Introduction

Zero-knowledge proof (ZKP) systems help principals to verify the veracity of a piece of information without sharing the data. They are widely used to preserve confidentiality and ownership of data. ZKP can be seen as a reusable building block for making the future internet trustworthy and secure. In this project (0KNOW) we aimed to develop a lightweight group-theoretic zero-knowledge proof system that can be employed as a cryptographic primitive in many security protocols such as identification, authentication, or credential ownership.

In 0KNOW, we have studied NP group-theoretic problems and selected the search version of the subgroup distance problem within the Hamming metric. Breifly, for given distance $k$, given element $g$, given subgroup H from the symmeric group of degree $n$ ($S_n$), problem asks to find an element h from the subgroup H which is at most $k$ distance from $g$. Our choice as platform subgroup is an elementary abelian subgroup. We have designed a novel black-box 3-round statistical zero knowledge proof of knowledge protocol called the Subgroup Distance Zero Knowledge Proof (SDZKP). It can be seen as a Stern-type protocol. It has 3-special-soundness property which assures knowledge soundness with error $\frac{2}{3}$.

All in all, we present a new zero-knowledge identification scheme rooted in the complexity of the subgroup distance problem within the Hamming metric. SDZKP incorporates a cryptographically secure pseudorandom number generator to obscure secrets and employs a Stern-type algorithm to ensure strong security features.

Articles

• Cansu Betin Onur, ``Intractable Group-theoretic Problems Around Zero-knowledge Proofs,'' arXiv:2206.13350 [cs.CR] [@onur2023intractablegrouptheoreticproblemszeroknowledge]
• Cansu Betin Onur, ``A Zero-Knowledge Proof of Knowledge for Subgroup Distance Problem,'' arXiv:2408.00395 [cs.CR] [@onur2024zeroknowledgeproofknowledgesubgroup]

Acknowledgement

This work is partially supported by the NLnet foundation under the MoU number 2021-12-510.

Installation

We present the details for installing SDZKP using pypi package or using the source code.

Installation (Package)

Create a project folder, in that folder preferably create a virtual environment:

python3 -m venv venv

source venv/bin/activate

Prerequisites

SDZKP is an interactive zero-knowledge protocols and we use gRPC.

pip install grpcio

pip install protobuf

You can easily install the required packages by pip install -r requirements.txt.

SDZKP package

Install the latest SDZKP package

pip install sdzkp

You can then copy sdzkp_verifier.py and sdzkp_prover.py from GitHub and run them in two terminals (do not forget to source venv/bin/activate in both terminals).

Installation (from source)

To install sdzkp from source, checkout the latest version from GitHub by

git clone https://github.com/cansubetin/sdzkp
cd sdzkp
pip install -e .

If you change the gRPC proto definitions, sdzkp/api/sdzkp.proto then under root project folder, run

pip install grpcio-tools
./compile_api.sh