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Conference Papers Year : 2015

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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Dates and versions

hal-01155635 , version 1 (27-05-2015)

Identifiers

  • HAL Id : hal-01155635 , version 1

Cite

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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