RSA public key decomposition and decryption method and system

Abstract

The invention discloses an RSA public key decomposition and decryption method and system, wherein the RSA public key decomposition method comprises the following steps: (1) acquiring an RSA public keyn; (2) acquiring a prime factor pair (p, q) less than or equal to n / 3, forming a corresponding two-dimensional Hermitian matrix according to the prime factor pair (p, q) and the public key n, meanwhile controlling an external electromagnetic field of a quantum system, so that the Hamiltonian of the quantum system is the two-dimensional Hermitian matrix, measuring an energy spectrum of the quantumsystem to check whether an eigenvalue of the two-dimensional Hermitian matrix is at x=0, if not, judging other prime factor pairs (p, q), and if yes, judging the prime factor pair (p, q) as two primefactor obtained by decomposing the RSA public key n, and performing output. According to the RSA public key decomposition and decryption method and system disclosed by the invention, the calculationtime is short, a small number of storage bits are required, the algorithm efficiency is high, and the stability is good.

Description

technical field [0001] The invention relates to the field of information security, in particular to an RSA public key decomposition method and system, and a decryption method and system based on RSA public key decomposition. Background technique [0002] The RSA public key encryption system is an important infrastructure for information security in the modern information society. The system was proposed by Ron Rivest, Adi Shamir and Leonard Adleman in 1978 [1]. It is an asymmetric key encryption system. As shown in Table 1, the basic principle is to randomly select two large prime numbers p, q, and calculate n=pq. Then choose a small odd number e that is coprime with (p-1)(q-1), and use (e, n) as the public key subject to release to the outside world. At the same time, the inverse element d of e is calculated in the (p-1)(q-1) multiplication group, and (d, n) is kept privately as the private key subject. The pair of keys can perform two-way encryption and decryption. Un...

AI Technical Summary

Problems solved by technology

[0007] Purpose of the invention: The present invention aims at the problems of too many qubit numbers and too high requirements for quantum control precision existing in the quantum algorithm of RSA public key prime factorization in the prior art, and provides a method and system for RSA public key decomposition and based on The decryption method and system of RSA public key decomposition, which is based on a single qubit system, by diagonalizing the public key N to be decomposed into a two-dimensional Hermitian matrix, monitoring the energy spectrum of the quantum system, and solving the 0 eigenvalue of the diagonal matrix, etc. Technical means to complete the prime factorization of the public key N

Images