Applications of Quantum Annealing in Cryptography

TL;DR

This paper introduces a novel method for reducing pseudo-Boolean function optimization to QUBO problems suitable for quantum annealers, improving coefficient and variable optimization, and demonstrates its application in integer factorization and cryptographic attacks.

Contribution

The paper proposes a new reduction method to QUBO problems with optimized coefficients and variables, enhancing quantum annealing applications in cryptography.

Findings

Achieved the largest integer factorization (4137131) with 93 variables.

Reduced coefficient range to [-1024,1024], smaller than previous results.

Presented an efficient method for quantum attacks on block ciphers.

Abstract

This paper presents a new method to reduce the optimization of a pseudo-Boolean function to QUBO problem which can be solved by quantum annealer. The new method has two aspects, one is coefficient optimization and the other is variable optimization. The former is an improvement on the existing algorithm in a special case. The latter is realized by means of the maximal independent point set in graph theory. We apply this new method in integer factorization on quantum annealers and achieve the largest integer factorization (4137131) with 93 variables, the range of coefficients is [-1024,1024] which is much smaller than the previous results. We also focus on the quantum attacks on block ciphers and present an efficient method with smaller coefficients to transform Boolean equation systems into QUBO problems.