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.

翻译：本研究聚焦于针对基于整数分解问题与离散对数问题的密码方案的量子密码分析方法。我们展示了如何通过改进一种结合量子与经典计算的方法，在实际中解决最大规模的因数分解问题实例，前提是使用当前公开可用的最优特殊类型量子计算机：量子退火器。我们通过解决迄今公开宣布的、利用量子退火解决的最大规模因数分解问题实例（规模为29位），获得了新的计算实验结果。改进方法的核心思想是利用已知的亚指数级经典方法将问题分解为多个更小的计算任务，并在量子计算机上执行其中最关键的步骤。该方法虽未降低问题的复杂度类别，但评估了攻击者的实际能力。这也标志着混合方法发展向前迈进了一步，这类方法在实践中可能比纯量子计算更早地在效率上超越经典方法。