Improving the success rate of quantum algorithm attacking RSA encryption system

Abstract

Shor’s factorization algorithm (SFA) aims at finding the non-trivial factor of a given composite number, but the algorithm does not always work. In some cases, it has to call back to the beginning of the algorithm to make recalculation. After the analysis of the principle of SFA and the characteristics of RSA public-key cryptography with a series of data calculations, it can be concluded that the random value selected by the algorithm is closely related to whether the obtained period is effective. Therefore, a new optimized scheme is proposed to tackle with this defect from two perspectives: (a) When the a value is a perfect square, the algorithm can be completed with an odd cycle r. (b) When the period r obtained by the randomly selected a value is a multiple of 3, the algorithm can be completed by modifying the decomposition method to relax the requirements for the period without affecting the complexity of the algorithm. Due to the limitations of hardware in applying the quantum algorithms, the classical algorithm is applied to simulate quantum algorithms to test the success rate of decomposition of some composite numbers. The result indicates the effectiveness of the improved algorithm, which significantly reduces the probability of repeated operations to save the quantum circuit resources.