A Zero-Knowledge Proof for the Syndrome Decoding Problem in the Lee Metric

TL;DR

This paper introduces a zero-knowledge proof for the Lee metric syndrome decoding problem, an NP-complete problem relevant to cryptography, enabling secure verification without revealing the solution.

Contribution

It presents the first zero-knowledge proof specifically designed for the Lee metric syndrome decoding problem, expanding cryptographic tools for this variant.

Findings

Proof is sound and zero-knowledge

Efficient verification process established

Potential for more secure cryptosystems

Abstract

The syndrome decoding problem is one of the NP-complete problems lying at the foundation of code-based cryptography. The variant thereof where the distance between vectors is measured with respect to the Lee metric, rather than the more commonly used Hamming metric, has been analyzed recently in several works due to its potential relevance for building more efficient code-based cryptosystems. The purpose of this article is to present a zero-knowledge proof of knowledge for this variant of the problem.