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New encryption scheme using k-Fibonacci-like sequence

Saida Lagheliel

Ecole Normale Superieure, Bachir El Ibrahim, Kouba, Algriers, Algeria

E-mail Address: s.lagheliel@hotmail.fr

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Abdelhakim Chillali

https://orcid.org/0000-0002-2033-0280

Sidi Mohamed Ben Abdellah University, FP, LSI, Taza, Morocco

E-mail Address: abdelhakim.chillali@usmba.ac.ma

Corresponding author.

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, and

Ahmed Ait Mokhtar

Ecole Normale Superieure, Bachir El Ibrahim, Kouba, Algriers, Algeria

E-mail Address: ahmed.aitmokhtar@yahoo.fr

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https://doi.org/10.1142/S1793557122500371Cited by:2 (Source: Crossref)

Abstract

In this paper, we present a new encryption scheme using generalization k-Fibonacci-like sequence, we code the points of an elliptic curve with the terms of a sequence of k-Fibonacci-like using of Fibonacci sequence and we call it as k-Fibonacci like sequence ${V_{k, n}}$ ${V_{k, n}}$ defined by the recurrence relation:

V_{k, n + 1} = k V_{k, n} + V_{k, n - 1}; n \geq 1, V_{k, 0} = 2 m (k + 1), V_{k, 1} = p k + k (k + 1) m (1)

and we present some relation among k-Fibonacci like sequence, k-Fibonacci sequence and k-Lucas sequence. After that, we give application of elliptic curves in cryptography using k-Fibonacci like sequence.

Communicated by A. Chillali

Keywords:

AMSC: 11Yxx, 11T71, 11Txx

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