Attacking ElGamal based cryptographic algorithms using Pollard´s rho algorithm

Summary form only given. In 1985 a powerful and practical public-key scheme was produced by ElGamal; his work was applied using large prime integers. El-Kassar et al. and El-Kassar and Haraty modified the ElGamal 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 finite fields, F[x], by extending the arithmetic needed for the modifications to these domains. In this work we implement the classical and modified ElGamal cryptosystem to compare and to test their functionality, reliability and security. To test the security of the algorithms we use a famous attack algorithm called Pollard´s rho algorithm that works in the domain of natural integers. We enhance the Pollard´s rho algorithm to work with the modified ElGamal cryptosystems.