Exponential Simplification Using Euler's and Fermat's Theorem

Abstract

In the current scenario, there is a tremendous necessity for strong cryptographic techniques for securely transmitting and storing data or information. The wide requirement of security in various areas develop the interest in doing research for producing variety of cryptographic algorithms which can provide security at various level. The algorithms can be implemented either in software or in hardware. The idea for secure algorithms evolved in the mid of 1970's. One of the most robust and secure asymmetric algorithm was proposed by Rivest, Shamir and Adelmann (RSA) in 1977 and proved to become a defacto standard, in cooperated with a large basis of products and applications that are still in operation. There are lots of work has been done in analysing the algorithm. Modular exponentiation is the basic operation for RSA. It consumes lots of time and resources for large values. To speed up the computation a naive approach is used in the exponential calculation in RSA by utilizing the Euler's and Fermat's Theorem . The method can be used in all scenarios where modular exponentiation plays a role.