ZK Incremental Merkle Tree (zk-IMT)

Introduction

Incremental Merkle Tree

Incremental Merkle Tree (IMT) is a specialized form of a Merkle tree designed to allow for efficient appending of new elements, making it useful in applications where the dataset is expected to grow over time and updates need to be processed efficiently.

What is zk-IMT?

zk-IMT is a zero-knowledge proof system for Incremental Merkle Trees. It allows a prover to prove tree membership and non-membership of a leaf in an IMT without revealing the leaf itself. The prover can also prove the consistency of two IMTs without revealing the entire tree.

What is MiMC5 Sponge?

MiMC5 is a family of hash functions that are based on the MiMC construction. It is a sponge-based hash function that is used to hash the inputs in zk-IMT.

MiMC is more suitable than SHA256 or Keccak for zk-SNARKs because it has low multiplicative complexity and is more efficient to implement in zk-SNARKs.

Working

Generate Commitment Hash

Generate a random nullifier ($n_i$) and secret ($s_i$).
Calculate the hash of them (commitment, $c_i = hash(n_i, s_i)$ ).

Insert Commitment to the Tree

Insert the commitment ($c_i$) to the tree as leaf (onchain).
After every the path from leaf to root is updated.

Prove that Commitment ($c_i$) is in the Tree

For a commitment ($c_2$) at index, $i=2$, the path $p_2 = [p_{2,0}, p_{2,1}, p_{2,2}]$

Generate $h_2 = H(H(p_{2,1},H(c_2, p_{2,0})),p_{2,2})$
Check if $h_2 = root$. If equal then $c_i$ is in the tree.

Prove Membership using zk-SNARK

Now to prove that $c_2$ is in the tree without revealing $c_2$ itself, we will use zk-SNARK.

Nullifier ($n_2$) and Secret ($s_2$) will be used to generate Groth16 proof.
Nullifier ($n_2$) is used as public parameter to prevent reusing the same commitment in the future.
Secret ($s_2$) is kept secret (private input) for anonymity.

Generate a proof such that that $h_2 = root$ where

leaf $\rightarrow n_2$
path $\rightarrow [s_2, p_{2,0}, p_{2,1}, p_{2,2}]$
$h_2 = H(H(p_{2,1},H(H(n_2, s_2), p_{2,0})),p_{2,2})$

Requirements

This project was developed and tested with the following software versions:

Python: 3.11.7
Node.js: 20.10.0
Circom Compiler: 2.1.8

Setup

Create a virtual environment

python3 -m venv env
source env/bin/activate

Install dependencies

pip install -r requirements.txt

Install SnarkJS

npm install -g snarkjs@latest

Usage

We will use ZK Incremental Merkle Tree using app.py script to perform local and onchain operations.

Insert New Commitment to the tree

It will generate random nullifier and secret and insert the hash of the both (commitment) to the tree (onchain).

python app.py --task insert

Prove Membership using zk-SNARK (local & onchain)

It will fetch the path of a leaf given it's index and generate a proof for the leaf's membership in the tree. The proof will be verified onchain for tree membership without revealing for which leaf the proof was generated.

python app.py --task zk-verify

sudiptab2100 / ZKIncrementalMerkleTree