Implementing the asymptotically fast version of the elliptic curve primality proving algorithm
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Abstract:
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 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.References
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Additional Information
- F. Morain
- Affiliation: LIX École Polytechnique, CNRS/UMR 7161, INRIA/Futurs, F-91128 Palaiseau Cedex, France
- Email: morain@lix.polytechnique.fr
- Received by editor(s): January 27, 2005
- Received by editor(s) in revised form: October 24, 2005
- Published electronically: September 1, 2006
- Additional Notes: Projet TANC, Pôle Commun de Recherche en Informatique du Plateau de Saclay, CNRS, École polytechnique, INRIA, Université Paris-Sud. The author is on leave from the French Department of Defense, Délégation Générale pour l’Armement.
- © Copyright 2006 by the author
- Journal: Math. Comp. 76 (2007), 493-505
- MSC (2000): Primary 11Y11, 11A51, 11G15, 11G20
- DOI: https://doi.org/10.1090/S0025-5718-06-01890-4
- MathSciNet review: 2261033