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

François Morain (1)

1 TANC - Algorithmic number theory for cryptology

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.

Mots clés: primality proving; elliptic curves

Domaines: Théorie des nombres [math.NT]

François Morain. Implementing the asymptotically fast version of the elliptic curve primality proving algorithm. 2005. ⟨hal-00004136v2⟩