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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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https://hal.archives-ouvertes.fr/hal-01155635
Contributor : Razvan Barbulescu <>
Submitted on : Wednesday, May 27, 2015 - 9:42:47 AM
Last modification on : Friday, April 10, 2020 - 5:09:54 PM
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  • HAL Id : hal-01155635, version 1

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Razvan Barbulescu, Pierrick Gaudry, Thorsten Kleinjung. The Tower Number Field Sieve. ASIACRYPT 2015, International Association of Cryptologic Research, Nov 2015, Auckland, New Zealand. pp.31-58. ⟨hal-01155635⟩

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