Elliptic Curve Cryptography: Importance, Applications and Comparison with RSA algorithm

Abstract

The security of communications in public networks has become a fundamental pillar of the current digital context, where asymmetric cryptography plays a central role. Elliptic Curve Cryptography (ECC), independently proposed by Neal Koblitz and Victor Miller in 1985, constitutes a relevant alternative to classical schemes based on the factorization of integers, such as the RSA algorithm. Its security relies on the Elliptic Curve Discrete Logarithm Problem (ECDLP), which enables equivalent security levels with significantly smaller key sizes. This article analyzes, through a systematic review of recent literature, the importance, applications, and comparative performance of ECC against the RSA algorithm. The methodology consisted of a qualitative search in Scopus, IEEE Xplore, ScienceDirect, MDPI, and SpringerLink, limited to publications from the last five years. The results show that ECC has consolidated as the preferred asymmetric scheme in resource-constrained scenarios, particularly in IoT, TLS, blockchain, and digital signatures, where its main variants (P-256, secp256k1, Curve25519, and Ed25519) present demonstrated advantages in computational efficiency, memory consumption, and key size. It is concluded that ECC redefines the conditions of viability of contemporary asymmetric cryptography.