An Approach of Cryptosystem using Polynomials and Lucas Numbers

Abstract

This paper presents an innovative approach to a cryptosystem that utilizes polynomials and Lucas numbers. Lucas numbers, a sequence similar to Fibonacci numbers, offer unique properties that can be leveraged for encryption and decryption. The proposed Lucas Polynomial Cryptosystem outlines the key generation, encryption, and decryption processes, highlighting the security considerations and key management aspects. The system's strength relies on the difficulty of factoring large prime numbers and the challenge of deriving the secret key from the public key. This paper aims to provide a comprehensive understanding of the cryptosystem and explores its potential applications in secure communications and data protection. Extensive analysis and cryptanalysis have been conducted to evaluate the system's security and effectiveness, making it a promising addition to the cryptographic landscape.