Criptografia com Curvas El\'ipticas

TL;DR

This paper provides an overview of elliptic curve cryptography, emphasizing its security based on the hard discrete logarithm problem and comparing it to traditional cryptosystems like RSA and Diffie-Hellman.

Contribution

It offers a comprehensive overview of elliptic curve cryptography and discusses its advantages over classical cryptosystems in terms of security.

Findings

Elliptic curve cryptography relies on a harder discrete logarithm problem.

ECC offers comparable security with smaller key sizes.

The paper discusses ECC schemes and their security benefits.

Abstract

This paper presents an overview of the use of elliptic curves in cryptography. The security of this cryptosystem is based on the discrete logarithm problem, which appears to be much harder compared to the discrete logarithm problem in other cryptosystems. An overview of common cryptosystems is given, such as Diffie-Hellman and RSA, and an elliptic curve cryptography scheme is discussed. -------- Este trabalho apresenta o uso das curvas el\'ipticas em criptografia. Sua seguran\c{c}a est\'a baseada no problema do logaritmo discreto. Este problema aparentemente \'e significativamente mais dif\'icil de resolver, comparado com o problema do logaritmo discreto usado por outros sistemas de criptografia. \'E dada uma vis\~ao geral de sistemas de criptografia comuns, como Diffie-Hellman e RSA, e discute-se um esquema de criptografia usando curvas el\'ipticas.