摘要
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.
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.
基金
Supported by the National Natural Science Foundation of China(61303212,61202386)
the State Key Program of National Natural Science of China(61332019)
the Major Research Plan of the National Natural Science Foundation of China(91018008,SKLSE-2015-A-02)
