English

ATKIN’S ECPP (Elliptic Curve Primality Proving) ALGORITHM

In contrast to using a strong generalization of Fermat’s theorem, as in Jacobisum Test, Goldwasser and Kilian used some results coming from Group Theory in order to prove the primality of a given integer N 2 N. They developed an algorithm which uses the group of rational points of elliptic curves over finite fields. Atkin and Morain extended the idea of Goldwasser and Kilian and used the elliptic curves with CM (complex multiplication) to obtain a more efficient algorithm, namely Atkin’s ECPP (elliptic curve primality proving) Algorithm. Aim of this thesis is to introduce some primality tests and explain the Atkin’s ECPP Algorithm.

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