In 1986, following the work of Schoof on counting points on elliptic curves over finite fields, new algorithms for primality proving emerged, due to Goldwasser and Kilian on the one hand, and Atkin on the other. The latter algorithm uses the theory of complex multiplication. The algorithm, now called ECPP, has been used for nearly ten years. The purpose of this paper is to give an account of the recent theoretical and practical improvements of ECPP, as well as new benchmarks for integers of various sizes and a new primality record.
CITATION STYLE
Morain, F. (1998). Primality proving using elliptic curves: An update. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1423, pp. 111–127). Springer Verlag. https://doi.org/10.1007/bfb0054855
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