The power-generalized k-Horadam sequences in different modules and a new cryptographic method with these sequences

Çelemoğlu Ç., Nalli A.

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, cilt.16, sa.5, 2024 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 5
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s1793830923500556
  • Dergi Adı: DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: ElGamal cryptosystem, Fibonacci sequence, integer-valued polynomial module, symmetric cryptography, the power-generalized k-Horadam sequence
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.