New encryption scheme using k-Fibonacci-like sequence

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 [Formula: see text] defined by the recurrence relation: [Formula: see text] 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.

Generalized Fibonacci Sequences for Elliptic Curve Cryptography

“…The theoretical properties of numbers obtained from homogeneous linear repetition relations relevant to our research context have been extensively studied by various authors, see, for example, refs. [12][13][14][15][16][17][18][19][20][21][22]. Their work has shed light on key aspects of this topic and provided valuable insights into the properties of Fibonacci-type sequences on elliptic curves.…”