Enhancing NTRUEncrypt Security Using Markov Chain Monte Carlo Methods: Theory and Practice

TL;DR

This paper introduces a new approach using Markov Chain Monte Carlo methods to enhance the quantum resistance and security of NTRUEncrypt, combining theoretical analysis with practical validation.

Contribution

It develops a novel framework that improves NTRUEncrypt's security against quantum attacks by integrating MCMC techniques with formal security bounds and practical experiments.

Findings

Enhanced security guarantees demonstrated through numerical experiments

Established bounds on sampling efficiency for high-dimensional lattices

Linked MCMC parameters to lattice hardness assumptions

Abstract

This paper presents a novel framework for enhancing the quantum resistance of NTRUEncrypt using Markov Chain Monte Carlo (MCMC) methods. We establish formal bounds on sampling efficiency and provide security reductions to lattice problems, bridging theoretical guarantees with practical implementations. Key contributions include: a new methodology for exploring private key vulnerabilities while maintaining quantum resistance, provable mixing time bounds for high-dimensional lattices, and concrete metrics linking MCMC parameters to lattice hardness assumptions. Numerical experiments validate our approach, demonstrating improved security guarantees and computational efficiency. These findings advance the theoretical understanding and practical adoption of NTRU- Encrypt in the post-quantum era.