Maximizing the practical achievability of quantum annealing attacks on factorization-based cryptography

TL;DR

This paper demonstrates how to practically solve large integer factorization problems using a hybrid quantum-classical approach with quantum annealing, highlighting potential real-world cryptanalysis capabilities.

Contribution

It introduces an improved hybrid method leveraging classical sub-exponential algorithms and quantum annealing to solve larger factorization instances than previously possible.

Findings

Solved the largest factorization instance (29 bits) using quantum annealing.

Showed hybrid quantum-classical approach can outperform classical methods in practice.

Assessed the pragmatic attack capabilities of quantum annealers on cryptographic schemes.

Abstract

This work focuses on quantum methods for cryptanalysis of schemes based on the integer factorization problem and the discrete logarithm problem. We demonstrate how to practically solve the largest instances of the factorization problem by improving an approach that combines quantum and classical computations, assuming the use of the best publicly available special-class quantum computer: the quantum annealer. We achieve new computational experiment results by solving the largest instance of the factorization problem ever announced as solved using quantum annealing, with a size of 29 bits. The core idea of the improved approach is to leverage known sub-exponential classical method to break the problem down into many smaller computations and perform the most critical ones on a quantum computer. This approach does not reduce the complexity class, but it assesses the pragmatic capabilities of an attacker. It also marks a step forward in the development of hybrid methods, which in practice may surpass classical methods in terms of efficiency sooner than purely quantum computations will.