winter_crypto/merkle/proofs.rs
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// Copyright (c) Facebook, Inc. and its affiliates.
//
// This source code is licensed under the MIT license found in the
// LICENSE file in the root directory of this source tree.
use alloc::{collections::BTreeMap, vec::Vec};
use utils::{ByteReader, Deserializable, DeserializationError, Serializable};
use super::MerkleTreeOpening;
use crate::{errors::MerkleTreeError, Hasher};
// BATCH MERKLE PROOF
// ================================================================================================
/// Multiple Merkle proofs aggregated into a single proof.
///
/// The aggregation is done in a way which removes all duplicate internal nodes, and thus,
/// it is possible to achieve non-negligible compression as compared to naively concatenating
/// individual Merkle proofs. The algorithm is for aggregation is a variation of
/// [Octopus](https://eprint.iacr.org/2017/933).
#[derive(Debug, Clone, PartialEq, Eq)]
pub struct BatchMerkleProof<H: Hasher> {
/// Hashes of Merkle Tree proof values above the leaf layer
pub nodes: Vec<Vec<H::Digest>>,
/// Depth of the leaves
pub depth: u8,
}
impl<H: Hasher> BatchMerkleProof<H> {
/// Constructs a batch Merkle proof from collection of single Merkle proofs.
///
/// # Panics
/// Panics if:
/// * No proofs have been provided (i.e., `proofs` is an empty slice).
/// * Number of proofs is not equal to the number of indexes.
/// * Not all proofs have the same length.
pub fn from_single_proofs(
proofs: &[MerkleTreeOpening<H>],
indexes: &[usize],
) -> BatchMerkleProof<H> {
// TODO: optimize this to reduce amount of vector cloning.
assert!(!proofs.is_empty(), "at least one proof must be provided");
assert_eq!(proofs.len(), indexes.len(), "number of proofs must equal number of indexes");
let depth = proofs[0].1.len();
// sort indexes in ascending order, and also re-arrange proofs accordingly
let mut proof_map = BTreeMap::new();
for (&index, proof) in indexes.iter().zip(proofs.iter().cloned()) {
assert_eq!(depth, proof.1.len(), "not all proofs have the same length");
proof_map.insert(index, proof);
}
let indexes = proof_map.keys().cloned().collect::<Vec<_>>();
let proofs = proof_map.values().cloned().collect::<Vec<_>>();
proof_map.clear();
let mut leaves = vec![H::Digest::default(); indexes.len()];
let mut nodes: Vec<Vec<H::Digest>> = Vec::with_capacity(indexes.len());
// populate values and the first layer of proof nodes
let mut i = 0;
while i < indexes.len() {
leaves[i] = proofs[i].0;
if indexes.len() > i + 1 && are_siblings(indexes[i], indexes[i + 1]) {
leaves[i + 1] = proofs[i].1[0];
nodes.push(vec![]);
i += 1;
} else {
nodes.push(vec![proofs[i].1[0]]);
}
proof_map.insert(indexes[i] >> 1, proofs[i].clone());
i += 1;
}
// populate all remaining layers of proof nodes
for d in 1..depth {
let indexes = proof_map.keys().cloned().collect::<Vec<_>>();
let mut next_proof_map = BTreeMap::new();
let mut i = 0;
while i < indexes.len() {
let index = indexes[i];
let proof = proof_map.get(&index).unwrap();
if indexes.len() > i + 1 && are_siblings(index, indexes[i + 1]) {
i += 1;
} else {
nodes[i].push(proof.1[d]);
}
next_proof_map.insert(index >> 1, proof.clone());
i += 1;
}
core::mem::swap(&mut proof_map, &mut next_proof_map);
}
BatchMerkleProof { nodes, depth: (depth) as u8 }
}
/// Computes a node to which all Merkle proofs aggregated in this proof resolve.
///
/// # Errors
/// Returns an error if:
/// * No indexes were provided (i.e., `indexes` is an empty slice).
/// * Any of the specified `indexes` is greater than or equal to the number of leaves in the
/// tree for which this batch proof was generated.
/// * List of indexes contains duplicates.
/// * The proof does not resolve to a single root.
pub fn get_root(
&self,
indexes: &[usize],
leaves: &[H::Digest],
) -> Result<H::Digest, MerkleTreeError> {
if indexes.is_empty() {
return Err(MerkleTreeError::TooFewLeafIndexes);
}
let mut buf = [H::Digest::default(); 2];
let mut v = BTreeMap::new();
// replace odd indexes, offset, and sort in ascending order
let index_map = super::map_indexes(indexes, self.depth as usize)?;
let indexes = super::normalize_indexes(indexes);
if indexes.len() != self.nodes.len() {
return Err(MerkleTreeError::InvalidProof);
}
// for each index use values to compute parent nodes
let offset = 2usize.pow(self.depth as u32);
let mut next_indexes: Vec<usize> = Vec::new();
let mut proof_pointers: Vec<usize> = Vec::with_capacity(indexes.len());
for (i, index) in indexes.into_iter().enumerate() {
// copy values of leaf sibling leaf nodes into the buffer
match index_map.get(&index) {
Some(&index1) => {
if leaves.len() <= index1 {
return Err(MerkleTreeError::InvalidProof);
}
buf[0] = leaves[index1];
match index_map.get(&(index + 1)) {
Some(&index2) => {
if leaves.len() <= index2 {
return Err(MerkleTreeError::InvalidProof);
}
buf[1] = leaves[index2];
proof_pointers.push(0);
},
None => {
if self.nodes[i].is_empty() {
return Err(MerkleTreeError::InvalidProof);
}
buf[1] = self.nodes[i][0];
proof_pointers.push(1);
},
}
},
None => {
if self.nodes[i].is_empty() {
return Err(MerkleTreeError::InvalidProof);
}
buf[0] = self.nodes[i][0];
match index_map.get(&(index + 1)) {
Some(&index2) => {
if leaves.len() <= index2 {
return Err(MerkleTreeError::InvalidProof);
}
buf[1] = leaves[index2];
},
None => return Err(MerkleTreeError::InvalidProof),
}
proof_pointers.push(1);
},
}
// hash sibling nodes into their parent
let parent = H::merge(&buf);
let parent_index = (offset + index) >> 1;
v.insert(parent_index, parent);
next_indexes.push(parent_index);
}
// iteratively move up, until we get to the root
for _ in 1..self.depth {
let indexes = next_indexes.clone();
next_indexes.truncate(0);
let mut i = 0;
while i < indexes.len() {
let node_index = indexes[i];
let sibling_index = node_index ^ 1;
// determine the sibling
let sibling: H::Digest;
if i + 1 < indexes.len() && indexes[i + 1] == sibling_index {
sibling = match v.get(&sibling_index) {
Some(sibling) => *sibling,
None => return Err(MerkleTreeError::InvalidProof),
};
i += 1;
} else {
let pointer = proof_pointers[i];
if self.nodes[i].len() <= pointer {
return Err(MerkleTreeError::InvalidProof);
}
sibling = self.nodes[i][pointer];
proof_pointers[i] += 1;
}
// get the node from the map of hashed nodes
let node = match v.get(&node_index) {
Some(node) => node,
None => return Err(MerkleTreeError::InvalidProof),
};
// compute parent node from node and sibling
if node_index & 1 != 0 {
buf[0] = sibling;
buf[1] = *node;
} else {
buf[0] = *node;
buf[1] = sibling;
}
let parent = H::merge(&buf);
// add the parent node to the next set of nodes
let parent_index = node_index >> 1;
v.insert(parent_index, parent);
next_indexes.push(parent_index);
i += 1;
}
}
v.remove(&1).ok_or(MerkleTreeError::InvalidProof)
}
/// Computes the uncompressed individual Merkle proofs which aggregate to this batch proof.
///
/// # Errors
/// Returns an error if:
/// * No indexes were provided (i.e., `indexes` is an empty slice).
/// * Number of provided indexes does not match the number of leaf nodes in the proof.
pub fn into_openings(
self,
leaves: &[H::Digest],
indexes: &[usize],
) -> Result<Vec<MerkleTreeOpening<H>>, MerkleTreeError> {
if indexes.is_empty() {
return Err(MerkleTreeError::TooFewLeafIndexes);
}
if indexes.len() != leaves.len() {
return Err(MerkleTreeError::InvalidProof);
}
let mut partial_tree_map = BTreeMap::new();
for (&i, leaf) in indexes.iter().zip(leaves.iter()) {
partial_tree_map.insert(i + (1 << (self.depth)), *leaf);
}
let mut buf = [H::Digest::default(); 2];
let mut v = BTreeMap::new();
// replace odd indexes, offset, and sort in ascending order
let original_indexes = indexes;
let index_map = super::map_indexes(indexes, self.depth as usize)?;
let indexes = super::normalize_indexes(indexes);
if indexes.len() != self.nodes.len() {
return Err(MerkleTreeError::InvalidProof);
}
// for each index use values to compute parent nodes
let offset = 2usize.pow(self.depth as u32);
let mut next_indexes: Vec<usize> = Vec::new();
let mut proof_pointers: Vec<usize> = Vec::with_capacity(indexes.len());
for (i, index) in indexes.into_iter().enumerate() {
// copy values of leaf sibling leaf nodes into the buffer
match index_map.get(&index) {
Some(&index1) => {
if leaves.len() <= index1 {
return Err(MerkleTreeError::InvalidProof);
}
buf[0] = leaves[index1];
match index_map.get(&(index + 1)) {
Some(&index2) => {
if leaves.len() <= index2 {
return Err(MerkleTreeError::InvalidProof);
}
buf[1] = leaves[index2];
proof_pointers.push(0);
},
None => {
if self.nodes[i].is_empty() {
return Err(MerkleTreeError::InvalidProof);
}
buf[1] = self.nodes[i][0];
proof_pointers.push(1);
},
}
},
None => {
if self.nodes[i].is_empty() {
return Err(MerkleTreeError::InvalidProof);
}
buf[0] = self.nodes[i][0];
match index_map.get(&(index + 1)) {
Some(&index2) => {
if leaves.len() <= index2 {
return Err(MerkleTreeError::InvalidProof);
}
buf[1] = leaves[index2];
},
None => return Err(MerkleTreeError::InvalidProof),
}
proof_pointers.push(1);
},
}
// hash sibling nodes into their parent and add it to partial_tree
let parent = H::merge(&buf);
partial_tree_map.insert(offset + index, buf[0]);
partial_tree_map.insert((offset + index) ^ 1, buf[1]);
let parent_index = (offset + index) >> 1;
v.insert(parent_index, parent);
next_indexes.push(parent_index);
partial_tree_map.insert(parent_index, parent);
}
// iteratively move up, until we get to the root
for _ in 1..self.depth {
let indexes = next_indexes.clone();
next_indexes.clear();
let mut i = 0;
while i < indexes.len() {
let node_index = indexes[i];
let sibling_index = node_index ^ 1;
// determine the sibling
let sibling = if i + 1 < indexes.len() && indexes[i + 1] == sibling_index {
i += 1;
match v.get(&sibling_index) {
Some(sibling) => *sibling,
None => return Err(MerkleTreeError::InvalidProof),
}
} else {
let pointer = proof_pointers[i];
if self.nodes[i].len() <= pointer {
return Err(MerkleTreeError::InvalidProof);
}
proof_pointers[i] += 1;
self.nodes[i][pointer]
};
// get the node from the map of hashed nodes
let node = match v.get(&node_index) {
Some(node) => node,
None => return Err(MerkleTreeError::InvalidProof),
};
// compute parent node from node and sibling
partial_tree_map.insert(node_index ^ 1, sibling);
let parent = if node_index & 1 != 0 {
H::merge(&[sibling, *node])
} else {
H::merge(&[*node, sibling])
};
// add the parent node to the next set of nodes and partial_tree
let parent_index = node_index >> 1;
v.insert(parent_index, parent);
next_indexes.push(parent_index);
partial_tree_map.insert(parent_index, parent);
i += 1;
}
}
original_indexes
.iter()
.map(|&i| get_proof::<H>(i, &partial_tree_map, self.depth as usize))
.collect()
}
}
// SERIALIZATION / DESERIALIZATION
// --------------------------------------------------------------------------------------------
impl<H: Hasher> Serializable for BatchMerkleProof<H> {
/// Writes all internal proof nodes into the provided target.
fn write_into<W: utils::ByteWriter>(&self, target: &mut W) {
target.write_u8(self.depth);
target.write_usize(self.nodes.len());
for nodes in self.nodes.iter() {
// record the number of nodes, and append all nodes to the proof buffer
nodes.write_into(target);
}
}
}
impl<H: Hasher> Deserializable for BatchMerkleProof<H> {
/// Parses internal nodes from the provided `source`, and constructs a batch Merkle proof
/// from these nodes.
///
/// # Errors
/// Returns an error if:
/// * `source` could not be deserialized into a valid set of internal nodes.
fn read_from<R: ByteReader>(source: &mut R) -> Result<Self, DeserializationError> {
let depth = source.read_u8()?;
let num_node_vectors = source.read_usize()?;
let mut nodes = Vec::with_capacity(num_node_vectors);
for _ in 0..num_node_vectors {
// read the digests and add them to the node vector
let digests = Vec::<_>::read_from(source)?;
nodes.push(digests);
}
Ok(BatchMerkleProof { nodes, depth })
}
}
// HELPER FUNCTIONS
// ================================================================================================
/// Two nodes are siblings if index of the left node is even and right node
/// immediately follows the left node.
fn are_siblings(left: usize, right: usize) -> bool {
left & 1 == 0 && right - 1 == left
}
/// Computes the Merkle proof from the computed (partial) tree.
pub fn get_proof<H: Hasher>(
index: usize,
tree: &BTreeMap<usize, <H as Hasher>::Digest>,
depth: usize,
) -> Result<MerkleTreeOpening<H>, MerkleTreeError> {
let mut index = index + (1 << depth);
let leaf = if let Some(leaf) = tree.get(&index) {
*leaf
} else {
return Err(MerkleTreeError::InvalidProof);
};
let mut proof = vec![];
while index > 1 {
let leaf = if let Some(leaf) = tree.get(&(index ^ 1)) {
*leaf
} else {
return Err(MerkleTreeError::InvalidProof);
};
proof.push(leaf);
index >>= 1;
}
Ok((leaf, proof))
}