commitment in the block header is replaced with a commitment to
the root of a Merkle Mountain Range (MMR), that in turn commits to various features of the
chain's history, including the Sapling commitment tree.
An MMR is a Merkle tree which allows for efficient appends, proofs, and verifications. Informally, appending data to an MMR consists of creating a new leaf and then iteratively merging neighboring subtrees with the same size. This takes at most \log(n) operations and only requires knowledge of the previous subtree roots, of which there are fewer than \log(n).
(example adapted from [6]) To illustrate this, consider a list of 11 leaves. We first construct the biggest perfect binary subtrees possible by joining any balanced sibling trees that are the same size. We do this starting from the left to the right, adding a parent as soon as 2 children exist. This leaves us with three subtrees ("mountains") of altitudes 3, 1, and 0:
/\
/ \
/\ /\
/\/\/\/\ /\ /
Note that the first leftmost peak is always the highest. We can number this structure in the order by which nodes would be created, if the leaves were inserted from left to right:
Altitude
3 14
/ \
/ \
/ \
/ \
2 6 13
/ \ / \
1 2 5 9 12 17
/ \ / \ / \ / \ / \ /
0 0 1 3 4 7 8 10 11 15 16 18
and represent this numbering in a flat list:
Position 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Altitude 0 0 1 0 0 1 2 0 0 1 0 0 1 2 3 0 0 1 0
Let h be the altitude of a given node. We can easily jump to the node's right sibling (if it has one) by adding 2^{h+1} - 1 to its position, and its left child (if it has one) by subtracting 2^h. This allows us to efficiently find the subtree roots ("peaks") of the mountains.
Once we have the positions of the mountain peaks, we "bag" them using the following algorithm:
- Generate a node connecting the 2 left-most peaks, forming a new peak.
- Repeat 1. until we have a single peak.
Note that the extra nodes generated during the bagging process do not follow the above rules for jumping between nodes.
Altitude
5 20g
/ \
4 19g \
/ \ \
/ \ \
/ \ \
3 14 \ \
/ \ \ \
/ \ \ \
/ \ \ \
/ \ \ \
2 6 13 \ \
/ \ / \ \ \
1 2 5 9 12 17 \
/ \ / \ / \ / \ / \ \
0 0 1 3 4 7 8 10 11 15 16 18
MMR trees allow for efficient incremental set update operations (push, pop, prune). In addition, MMR update operations and Merkle proofs for recent additions to the leaf set are more efficient than other incremental Merkle tree implementations (e.g. Bitcoin's padded leafset, sparse Merkle trees, and Zcash's incremental note commitment trees).
MMR proofs are used in the FlyClient protocol [2], to reduce the proof size needed for light clients to verify:
- the validity of a block chain received from a full node, and
- the inclusion of a block B in that chain, and
- certain metadata of any block or range of blocks in that chain.
The protocol requires that an MMR that commits to the inclusion of all blocks since the preceding network upgrade (B_x, \ldots, B_{n-1}) is formed for each block B_n. The root M_n of the MMR MUST be included in the header of B_n.
(x is the activation height of the preceding network upgrade.)
FlyClient reduces the number of block headers needed for light client verification of a valid chain, from linear (as in the current reference protocol) to logarithmic in block chain length. This verification is correct with high probability. It also allows creation of subtree proofs, so light clients need only check blocks later than the most recently verified block index. Following that, verification of a transaction inclusion within that block follows the usual reference protocol [11].
A smaller proof size could enable the verification of Zcash SPV Proofs in block-chain protocols such as Ethereum, enabling efficient cross-chain communication and pegs. It also reduces bandwidth and storage requirements for resource-limited clients like mobile or IoT devices.
For a block B_n at height n > 0 in a given block chain, define the "preceding network upgrade height" x of B_n to be the last network upgrade activation height in the chain that is less than n. (For this definition, block height 0 is considered to be the height of a network upgrade activation. The preceding network upgrade height of the genesis block is undefined.)
The leaves of the MMR at block B_n are hash commitments to the header data and metadata of each previous block B_x, \ldots, B_{n-1}, where x is defined as above. We extend the standard MMR to allow metadata to propagate upwards through the tree by either summing the metadata of both children, or inheriting the metadata of a specific child as necessary. This allows us to create efficient proofs of selected properties of a range of blocks without transmitting the entire range of blocks or headers.
Unless otherwise noted, all hashes use BLAKE2b-256 with the personalization field set
to 'ZcashHistory' || CONSENSUS_BRANCH_ID. CONSENSUS_BRANCH_ID is the 4-byte
little-endian encoding of the consensus branch ID for the epoch of the block containing
the commitment. [8] Which is to say, each node in the tree commits to the
consensus branch that produced it.
Each MMR node is defined as follows:
hashSubtreeCommitment- Leaf node
The consensus-defined block hash for the corresponding block.
- This hash is encoded in internal byte order, and does NOT use the BLAKE2b-256 personalization string described above.
- For clarity, in a given consensus branch, the
hashSubtreeCommitmentfield of leaf n-1 is precisely equal to thehashPrevBlockfield in the header of the block at height x+n, where x is the network upgrade activation height of that consensus branch.
- Internal or root node
- Both child nodes are serialized.
hashSubtreeCommitmentis the BLAKE2b-256 hash ofleft_child || right_child.- For clarity, this digest uses the BLAKE2b-256 personalization string described above.
Serialized as
char[32].nEarliestTimestamp- Leaf node
The header's timestamp.
- Internal or root node
Inherited from the left child.
Serialized as
nTime(uint32).Note that a
uint32time value would overflow on 2106-02-07, but this field (andnLatestTimestampbelow) can only hold values that occur in thenTimefield of a block header, which is also of typeuint32.nLatestTimestamp- Leaf node
The header's timestamp.
- Internal or root node
Inherited from the right child.
Note that due to timestamp consensus rules,
nLatestTimestampmay be smaller thannEarliestTimestampin some subtrees. This may occur within subtrees smaller thanPoWMedianBlockSpanblocks.Serialized as
nTime(uint32).nEarliestTargetBits- Leaf node
The header's
nBitsfield.- Internal or root node
Inherited from the left child.
Serialized as
nBits(uint32).nLatestTargetBits- Leaf node
The header's
nBitsfield.- Internal or root node
Inherited from the right child.
Serialized as
nBits(uint32).hashEarliestSaplingRoot- Leaf node
Calculated as
hashFinalSaplingRoot, as implemented in Sapling.- Internal or root node
Inherited from the left child.
Serialized as
char[32].hashLatestSaplingRoot- Leaf node
Calculated as
hashFinalSaplingRoot, as implemented in Sapling.- Internal or root node
Inherited from the right child.
Serialized as
char[32].nSubTreeTotalWork- Leaf node
The protocol-defined work of the block: \mathsf{floor}(2^{256} / (\mathsf{ToTarget}(\mathsf{nBits}) + 1)). [3]
- Internal or root node
The sum of the
nSubTreeTotalWorkfields of both children.Computations modulo 2^{256} are fine here; cumulative chain work is similarly assumed elsewhere in the Zcash ecosystem to be at most 2^{256} (as inherited from Bitcoin). The computed work factors are, on average, equal to the computational efforts involved in the creation of the corresponding blocks, and an aggregate effort of 2^{256} or more is infeasible in practice.
Serialized as
uint256.nEarliestHeight- Leaf node
The header's height.
- Internal or root node
Inherited from the left child.
Serialized as
CompactSize uint.nLatestHeight- Leaf node
The header's height.
- Internal or root node
Inherited from the right child.
Serialized as
CompactSize uint.nSaplingTxCount- Leaf node
The number of transactions in the leaf block where either of
vShieldedSpendorvShieldedOutputis non-empty.- Internal or root node
The sum of the
nSaplingTxCountfield of both children.
Serialized as
CompactSize uint.
Each node, when serialized, is between 147 and 171 bytes long. The canonical serialized representation of a node is used whenever creating child commitments for future nodes. Other than the metadata commitments, the MMR tree's construction is standard.
Once the MMR has been generated, we produce hashChainHistoryRoot, which we define as
the BLAKE2b-256 digest of the serialization of the root node.
def H(msg: bytes, consensusBranchId: bytes) -> bytes:
return blake2b256(msg, personalization=b'ZcashHistory' + consensusBranchId)
class ZcashMMRNode():
# leaf nodes have no children
left_child: Optional[ZcashMMRNode]
right_child: Optional[ZcashMMRNode]
# commitments
hashSubtreeCommitment: bytes
nEarliestTimestamp: int
nLatestTimestamp: int
nEarliestTargetBits: int
nLatestTargetBits: int
hashEarliestSaplingRoot: bytes # left child's sapling root
hashLatestSaplingRoot: bytes # right child's sapling root
nSubTreeTotalWork: int # total difficulty accumulated within each subtree
nEarliestHeight: int
nLatestHeight: int
nSaplingTxCount: int # number of Sapling transactions in block
consensusBranchId: bytes
@classmethod
def from_block(Z, block: ZcashBlock) -> ZcashMMRNode:
'''Create a leaf node from a block'''
return Z(
left_child=None,
right_child=None,
hashSubtreeCommitment=block.header_hash,
nEarliestTimestamp=block.timestamp,
nLatestTimestamp=block.timestamp,
nEarliestTargetBits=block.nBits,
nLatestTargetBits=block.nBits,
hashEarliestSaplingRoot=block.sapling_root,
hashLatestSaplingRoot=block.sapling_root,
nSubTreeTotalWork=calculate_work(block.nBits),
nEarliestHeight=block.height,
nLatestHeight=block.height,
nSaplingTxCount=block.sapling_tx_count,
consensusBranchId=block.consensusBranchId)
def serialize(self) -> bytes:
'''serializes a node'''
return (
self.hashSubtreeCommitment
+ serialize_uint32(self.nEarliestTimestamp)
+ serialize_uint32(self.nLatestTimestamp)
+ serialize_uint32(self.nEarliestTargetBits)
+ serialize_uint32(self.nLatestTargetBits)
+ hashEarliestSaplingRoot
+ hashLatestSaplingRoot
+ serialize_uint256(self.nSubTreeTotalWork)
+ serialize_compact_uint(self.nEarliestHeight)
+ serialize_compact_uint(self.nLatestHeight)
+ serialize_compact_uint(self.nSaplingTxCount))
def make_parent(
left_child: ZcashMMRNode,
right_child: ZcashMMRNode) -> ZcashMMRNode:
return ZcashMMRNode(
left_child=left_child,
right_child=right_child,
hashSubtreeCommitment=H(left_child.serialize() + right_child.serialize(),
left_child.consensusBranchId),
nEarliestTimestamp=left_child.nEarliestTimestamp,
nLatestTimestamp=right_child.nLatestTimestamp,
nEarliestTargetBits=left_child.nEarliestTargetBits,
nLatestTargetBits=right_child.nLatestTargetBits,
hashEarliestSaplingRoot=left_child.sapling_root,
hashLatestSaplingRoot=right_child.sapling_root,
nSubTreeTotalWork=left_child.nSubTreeTotalWork + right_child.nSubTreeTotalWork,
nEarliestHeight=left_child.nEarliestHeight,
nLatestHeight=right_child.nLatestHeight,
nSaplingTxCount=left_child.nSaplingTxCount + right_child.nSaplingTxCount,
consensusBranchId=left_child.consensusBranchId)
def make_root_commitment(root: ZcashMMRNode) -> bytes:
'''Makes the root commitment for a blockheader'''
return H(root.serialize(), root.consensusBranchId)With each new block B_n, we append a new MMR leaf node corresponding to block
B_{n-1}. The append operation is detailed below in pseudocode (adapted from
[2]):
def get_peaks(node: ZcashMMRNode) -> List[ZcashMMRNode]:
peaks: List[ZcashMMRNode] = []
# Get number of leaves.
leaves = latest_height - (earliest_height - 1)
assert(leaves > 0)
# Check if the number of leaves is a power of two.
if (leaves & (leaves - 1)) == 0:
# Tree is full, hence a single peak. This also covers the
# case of a single isolated leaf.
peaks.append(node)
else:
# If the number of leaves is not a power of two, then this
# node must be internal, and cannot be a peak.
peaks.extend(get_peaks(left_child))
peaks.extend(get_peaks(right_child))
return peaks
def bag_peaks(peaks: List[ZcashMMRNode]) -> ZcashMMRNode:
'''
"Bag" a list of peaks, and return the final root
'''
root = peaks[0]
for i in range(1, len(peaks)):
root = make_parent(root, peaks[i])
return root
def append(root: ZcashMMRNode, leaf: ZcashMMRNode) -> ZcashMMRNode:
'''Append a leaf to an existing tree, return the new tree root'''
# recursively find a list of peaks in the current tree
peaks: List[ZcashMMRNode] = get_peaks(root)
merged: List[ZcashMMRNode] = []
# Merge peaks from right to left.
# This will produce a list of peaks in reverse order
current = leaf
for peak in peaks[::-1]:
current_leaves = current.latest_height - (current.earliest_height - 1)
peak_leaves = peak.latest_height - (peak.earliest_height - 1)
if current_leaves == peak_leaves:
current = make_parent(peak, current)
else:
merged.append(current)
current = peak
merged.append(current)
# finally, bag the merged peaks
return bag_peaks(merged[::-1])In case of a block reorg, we have to delete the latest (i.e. rightmost) MMR leaf nodes, up to the reorg length. This operation is O(\log(k)) where k is the number of leaves in the right subtree of the MMR root.
def delete(root: ZcashMMRNode) -> ZcashMMRNode:
'''
Delete the rightmost leaf node from an existing MMR
Return the new tree root
'''
n_leaves = root.latest_height - (root.earliest_height - 1)
# if there were an odd number of leaves,
# simply replace root with left_child
if n_leaves & 1:
return root.left_child
# otherwise, we need to re-bag the peaks.
else:
# first peak
peaks = [root.left_child]
# we do this traversing the right (unbalanced) side of the tree
# we keep the left side (balanced subtree or leaf) of each subtree
# until we reach a leaf
subtree_root = root.right_child
while subtree_root.left_child:
peaks.push(subtree_root.left_child)
subtree_root = subtree_root.right_child
new_root = bag_peaks(peaks)
return new_rootThe hashFinalSaplingRoot block header field (which was named hashReserved prior to
the Sapling network upgrade) is renamed to hashLightClientRoot, to reflect its usage
by light clients.
Prior to activation of the network upgrade that deploys this ZIP, this existing consensus rule on block headers (adjusted for the renamed field) is enforced: [4]
[Sapling onward] hashLightClientRoot MUST be \mathsf{LEBS2OSP}_{256}(\mathsf{rt})
where \mathsf{rt} is the root of the Sapling note commitment tree for the final
Sapling tree state of this block.
In the block that activates this ZIP, hashLightClientRoot MUST be set to all zero bytes.
This MUST NOT be interpreted as a root hash.
In subsequent blocks, hashLightClientRoot MUST be set to the value of hashChainHistoryRoot
as specified above.
The block header byte format and version are not altered by this ZIP.
Nodes in the commitment tree are canonical and immutable. They are cheap to generate, as
(with the exception of nSaplingTxCount) all metadata is already generated during
block construction and/or checked during block validation. Nodes are relatively compact in
memory. Approximately 140,000 blocks have elapsed since Sapling activation. Assuming a 164
byte commitment to each of these, we would have generated approximately 24 MB of
additional storage cost for the set of leaf nodes (and an additional ~24 MB for storage of
intermediate nodes).
hashSubtreeCommitment forms the strucuture of the commitment tree. Other metadata
commitments were chosen to serve specific purposes. Variable-length commitments are placed
last, so that most metadata in a node can be directly indexed. We considered using
fixed-length commitments here, but opted for variable-length, in order to marginally
reduce the memory requirements for managing and updating the commitment trees.
In leaf nodes, some information is repeated. We chose to do this so that leaf nodes could
be treated identically to internal and root nodes for all algorithms and (de)serializers.
Leaf nodes are easily identifiable, as they will show proof of work in the
hashSubtreeCommitment field (which commits to the block hash for leaf nodes), and
their block range (calculated as nLatestHeight - (nEarliestHeight - 1))
will be precisely 1.
Personalized BLAKE2b-256 was selected to match existing Zcash conventions. Adding the consensus branch ID to the hash personalization string ensures that valid nodes from one consensus branch cannot be used to make false statements about parallel consensus branches.
These commitments enable FlyClient in the variable-difficulty model. Specifically, they allow light clients to reason about application of the difficulty adjustment algorithm over a range of blocks. They were chosen via discussion with an author of the FlyClient paper.
nEarliestTimestampnLatestTimestampnEarliestTargetBitsnLatestTargetBitsnEarliestHeightnLatestHeightnSubTreeTotalWork
Additional metadata commitments were chosen primarily to improve light client security guarantees. We specified commitments where we could see an obvious security benefit, but there may be other useful metadata that we missed. We're interested in feedback and suggestions from the implementers of the current light client.
We considered adding a commitment to the nullifier vector at each block. We would appreciate comments from light client teams on the utility of this commitment, as well as the proper serialization and commitment format for the nullifier vector, for possible inclusion in a future upgrade.
hashEarliestSaplingRoot- Committing to the earliest Sapling root of a range of blocks allows light clients to check the consistency of treestate transitions over a range of blocks, without recalculating the root from genesis.
hashLatestSaplingRoot- This commitment serves the same purpose as
hashFinalSaplingRootin current Sapling semantics. - However, because the MMR tree commits to blocks B_x \ldots B_{n-1}, the latest commitment will describe the final treestate of the previous block, rather than the current block.
- Concretely: block 500 currently commits to the final treestate of block 500 in its header. With this ZIP, block 500 will commit to all roots up to block 499, but not the final root of block 500.
- We feel this is an acceptable tradeoff. Using the most recent treestate as a transaction anchor is already unsafe in reorgs. Clients should never use the most recent treestate to generate transactions, so it is acceptable to delay commitment by one block.
- This commitment serves the same purpose as
nSaplingTxCount- By committing to the number of Sapling transactions in blocks (and ranges of blocks), a light client may reliably learn whether a malicious server is witholding any Sapling transactions.
- In addition, this commitment allows light clients to avoid syncing header ranges that do not contain Sapling transactions. As the primary cost of a light client is transmission of Equihash solution information in block headers, this optimization would significantly decrease the bandwidth requirements of light clients.
- An earlier draft of this ZIP committed to the number of shielded transactions, counting both Sprout and Sapling. This commitment would not have been useful to light clients that only support Sapling addresses; they would not be able to distinguish between Sapling transactions being maliciously withheld, and Sprout transactions not being requested.
- A commitment to the number of Sprout transactions in blocks was not included, because Sprout addresses are effectively deprecated at this point, and will not be supported by any light clients.
- If a future network upgrade introduced a new shielded pool, a new commitment to that pool's transactions would be added, to similarly enable future light clients that do not support Sapling addresses.
The primary goal of the original authors was to minimize header changes; in particular,
they preferred not to introduce changes that could affect mining hardware or embedded
software. Altering the block header format would require changes throughout the ecosystem,
so we decided against adding hashChainHistoryRoot to the header as a new field.
ZIP 301 states that "[Miner client software] SHOULD alert the user upon receiving jobs containing block header versions they do not know about or support, and MUST ignore such jobs." [10] As the only formally defined block header version is 4, any header version change requires changes to miner client software in order for miners to handle new jobs from mining pools. We therefore do not alter the block version for this semantic change. This does not make block headers ambiguous to interpret, because blocks commit to their block height inside their coinbase transaction, [7] and they are never handled in a standalone context (unlike transactions, which exist in the mempool outside of blocks).
Replacing hashFinalSaplingRoot with hashChainHistoryRoot does introduce the
theoretical possibility of an attack where a miner constructs a Sapling commitment tree
update that results in the same 32-byte value as the MMR root. We don't consider this a
realistic attack, both because the adversary would need to find a preimage over 32 layers
of Pedersen hash, and because light clients already need to update their code to include
the consensus branch ID for the Heartwood network upgrade, and can simultaneously make
changes to not rely on the value of this header field being the Sapling tree root.
We also considered putting hashChainHistoryRoot in the hashPrevBlock field as it
commits to the entire chain history, but quickly realized it would require massive
refactoring of the existing code base and would negatively impact performance. Reorgs in
particular are fragile, performance-critical, and rely on backwards iteration over the
chain history. If a chain were to be designed from scratch there may be some efficient
implementation that would join these commitments, but it is clearly not appropriate for
Zcash as it exists.
The calculation of hashChainHistoryRoot is not well-defined for the genesis block,
since then n = 0 and there is no block B_{n-1}. Also, in the case of
chains that activate this ZIP after genesis (including Zcash Mainnet and Testnet), the
hashChainHistoryRoot of the activation block would commit to the whole previous epoch
if a special case were not made. It would be impractical to calculate this commitment all
at once, and so we specify that hashLightClientRoot is set to all zero bytes for that
block instead. The hash of the final Sapling note commitment tree root for the activation
block will not be encoded in that block, but will be committed to one block later in the
hashLatestSaplingRoot field of the MMR root commitment.
This ZIP imposes an additional validation cost on new blocks. While this validation cost is small, it may exacerbate any existing DoS opportunities, particularly during abnormal events like long reorgs. Fortunately, these costs are logarithmic in the number of delete and append operations. In the worst case scenario, a well-resourced attacker could maintain 2 chains of approximately equal length, and alternate which chain they extend. This would result in repeated reorgs of increasing length.
Given the performance of BLAKE2b, we expect this validation cost to be negligible. However, it seems prudent to benchmark potential MMR implementations during the implementation process. Should the validation cost be higher than expected, there are several potential mitigations, e.g. holding recently seen nodes in memory after a reorg.
Generally, header commitments have no impact on privacy. However, FlyClient has additional security and privacy implications. Because FlyClient is a motivating factor for this ZIP, it seems prudent to include a brief overview. A more in-depth security analysis of FlyClient should be performed before designing a FlyClient-based light client ecosystem for Zcash.
FlyClient, like all light clients, requires a connection to a light client server. That server may collect information about client requests, and may use that information to attempt to deanonymize clients. However, because FlyClient proofs are non-interactive and publicly verifiable, they could be shared among many light clients after the initial server interaction.
FlyClient proofs are probabilistic. When properly constructed, there is negligible probability that a dishonest chain commitment will be accepted by the verifier. The security analysis assumes adversary mining power is bounded by a known fraction of combined mining power of honest nodes, and cannot drop or tamper with messages between client and full nodes. It also assumes the client is connected to at least one full node and knows the genesis block.
In addition, [2] only analyses these security properties in chain models with slowly adjusting difficulty, such as Bitcoin. That paper leaves their analysis in chains with rapidly adjusting difficulty –such as Zcash or Ethereum– as an open problem, and states that the FlyClient protocol provides only heuristic security guarantees in that case. However, as mentioned in FlyClient Requirements and Recommendations, additional commitments allowing light clients to reason about application of the difficulty adjustment algorithm were added in discussion with an author of the FlyClient paper. The use of these fields has not been analysed in the academic security literature. It would be possible to update them in a future network upgrade if further security analysis were to find any deficiencies.
On the Zcash Mainnet and Testnet, this proposal will be deployed with the Heartwood network upgrade. [9]
- Flyclient enabled geth fork by FlyClient authors
- ECIP-1055: Succinct PoW Using Merkle Mountain Ranges
- Grin project MMR implementation in Rust
- Tari Project MMR implementation in Rust
- Beam Project MMR implementation in C++
- Mimblewimble MMR docs
- MMR Python implementation
- Tari MMR documentation
- Zcash Protocol Specification, Version 2020.1.1 [Overwinter+Sapling+Blossom] or later
- opentimestamps-server Merkle Mountain Range documentation
| [1] | Key words for use in RFCs to Indicate Requirement Levels |
| [2] | (1, 2, 3, 4) FlyClient protocol |
| [3] | Section 7.6.5: Definition of Work. Zcash Protocol Specification, Version 2020.1.1 [Overwinter+Sapling+Blossom] or later |
| [4] | Section 7.5: Block Header. Zcash Protocol Specification, Version 2020.1.1 [Overwinter+Sapling+Blossom] or later |
| [5] | Zcash block primitive |
| [6] | MimbleWimble Grin MMR implementation |
| [7] | BIP 34: Block v2, Height in Coinbase |
| [8] | (1, 2) ZIP 200: Network Upgrade Mechanism |
| [9] | ZIP 250: Deployment of the Heartwood Network Upgrade |
| [10] | ZIP 301: Zcash Stratum Protocol |
| [11] | ZIP 307: Light Client Protocol for Payment Detection |