dusk-merkle

A sparsely populated Merkle Tree, parametrized over its height and arity.

Height 0             h
                    / \
                   /   \
                  /     \
                 /       \
                /         \
Height 1       h           h
              / \         / \
             /   \       /   \
Height 2    h     x     h     h
           / \         / \   / \
Height 3  h   x       x   h h   h
Position  0               5 6   7

The Aggregate trait defines how to calculate a parent from its children. There is no restrictions on the way the children are aggregated, it can be done with a hash function or any other custom aggregation. Empty subtrees (noted as x in the tree above) are filled with the constant EMPTY_SUBTREE from Aggregate.

Here an example where the parent is the sum of its children:

Usage

use dusk_merkle::{Tree, Aggregate};

#[derive(Debug, Clone, Copy, PartialEq)]
struct U8(u8);

impl From<u8> for U8 {
    fn from(n: u8) -> Self {
        Self(n)
    }
}

const EMPTY_ITEM: U8 = U8(0);

impl Aggregate<A> for U8 {
    const EMPTY_SUBTREE: U8 = EMPTY_ITEM;

    fn aggregate(items: [&Self; A]) -> Self
    {
        items.into_iter().fold(U8(0), |acc, c| U8(acc.0 + c.0))
    }
}

// Set the height and arity of the tree. 
const H: usize = 3;
const A: usize = 2;

let mut tree = Tree::<U8, H, A>::new();

// No elements have been inserted so the root is the empty subtree.
assert_eq!(*tree.root(), U8::EMPTY_SUBTREE);

tree.insert(4, 21);
tree.insert(7, 21);

// After elements have been inserted, the root will be modified.
assert_eq!(*tree.root(), U8(42));

An implementation of a Merkle tree using the blake3 hash algorithm is included as an example.

Another implementation of a Merkle tree with the poseidon252 hash and the creation of the opening proof in zero-knowledge using PLONK is included as a member of this workspace poseidon_merkle.

Benchmarks

Benchmarks are also included and can be run using:

For the blake3 tree:

cargo bench

For the poseidon tree:

cargo bench -p poseidon-merkle

For the opening proof creation in zero-knowledge:

cargo bench -p poseidon-merkle --features zk

This requires a nightly toolchain.

Implementations

A merkle tree using the poseidon hash function for aggregation and plonk to generate an opening proof in zero-knowledge can be found in the same workspace under 'poseidon-merkle'.

License

This project is licensed under the Mozilla Public License, version 2.0. See the license file for more details.