Atac quàntic a la criptografia amb corbes el·líptiques

Abstract

[en] Generally, the majority of classical cryptography methods that use elliptical curves are based on the difficulty of classical computers to solve the discrete logarithm problem in polynomial time. Here we will study Peter Shor’s quantum attack derived from the algorithm for the discrete logarithm problem, published in 1994 [14]. We start with an introduction to elliptical curves and their use in criptography. Then we understand the mathematical foundations of the corresponding quantum computation to understand Shor’s algorithm, from which we will study how to reach it and why it works.