A Comparative Study of RSA based Cryptographic Algorithms

In 1978 a powerful and practical public-key scheme Hadi Otrokwas produced by RSA; there work was applied using 2 large random odd primes p and q, each roughly of the same size. El-Kassar and Awad modi...ed the RSA public-key encryption scheme from the domain of natural integers, Z , to two principal ideal domains, namely the domain of Gaussian integers, Z [i], and the domain of the rings of polynomials over ...nite ...elds, F [x], by extending the arithmetic needed for the modi...cations to these domains. In this work we implement the classical and modi...ed RSA cryptosystem to compare and to test their functionality, realiability and security. To test the security of the algorithms we implement an attack algorithm to solve the integer factorization problem. After factorization is found, the RSA problem could be solved by computing the order ©(n), and then ...nding the private key using the extended Euclidean algorithm for integers.