A Zero-Knowledge Proof of Knowledge for Subgroup Distance Problem

TL;DR

This paper presents a new zero-knowledge identification protocol based on the subgroup distance problem, leveraging cryptographic tools to ensure security and privacy in proof systems.

Contribution

It introduces the SDZKP protocol, the first to use subgroup distance problem in a zero-knowledge setting with novel security mechanisms.

Findings

Protocol achieves zero-knowledge property.

Security relies on hardness of subgroup distance problem.

Efficient implementation with cryptographic primitives.

Abstract

In this study, we introduce a novel zero-knowledge identification scheme based on the hardness of the subgroup distance problem in the Hamming metric. The proposed protocol, named Subgroup Distance Zero Knowledge Proof (SDZKP), employs a cryptographically secure pseudorandom number generator to mask secrets and utilizes a Stern-type algorithm to ensure robust security properties.