Implementing the asymptotically fast version of the elliptic curve primality proving algorithm

Details Implementing the asymptotically fast version of the elliptic curve primality proving algorithm Implementing the asymptotically fast version of the elliptic curve primality proving algorithm

2005-02-04

arxiv.org/abs/math/0502097v1

Mathematics

Number Theory

Scientific paper

The elliptic curve primality proving (ECPP) algorithm is one of the current fastest practical algorithms for proving the primality of large numbers. Its running time cannot be proven rigorously, but heuristic arguments show that it should run in time O ((log N)^5) to prove the primality of N. An asymptotically fast version of it, attributed to J. O. Shallit, runs in time O ((log N)^4). The aim of this article is to describe this version in more details, leading to actual implementations able to handle numbers with several thousands of decimal digits.

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