Zero-Knowledge Proofs of the Conjugacy for Permutation Groups

TL;DR

This paper introduces a perfect zero-knowledge proof system to verify whether two permutation groups are conjugate, enhancing privacy-preserving verification methods in group theory.

Contribution

It presents the first zero-knowledge proof system specifically for the conjugacy problem in permutation groups, ensuring perfect privacy during verification.

Findings

Achieves perfect zero-knowledge property

Efficient verification process for conjugacy

Applicable to cryptographic protocols involving permutation groups

Abstract

We design a perfect zero-knowledge proof system for recognition if two permutation groups are conjugate.