Research On RSA And Elliptic Curve Cryptographic Algorithms

Before the history of appearing Public-key cryptography, all the encryption and decryption algorithms including the original manual calculations, implemented by mechanical equipment or computer, they are based on these two basic tools: replacement and substitution. Public key cryptography has provided a new theoretical and technical basis for the development of cryptography. On the one hand, the basic tools of Public key algorithm translate into mathematical function;on the other hand,the public key algorithm use two keys in asymmetric form,which has profound significance for confidentiality, key distribution, authentication ,and so on.As one of the public key algorithm, RSA algorithm is applied most widely. This article provides a brief description of RSA public key cryptography, an analysis and compare of all kinds of present existed modular exponentiation in RSA public key cryptography, a colligation of the fastest accelerating software algorithm-VLNW sliding window methods and hardware mapping fast Montgomery modular multiplication algorithm that can improve the implementary efficiency of RSA public key cryptography for achieving the novel algorithm-Mnexp algorithm.ECC is considered to be an alternative to RSA. This article provides a brief description of RSA public key cryptography and the associated knowledge, in particular introduces non-supersingular elliptic curves E which is established on the finite field Fp with p > 3, in-depth studies present existed scalar multiplication, further proposes an improved signed sliding window algorithm on ECC under the mixed coordinates, The improved algorithm compatible the advantage of the NAF, has the least number of zero window and avoid a large number of inverse operation, successfully reduce scalar multiplication calculation. Finally, I summarize and draw some useful conclusions.The main place of innovation of this paper is to grasp the advantage of different algorithms, from different angles and levels improve modular exponentiation algorithm and scalar multiplication algorithm, and achieve new algorithm which can provide reference to the implementation of RSA and ECC,meantime the new algorithm have greater practical value.