The Beta Cryptosystem

This paper, we introduce mainly the concept of beta cryptosystem, whose security is based on generalized discrete logarithm problem and integer factorization problem in the multiplicative group of finite fields. We show that the proposed public key cryptosystem based on generalized discrete logarithm problem and integer factorization problem, provides more security because of double computation comparing with the generalized discrete logarithm problem and integer factorization problem. Hence the adversary has to solve distinct discrete logarithm problems and integer factorization problem simultaneously in the multiplicative group of finite fields 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.