The Power-Generalized K-Horadam Sequences in Different Modules and a New Cryptographic Method with These Sequences

Abstract

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.