Elliptic Curve Cryptography

Abstract

This master memory studies Elliptic Curve Cryptography (ECC) as one of the most important modern public-key cryptographic systems, due to its high level of security and computational efficiency compared to the RSA algorithm. The work begins with an introduction to the fundamental algebraic concepts used in cryptography, such as groups, cyclic groups and finite fields. It also discusses the Discrete Logarithm Problem (DLP) and its essential role in securing cryptographic systems. The study focuses on both the theoretical and practical aspects of ECC through the presentation of its main protocols, including ECDLP, ECDH, and ECDSA, together with the associated operations and algorithms. This work highlights the importance of ECC in achieving information security with high efficiency using relatively small key sizes.