Domain-Informed Representation for Evolutionary Sieving in Integral and Module Lattices

2026-05-27

AI Summary

This work addresses the threat posed by quantum computing to classical cryptographic schemes based on integer factorization and discrete logarithms by advancing the efficiency of solving the Shortest Vector Problem (SVP), a cornerstone of lattice-based post-quantum cryptography. We propose a novel approach that integrates domain-specific knowledge into a genetic algorithm, introducing a lattice-structure-aware encoding for SVP instances and a knowledge-guided crossover operator. This framework naturally extends to modular lattices, enabling a unified and efficient solution strategy for SVP in both integer and modular lattices. Our method significantly outperforms Laarhoven’s lattice sieving algorithm, thereby establishing a stronger foundation for assessing the hardness assumptions underlying post-quantum cryptographic constructions.

Abstract

Traditional cryptography, rooted in problems, e.g., integer factorisation or discrete log, is inevitably vulnerable to a fully operational quantum computer. Although it remains an engineering frontier, the looming threat extends to encrypted data stored today, which could be decrypted in the future with quantum capabilities. To safeguard against this eventuality, the backbone of the modern quantum-safe cryptography is the Shortest Vector Problem (SVP). We enhance Laarhoven's treatment of Ajtai et al.'s sieving as a genetic algorithm (GA) for the SVP by incorporating domain-informed SVP representation and crossover while naturally extending application to the module lattices.

Problem

• Shortest Vector Problem
• quantum-safe cryptography
• evolutionary sieving
• module lattices
• lattice-based cryptography

Innovation

• domain-informed representation
• evolutionary sieving
• Shortest Vector Problem
• genetic algorithm
• module lattices