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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 crate::{errors::MerkleTreeError, hash::Hasher};
use core::slice;
use math::log2;
use utils::collections::{BTreeMap, BTreeSet, Vec};
mod proofs;
pub use proofs::BatchMerkleProof;
#[cfg(feature = "concurrent")]
pub mod concurrent;
#[cfg(test)]
mod tests;
// TYPES AND INTERFACES
// ================================================================================================
/// A fully-balanced Merkle tree.
///
/// In this implementation, a Merkle tree consists of two types of nodes: leaves and internal nodes
/// (one of which is a tree root). All nodes must be instances of the digest specified by the
/// [Hasher] used to build the tree.
///
/// ```text
/// * <- tree root
/// / \
/// / \
/// * * <- internal nodes
/// / \ / \
/// o o o o <- leaves
/// | | | |
/// # # # # <- values
/// ```
///
/// A tree can be built from a slice of leaves using [MerkleTree::new()] function. Thus, the user
/// is responsible for performing the first level of hashing (i.e., hashing values into leaf
/// nodes). The number of leaves must always be a power of two so that the tree is fully balanced,
/// and a tree must contain at least two leaves.
///
/// The depth of a tree is zero-based. Thus, a tree with two leaves has depth 1, a tree with four
/// leaves has depth 2 etc.
///
/// When the crate is compiled with `concurrent` feature enabled, tree construction will be
/// performed in multiple threads (usually, as many threads as there are logical cores on the
/// machine). The number of threads can be configured via `RAYON_NUM_THREADS` environment variable.
///
/// To generate an inclusion proof for a given leaf, [MerkleTree::prove()] method can be used.
/// You can also use [MerkleTree::prove_batch()] method to generate inclusion proofs for multiple
/// leaves. The advantage of the batch method is that redundant internal nodes are removed from
/// the batch proof, thereby compressing it (we use a variation of the
/// [Octopus](https://eprint.iacr.org/2017/933) algorithm).
///
/// To verify proofs, [MerkleTree::verify()] and [MerkleTree::verify_batch()] functions can be
/// used respectively.
///
/// # Examples
/// ```
/// # use winter_crypto::{MerkleTree, Hasher, hashers::Blake3_256};
/// # use math::fields::f128::BaseElement;
/// type Blake3 = Blake3_256::<BaseElement>;
///
/// // build a tree
/// let leaves = [
/// Blake3::hash(&[1u8]),
/// Blake3::hash(&[2u8]),
/// Blake3::hash(&[3u8]),
/// Blake3::hash(&[4u8]),
/// ];
/// let tree = MerkleTree::<Blake3>::new(leaves.to_vec()).unwrap();
/// assert_eq!(2, tree.depth());
/// assert_eq!(leaves, tree.leaves());
///
/// // generate a proof
/// let proof = tree.prove(2).unwrap();
/// assert_eq!(3, proof.len());
/// assert_eq!(leaves[2], proof[0]);
///
/// // verify proof
/// assert!(MerkleTree::<Blake3>::verify(*tree.root(), 2, &proof).is_ok());
/// assert!(MerkleTree::<Blake3>::verify(*tree.root(), 1, &proof).is_err());
/// ```
#[derive(Debug)]
pub struct MerkleTree<H: Hasher> {
nodes: Vec<H::Digest>,
leaves: Vec<H::Digest>,
}
// MERKLE TREE IMPLEMENTATION
// ================================================================================================
impl<H: Hasher> MerkleTree<H> {
// CONSTRUCTOR
// --------------------------------------------------------------------------------------------
/// Returns new Merkle tree built from the provide leaves using hash function specified by the
/// `H` generic parameter.
///
/// When `concurrent` feature is enabled, the tree is built using multiple threads.
///
/// # Errors
/// Returns an error if:
/// * Fewer than two leaves were provided.
/// * Number of leaves is not a power of two.
pub fn new(leaves: Vec<H::Digest>) -> Result<Self, MerkleTreeError> {
if leaves.len() < 2 {
return Err(MerkleTreeError::TooFewLeaves(2, leaves.len()));
}
if !leaves.len().is_power_of_two() {
return Err(MerkleTreeError::NumberOfLeavesNotPowerOfTwo(leaves.len()));
}
#[cfg(not(feature = "concurrent"))]
let nodes = build_merkle_nodes::<H>(&leaves);
#[cfg(feature = "concurrent")]
let nodes = if leaves.len() <= concurrent::MIN_CONCURRENT_LEAVES {
build_merkle_nodes::<H>(&leaves)
} else {
concurrent::build_merkle_nodes::<H>(&leaves)
};
Ok(MerkleTree { nodes, leaves })
}
// PUBLIC ACCESSORS
// --------------------------------------------------------------------------------------------
/// Returns the root of the tree.
pub fn root(&self) -> &H::Digest {
&self.nodes[1]
}
/// Returns depth of the tree.
///
/// The depth of a tree is zero-based. Thus, a tree with two leaves has depth 1, a tree with
/// four leaves has depth 2 etc.
pub fn depth(&self) -> usize {
log2(self.leaves.len()) as usize
}
/// Returns leaf nodes of the tree.
pub fn leaves(&self) -> &[H::Digest] {
&self.leaves
}
// PROVING METHODS
// --------------------------------------------------------------------------------------------
/// Returns a Merkle path to a leaf at the specified `index`.
///
/// The leaf itself will be the first element in the path.
///
/// # Errors
/// Returns an error if the specified index is greater than or equal to the number of leaves
/// in the tree.
pub fn prove(&self, index: usize) -> Result<Vec<H::Digest>, MerkleTreeError> {
if index >= self.leaves.len() {
return Err(MerkleTreeError::LeafIndexOutOfBounds(
self.leaves.len(),
index,
));
}
let mut proof = vec![self.leaves[index], self.leaves[index ^ 1]];
let mut index = (index + self.nodes.len()) >> 1;
while index > 1 {
proof.push(self.nodes[index ^ 1]);
index >>= 1;
}
Ok(proof)
}
/// Computes Merkle paths for the provided indexes and compresses the paths into a single proof.
///
/// # Errors
/// Returns an error if:
/// * No indexes were provided (i.e., `indexes` is an empty slice).
/// * Number of provided indexes is greater than 255.
/// * Any of the provided indexes are greater than or equal to the number of leaves in the
/// tree.
/// * List of indexes contains duplicates.
pub fn prove_batch(&self, indexes: &[usize]) -> Result<BatchMerkleProof<H>, MerkleTreeError> {
if indexes.is_empty() {
return Err(MerkleTreeError::TooFewLeafIndexes);
}
if indexes.len() > proofs::MAX_PATHS {
return Err(MerkleTreeError::TooManyLeafIndexes(
proofs::MAX_PATHS,
indexes.len(),
));
}
let index_map = map_indexes(indexes, self.depth())?;
let indexes = normalize_indexes(indexes);
let mut leaves = vec![H::Digest::default(); index_map.len()];
let mut nodes: Vec<Vec<H::Digest>> = Vec::with_capacity(indexes.len());
// populate the proof with leaf node values
let n = self.leaves.len();
let mut next_indexes: Vec<usize> = Vec::new();
for index in indexes {
let missing: Vec<H::Digest> = (index..index + 2)
.flat_map(|i| {
let v = self.leaves[i];
if let Some(idx) = index_map.get(&i) {
leaves[*idx] = v;
None
} else {
Some(v)
}
})
.collect();
nodes.push(missing);
next_indexes.push((index + n) >> 1);
}
// add required internal nodes to the proof, skipping redundancies
for _ in 1..self.depth() {
let indexes = next_indexes.clone();
next_indexes.truncate(0);
let mut i = 0;
while i < indexes.len() {
let sibling_index = indexes[i] ^ 1;
if i + 1 < indexes.len() && indexes[i + 1] == sibling_index {
i += 1;
} else {
nodes[i].push(self.nodes[sibling_index]);
}
// add parent index to the set of next indexes
next_indexes.push(sibling_index >> 1);
i += 1;
}
}
Ok(BatchMerkleProof {
leaves,
nodes,
depth: self.depth() as u8,
})
}
// VERIFICATION METHODS
// --------------------------------------------------------------------------------------------
/// Checks whether the `proof` for the specified `index` is valid.
///
/// # Errors
/// Returns an error if the specified `proof` (which is a Merkle path) does not resolve to the
/// specified `root`.
pub fn verify(
root: H::Digest,
index: usize,
proof: &[H::Digest],
) -> Result<(), MerkleTreeError> {
let r = index & 1;
let mut v = H::merge(&[proof[r], proof[1 - r]]);
let mut index = (index + 2usize.pow((proof.len() - 1) as u32)) >> 1;
for &p in proof.iter().skip(2) {
v = if index & 1 == 0 {
H::merge(&[v, p])
} else {
H::merge(&[p, v])
};
index >>= 1;
}
if v != root {
return Err(MerkleTreeError::InvalidProof);
}
Ok(())
}
/// Checks whether the batch proof contains Merkle paths for the of the specified `indexes`.
///
/// # Errors
/// Returns an error if:
/// * No indexes were provided (i.e., `indexes` is an empty slice).
/// * Number of provided indexes is greater than 255.
/// * Any of the specified `indexes` is greater than or equal to the number of leaves in the
/// tree from which the batch proof was generated.
/// * List of indexes contains duplicates.
/// * Any of the paths in the batch proof does not resolve to the specified `root`.
pub fn verify_batch(
root: &H::Digest,
indexes: &[usize],
proof: &BatchMerkleProof<H>,
) -> Result<(), MerkleTreeError> {
if *root != proof.get_root(indexes)? {
return Err(MerkleTreeError::InvalidProof);
}
Ok(())
}
}
// HELPER FUNCTIONS
// ================================================================================================
/// Returns the internal nodes of a Merkle tree defined by the specified leaves.
///
/// The internal nodes are turned as a vector where the root is stored at position 1, its children
/// are stored at positions 2, 3, their children are stored at positions 4, 5, 6, 7 etc.
///
/// This function is exposed primarily for benchmarking purposes. It is not intended to be used
/// directly by the end users of the crate.
pub fn build_merkle_nodes<H: Hasher>(leaves: &[H::Digest]) -> Vec<H::Digest> {
let n = leaves.len() / 2;
// create un-initialized array to hold all intermediate nodes
let mut nodes = unsafe { utils::uninit_vector::<H::Digest>(2 * n) };
nodes[0] = H::Digest::default();
// re-interpret leaves as an array of two leaves fused together
let two_leaves = unsafe { slice::from_raw_parts(leaves.as_ptr() as *const [H::Digest; 2], n) };
// build first row of internal nodes (parents of leaves)
for (i, j) in (0..n).zip(n..nodes.len()) {
nodes[j] = H::merge(&two_leaves[i]);
}
// re-interpret nodes as an array of two nodes fused together
let two_nodes = unsafe { slice::from_raw_parts(nodes.as_ptr() as *const [H::Digest; 2], n) };
// calculate all other tree nodes
for i in (1..n).rev() {
nodes[i] = H::merge(&two_nodes[i]);
}
nodes
}
fn map_indexes(
indexes: &[usize],
tree_depth: usize,
) -> Result<BTreeMap<usize, usize>, MerkleTreeError> {
let num_leaves = 2usize.pow(tree_depth as u32);
let mut map = BTreeMap::new();
for (i, index) in indexes.iter().cloned().enumerate() {
map.insert(index, i);
if index >= num_leaves {
return Err(MerkleTreeError::LeafIndexOutOfBounds(num_leaves, index));
}
}
if indexes.len() != map.len() {
return Err(MerkleTreeError::DuplicateLeafIndex);
}
Ok(map)
}
fn normalize_indexes(indexes: &[usize]) -> Vec<usize> {
let mut set = BTreeSet::new();
for &index in indexes {
set.insert(index - (index & 1));
}
set.into_iter().collect()
}