O algoritmo AKS para verificar primalidade em tempo polinomial

Abstract

The public-key cryptography is a method of encryption very using nowadays, and relevant studies were made for development of security of this system. However, this science need to be continuously improved, because the fast development speed of computers, with this situation the computers can be able to execute the criptoanalyze fastly. An important point to secure the security of one encrypted message it‟s size of key, that are prime numbers. Nowadays there are probabilistic algorithms that execute in polynomial time and accuse if a number is prime with lowest percentual of mistake. The AKS is the first deterministic algorithmic to execute this test in polynomial time. The goal of this work is to understand why this new AKS didn‟t break the security of the cryptography based on prime numbers. Some of the most important algorithmic of certification for prime numbers will be implemented and also for the AKS, all of them in C/C++. At the end, a study about the impact of security caused by the AKS will be raised.