A new quantum algorithm for computing RSA ciphertext period

Shor proposed a quantum polynomial-time integer factorization algorithm to break the RSA public-key cryptosystem. In this paper, we propose a new quantum algorithm for breaking RSA by computing the order of the RSA ciphertext C. The new algorithm has the following properties: 1) recovering the RSA plaintext M from the ciphertext C without factoring n; 2) avoiding the even order of the element; 3) having higher success probability than Shor’s; 4) having the same complexity as Shor’s.