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 restructed Discreate Logarithm Problem which is one of mathematical difficult problems by using power Fibonacci sequence module m and by means of this sequences, we have made the mathematical difficult problem which is used only in prime modules is also useful for composite modules. Then we have constructed cryptographic system based on this more difficult problem which we have rearranged. Hence, we have obtained a new cryptosystem as ElGamal Cryptosystem. Lastly, we have compared that ElGamal Cryptosystem and a new cryptosystem which we constitute in terms of cryptography and we have obtained that a new cryptosystem is more advantageuos than ElGamal Cryptosystem.