Better polynomials for GNFS (original) (raw)
Article Dans Une Revue Mathematics of Computation Année : 2016
Résumé
The general number field sieve (GNFS) is the most efficient algo-rithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomials for GNFS: with a new degree of freedom, we further improve the size property. We demonstrate the efficiency of our algorithm by exhibiting a better polynomial than the one used for the factorization of RSA-768, and a polynomial for RSA-1024 that outperforms the best published one.
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https://inria.hal.science/hal-01089507
Soumis le : lundi 1 décembre 2014-20:47:56
Dernière modification le : mardi 4 novembre 2025-12:03:06
Archivage à long terme le : lundi 2 mars 2015-13:38:18
Dates et versions
hal-01089507 , version 1 (01-12-2014)
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- HAL Id : hal-01089507 , version 1
- DOI : 10.1090/mcom3048
Citer
Shi Bai, Cyril Bouvier, Alexander Kruppa, Paul Zimmermann. Better polynomials for GNFS. Mathematics of Computation, 2016, 85, pp.12. ⟨10.1090/mcom3048⟩. ⟨hal-01089507⟩
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