The Tower Number Field Sieve

Abstract : The security of pairing-based crypto-systems relies on the difficulty to compute discrete logarithms in finite fields Fpn where n is a small integer larger than 1. The state-of-art algorithm is the number field sieve (NFS) together with its many variants. When p has a special form (SNFS), as in many pairings constructions, NFS has a faster variant due to Joux and Pierrot. We present a new NFS variant for SNFS computations, which is better for some cryptographically relevant cases, according to a precise comparison of norm sizes. The new algorithm is an adaptation of Schirokauer's variant of NFS based on tower extensions, for which we give a middlebrow presentation.
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Communication dans un congrès
Tetsu Iwata and Jung Hee Cheon. ASIACRYPT 2015, Nov 2015, Auckland, New Zealand. Springer, 9453, pp.31-58, 2015, Advances in cryptology-Asiacrypt 2015. <https://www.math.auckland.ac.nz/~sgal018/AC2015/index.html>
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Contributeur : Razvan Barbulescu <>
Soumis le : mercredi 27 mai 2015 - 09:42:47
Dernière modification le : mardi 13 décembre 2016 - 15:40:18
Document(s) archivé(s) le : lundi 24 avril 2017 - 15:25:57

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Razvan Barbulescu, Pierrick Gaudry, Thorsten Kleinjung. The Tower Number Field Sieve. Tetsu Iwata and Jung Hee Cheon. ASIACRYPT 2015, Nov 2015, Auckland, New Zealand. Springer, 9453, pp.31-58, 2015, Advances in cryptology-Asiacrypt 2015. <https://www.math.auckland.ac.nz/~sgal018/AC2015/index.html>. <hal-01155635>

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