NOVEL CRYPTOGRAPHY METHOD BASED ON ELLIPTIC CURVE USING LIE ALGEBRAS

Abstract

This paper explores a novel approach to elliptic curve cryptography by leveraging Lie algebras, a branch of mathematics that provides powerful tools for studying symmetries in geometric objects we begin by introducing the fundamental concepts of elliptic curves and Lie algebras, highlighting their relevance in contemporary cryptographic systems. Subsequently, we delve into the intricate connections between elliptic curves and Lie algebras, elucidating how Lie algebras offer a unique framework for understanding the underlying structures of elliptic curves. Our paper presents a comprehensive analysis of how Lie algebras can be effectively utilized to enhance various aspects of elliptic curve cryptography, including key generation, encryption, and decryption processes. We explore the advantages of employing Lie algebras, such as increased computational efficiency and resistance against emerging cryptographic attacks. Furthermore, we discuss practical implementations and provide insights into the feasibility of integrating Lie algebras techniques into existing elliptic curve cryptographic systems. We also discuss potential avenues for future research and development in this promising area of cryptographic study. Through theoretical analysis and practical considerations, this paper underscores the potential of Lie algebras as a valuable tool for advancing elliptic curve cryptography, offering new perspectives and avenues for enhancing the security and efficiency o cryptographic systems in the digital age.