Generalized Fibonacci Sequences for Elliptic Curve Cryptography

Abstract

The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves. These sequences have a number of exciting properties and can be used to build new encryption systems. This paper presents a further generalization of the Fibonacci sequence defined on elliptic curves. We also describe an encryption system using this sequence which is based on the discrete logarithm problem on elliptic curves.

Keywords

• cryptosystem
• elliptic curve
• elliptic curve discrete logarithm problem
• Fibonacci sequence
• fully homomorphic encryption
• matrices