A Reduced RSA Public Key Cryptography Algorithm

Under push of computer technology and communication technology, information has become the decisive force of human society, which dominates the development process of human society. Information technology is used in bank on internet, electronic commerce, electronic government and so on. Modern information technology is a sword with two blades. It brings great convenience to people's life and production, but at the same time, it has many advantages for some hackers, thus it brings some threats into our life. Information security has become a global problem, strengthening our planning for information security stared us in the face.In 1978, Rivest, Shamir and Adleman proposed the first practical RSA public-key cryptosystem. Even today, RSA is still the most understandable and widely used encryption method, whose security based on the great integer factorization problem. As the computer hardware and calculation methods are improved greatly, the required keys length of RSA public-key cryptography is getting longer and longer, which leads to the necessary cost higher and higher. In this connection, on the basis of the in-depth research of RSA code system, we construct a new RSA algorithm to which the idea of k-th residue theorem and RSA algorithm are combined, named a reduced RSA public-key cryptography algorithm. The new algorithm reduced the value of parameters.This paper gives detailed explanation and analysis of the reduced RSA algorithm and its implementation principle, and performances and functions are compared with RSA. It has higher safety. Its security is based on the double difficulties of the discrete logarithm in finite fields and the great integer factorization problem. Its expression is simple. The new algorithm not only has great flexibility of parameters and stronger confidential, but also effectively solved the storage problem by adding computing cost. The most important is it has multiple functions and resolves the problem of the management and distribution of key. It is particularly useful for modern confidential communication.In the end of this paper, we point out some disadvantages of the new algorithm. In order to make further perfection and enhance practicability, we make a description for further improvement.