Work done for Nillion web3 network March 2024

Chaum-Pedersen Zero Knowledge Proof

This program is an implementation of the Chaum-Pedersen ZKP protocol that allows the registration of a user client in a server without exposing the secret / password

Features

The code currently supports:

• Integer cyclic group activated by default or with the --scalar command line option.
• Elliptic curve secp256k1 cyclic group activated with the --elliptic curve command line option.
• Support for very large integers by using the num-bigint Rust crate.
• Docker containerization.

Default parameters

For the integer and elliptic curve cyclic groups the known parameters of the algorithm are hardcoded.

1. Scalar or integer cyclic groups:

p = 10009
q = 5004
g = 3
h = 2892 (g^13 mod p)

Note that these numbers are very small. They shouldn't be use in production.

2. An elliptic curve cyclic group based on the secp256k1 curve

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
q = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
g = (
    x:0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,
    y:0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
    )
h = 13 * g

An adapted src/secp256k1.rs library is included in the code.

Note that the constant 13 for computing h was arbitrary selected. From what [1] states g and h should be of prime order q:

g ^ q mod p = 1
h ^ q mod p = 1

Dependencies

• rustc (compiler) and rustup (package manager)
• cmake for the gRPC library
• docker and docker-compose if you are going to run in a docker container

If you have all the dependencies installed, then run from the main directory the following command:

$ cargo build --release

Note that this should generate on the ./src folder a file called zpk_auth.rs. This file is the interface generated with tonic from the ./proto/zkp_auth.proto Protobuf file. This file specifies the communication protocol between server and client.

Then, test that everything works fine by executing:

$ cargo test

Run locally

open 2 separate terminals, one for running the server and the other for the client since both produce useful outputs for debugging and understanding what happens.

Execute the server:

$ cargo run --bin server -- [--scalar(default)|--elliptic]

The server listens all the time for any message of any client and communicates using the gRPC protocol.

Execute the client:

$ cargo run --bin client -- [--scalar(default)|--elliptic]

Note that both, the server and the client, should use the same cyclic group, i.e, both using the integer (--scalar) fields, or both using the elliptic curves field (--elliptic).

Run with Docker

You will need to have docker and docker-compose. Open two terminals and in one build the docker image and run the server:

On the other terminal, connect to the running docker container and run the client:

The client connects to the server and then runs a for-loop that:

1. Ask for a username.
2. Ask if you want to send the solved challenge verification.
3. Logs and shows if the login was successful or not.

References

1. Bitcoin Rust