Improvements to the general number field sieve for discrete logarithms in prime fields: A comparison with the Gaussian integer method

Antoine Joux 1 Reynald Lercier 2
1 UPMC - Université Pierre et Marie Curie - Paris 6
2 IRMAR - Institut de Recherche Mathématique de Rennes
Abstract : In this paper, we describe many improvements to the number field sieve. Our main contribution consists of a new way to compute individual logarithms with the number field sieve without solving a very large linear system for each logarithm. We show that, with these improvements, the number field sieve outperforms the gaussian integer method in the hundred digit range. We also illustrate our results by successfully computing discrete logarithms with GNFS in a large prime field.
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Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2003, 72, pp.953-967. 〈10.1090/S0025-5718-02-01482-5〉
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https://hal.archives-ouvertes.fr/hal-01102016
Contributeur : Reynald Lercier <>
Soumis le : dimanche 11 janvier 2015 - 22:36:46
Dernière modification le : mercredi 5 décembre 2018 - 01:24:21

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Antoine Joux, Reynald Lercier. Improvements to the general number field sieve for discrete logarithms in prime fields: A comparison with the Gaussian integer method. Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2003, 72, pp.953-967. 〈10.1090/S0025-5718-02-01482-5〉. 〈hal-01102016〉

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