A Cryptosystem based on Double Generalized Discrete Logarithm Problem

This paper introduces mainly the concept of public key cryptosystem, whose security is based on double generalized discrete logarithm problem with distinct discrete exponents in the multiplicative group of finite fields. We show that the proposed public key cryptosystem based on double generalized discrete logarithm problem, provides more security because of double computation comparing with the generalized discrete logarithm problem. Hence the adversary has to solve distinct discrete logarithm problems simultaneously in order to recover a corresponding plaintext from the received cipertext. Therefore, this scheme is expected to gain a higher level of security. We next show that, the newly developed scheme is efficient with respect to encryption and decryption and the validity of this algorithm is proven by applying to message that are text and returning the original message in numerical examples.