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

Mathematics of Computation
 Pub Date:
 March 2007
 DOI:
 10.1090/S0025571806018904
 Bibcode:
 2007MaCom..76..493M
 Keywords:

 Primality proving;
 elliptic curves;
 ECPP algorithm.