Implementação Eficiente de Algoritmos para Teste de Primalidade

Bruno C. Dias RibeiroDiego F. Aranha

The development of cryptography, public key cryptography in particular, was a crucial factor for the growth and popularization of computer networks. It was responsible for demands of secure email communication, e-commerce, digital signatures and certification. The proper use of cryptographic techniques requires the development of efficient implementations capable of running in all kind of devices, which are more and more integrated into people's lives. The generation of cryptographic keys, for example, is not only a critical security operation but also has a high computational cost in the RSA algorithm. This work aims to study techniques for primality testing, the core element of the key generation process in this algorithm. Our focus is on the implementation,optimization and performance analysis of Simplified Quadratic Frobenius Test,a primality test from 2005 which did not receive enough attention in the literature. The achieved results points to a 30% efficiency increase for integers up to 256 bits, a positive outcome regarding the feasibility of reducing the computational cost of generating prime numbers.

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