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    The power-generalized k-Horadam sequences in different modules and a new cryptographic method with these sequences
    (World Scientific Publ Co Pte Ltd, 2024) Celemoglu, Cagla; Nalli, Ayse
    In this study, unlike other power sequences, we define new ones in the integer and integer-valued polynomial module. We call these sequences the power-generalized k-Horadam sequence in the integer module and the power-generalized k-Horadam sequence in the integer-valued polynomial module. Using these sequences, we rebuild the ElGamal cryptosystem and then obtain a new cryptographic method by combining this and symmetric systems. We provide an encryption example where our method is applied. Finally, we see the advantages of the new cryptographic method when we compare the obtained new cryptographic method with some of the asymmetric cryptographic systems such as RSA and ElGamal. And we achieve that new cryptographic method that has more advantageous.
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    RESTRUCTURING OF DISCRETE LOGARITHM PROBLEM AND ELGAMAL CRYPTOSYSTEM BY USING THE POWER FIBONACCI SEQUENCE MODULE M
    (Editura Bibliotheca-Bibliotheca Publ House, 2019) Ozyilmaz, Cagla; Nalli, Ayse
    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.
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    The third order variations on the Fibonacci universal code
    (Academic Press Inc Elsevier Science, 2015) Nalli, Ayse; Ozyilmaz, Cagla
    Text. In this paper, we have studied the third order variations on the Fibonacci universal code and we have displayed tables GH(a)((3)) (n) we have defined for -20 <= a <= -2 and 1 <= n <= 100. Also, we have compared with the third order variations on the Fibonacci universal code and the second order variations on the Fibonacci universal code [2] in terms of cryptography and we have found that the third order variations on the Fibonacci universal code are more advantageous than the second order variations on the Fibonacci universal code. (C) 2014 Elsevier Inc. All rights reserved.