merkle

zokrates-merkle

Merkle tree membership proof circuit in ZoKrates. Proves that a value exists in a Poseidon-based Merkle tree (depth 3, 8 leaves) without revealing the value or its position.

Equivalent to the circom and Noir versions, using ZoKrates' stdlib Poseidon hash and the Groth16 proving system with the bellman backend (faster and more memory-efficient than the default arkworks backend).

Prerequisites

• ZoKrates ≥ 0.8.8 — curl -LSfs get.zokrat.es | sh then export PATH=$PATH:$HOME/.zokrates/bin
• Node.js ≥ 18 (for input generation and visualization scripts)

Setup

npm install

Commands

1. Compile the circuit

zokrates compile -i circuits/merkle.zok -o build/merkle

Outputs build/merkle (compiled circuit). 1072 constraints.

2. Generate test inputs

node scripts/generate_input.js [leafIndex]

Computes the Poseidon Merkle tree and prints the witness arguments needed for compute-witness. Default leaf index is 3 (value 42).

3. Compute witness

zokrates compute-witness -i build/merkle -o build/witness -a <args from step 2>

For the default (leaf 42 at index 3):

zokrates compute-witness -i build/merkle -o build/witness -a 42 3 30 18520321019059006606511285595387750999043784958310087972051959520693448686063 3420474571345144317592756791686222517137740774669488698617074013334764505433 14137441823196867098576785772577409116077936272054299522801628487819529363847

4. Trusted setup

zokrates setup -i build/merkle -b bellman -s g16 -p build/proving.key -v build/verification.key

5. Generate proof

zokrates generate-proof -i build/merkle -b bellman -s g16 -p build/proving.key -w build/witness -j build/proof.json

6. Verify proof

zokrates verify -v build/verification.key -j build/proof.json

Expected output: PASSED

7. Visualize the tree and proof path

node scripts/visualize_tree.js [leafIndex]

Prints an ASCII tree with color-coded proof path (green), sibling witnesses (yellow), and other nodes (dim). Default leaf index is 3 (value 42).

8. (Optional) Export Solidity verifier

zokrates export-verifier -i build/verification.key -o build/Verifier.sol

Circuit overview

Signal	Visibility	Description
leaf	private	The leaf value to prove membership of
index	private	Leaf position (u32, bit-decomposed for path selection)
siblings[3]	private	Sibling hashes along the authentication path
root	public	Expected Merkle root

The circuit decomposes index into bits, then walks up the tree hashing with poseidon([left, right]) at each level, selecting left/right based on the index bits. It asserts the computed root equals the provided root.

Comparison with circom and Noir versions

	Circom	Noir	ZoKrates
Hash function	Poseidon	Poseidon2	Poseidon
Proving system	Groth16 (snarkjs)	UltraHonk (Barretenberg)	Groth16 (built-in)
Leaf handling	Hashes value before insertion	Raw values as leaves	Raw values as leaves
Setup	Separate ceremony steps	No trusted setup	Single setup command
Constraints	951	N/A (gates)	1072