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A strategy for elliptic curve primality proving. (English) Zbl 1345.11089
Summary: This paper deals with an implementation of the elliptic curve primality proving (ECPP) algorithm of A. O. L. Atkin and F. Morain [Math. Comput. 61, No. 203, 29–68 (1993; Zbl 0792.11056)]. As the ECPP algorithm is not deterministic, we are developing a strategy to avoid certain situations in which the original implementation could get stuck and to get closer to the situation where the probability that the algorithm terminates successfully is 1. We apply heuristics and tricks in order to test the strategy in our implementation in Magma on numbers of up to 7000 decimal digits and collect data to show the advantages over previous implementations in practice.
MSC:
11Y11 Primality
11G05 Elliptic curves over global fields
Software:
ECPP; Magma
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References:
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