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.