一个数据膨胀率为1的概率公钥密码系统

A Probabilistic Public Key Cryptosystem with a Message Expansion of 1

在RSA公钥密码的基础上,采用时间戳和hash函数技术,并利用以Blum数为模的二次同余式中求平方根的不可计算性,设计了一个概率公钥密码系统,此密码系统的密码强度不低于RSA的密码强度和求以Blum数为模的二次同余式平方根的难度,加、解密的时间复杂度为O(k3),其中k为模数的长度,密码的数据膨胀率等于1,因此在数据膨胀率上,此概率公钥密码系统是最优的。

Based on the RSA public key cryptosystem, a probabilistic public key cryptosystem is proposed, using the techniques of time stamp and hash function. The new scheme makes use of the intractability of solving the square roots in quadratic congruence equation with a Blum integer modulus, whose cipher intensity is no lower than that of RSA scheme and of the difficulty of solving the square root in quadratic congruence equation. In our scheme encoding and de coding requires O（k^3） operation, where k is the length of modulus. And the message expansion is 1, so the scheme is optimal in the message expansion.