Criptografia: aplicações de teoria dos números e álgebra.

Abstract

In this work we will discuss about two types of asymmetric cryptographic systems: RSA cryptography and elliptic curve based cryptography. Initially, we will present some historical aspects that deeply marked the development of cryptography, we will address the main characteristics of the existing types of cryptography (symmetric and asymmetric) and then, we will present the main mathematical tools, indispensable to the development and understanding of the aforementioned cryptographic systems. In addition, we will describe the details of how these cryptosystems work and understand why they are considered secure. Finally, we'll make a brief comparison between them.