Enhancement on Implementation of Multi-Prime and Multi Power RSA Algorithm

Abstract

The RSA algorithm is the most widely known and used public-key cryptosystem in today’s scenario. It makes use of a pair of keys, namely the public key and the private key. It may be used for both secrecy and digital signatures and its security is based on the intractability of the integer factorization problem. RSA algorithm has an intricate connection with the number theory of mathematics. The Fermat’s theorem, Fundamental theorem, Euler’s theorem, Euler’s Totient function, Chinese Remainder theorem, etc. are used in RSA algorithm. RSA algorithm is a discipline of cryptography which is used for making the network secure. The intricacies of RSA and its characteristics like security issues, computational aspects make it the most sought after asymmetric key algorithm till date. In order to overcome the deficiencies in the original RSA many variants have been proposed which include RSA-CRT, rebalanced RSA, dual RSA, multi-prime RSA and multi-power RSA. This thesis presents an insight into the basics of cryptography and different types of cryptography. It describes RSA and explores its intricacies and its characteristics. It even illustrates in general the different variants of the RSA algorithm and presents various comparisons among them on the basis of complexity and security. It also describes the shortcomings in implementation like the flaws in security and functionality which have occurred in the RSA algorithms implemented so far. It portrays that much work can be done on RSA. In particular, the work discussed in this thesis is about the implementation of multi-prime and multi-power RSA on 2048-bits. Keywords: Multi-Prime RSA, Multi-Power RSA, Implementation of RSA algorithm on 2048-bit.