Restructuring of Discrete Logarithm Problem and Elgamal Cryptosystem By Using the Power Fibonacci Sequence Module M

Abstract

In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence module m . To do this, we have restructured generalized discrete logarithm problem which is one of mathematical difficult problems and generalized ElGamal cryptosystem which is based on this problem by using power Fibonacci sequence module m. Then by means of these sequences, we have made a new and different application of generalized ElGamal cryptosystem by using composite modules. Lastly, we have compared that ElGamal Cryptosystem and a new application of generalized ElGamal cryptosystem which we made in terms of cryptography and we have obtained that the application of generalized ElGamal cryptosystem we restructured by using power Fibonacci sequence module m is more advantageous than ElGamal cryptosystem for m is selected most appropriately large.