Enhancing NTRUEncrypt Security Using Markov Chain Monte Carlo Methods: Theory and Practice
Gautier Filardo, Thibaut Heckmann
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.
