RSA public key algorithm and design of fast modular exponentiation operation
Qun Ding · Journal of Engineering of Heilongjiang University · 2013
RSA public-key cryptosystem is an asymmetric encryption system.Its security is based on factoring large numbers which is computationally infeasible and using trapdoor function to construct encryption and decryption rules,making communication established in a safe channel without previous exchange of key,so currently,RSA is the most widely used public cryptosystem.However,the speed and resources needed in large integer arithmetic computation become a major bottleneck in its application,especially modular exponentiation,whose computational complexity and redundancy greatly restrict the speed of RSA.So,this article,base on the research of the basic theory of the RSA cryptosystem,apply the famous square-multiplication algorithm,which can turn modular exponentiation into modular multiplication,making the computing process simple and quickly.Meanwhile,use Matlab simulation software to further study key algorithm in RSA cryptosystem,such as Euclidean and its extension theorem,prime number test and modular multiplication.The Matlab simulation results show that: the square-multiply algorithm is feasible,and other key algorithms have also been fully validated and laid the foundation for subsequent hardware implementation.