A Cryptosystem Based on DLP gamma = alphaabetab mod p

This paper introduces mainly the concept of the Public Key Cryptosystem or PKC, whose security is based on the new Discrete Logarithm Problem known as DLP-III and DLP-IV with the two distinct exponentiations, i.e. γ ≡ αβ mod p in the multiplicative group of the finite field Z∗ p of the order p − 1. We show that the proposed Public Key Cryptosystem based on DLP-IV provides more security because of double computation comparing with the well known the Discrete Logarithm Problem II or DLP-II with one exponentiation, i.e. β ≡ α mod p in the multiplicative group of the finite field Z∗ p of the order p− 1 at the same efficiency level.