[Resource Topic] 2015/505: The Tower Number Field Sieve

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The Tower Number Field Sieve

Authors: Razvan Barbulescu, Pierrick Gaudry, Thorsten Kleinjung


The security of pairing-based crypto-systems relies on the difficulty to compute discrete logarithms in finite fields GF(p^n) 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.

ePrint: https://eprint.iacr.org/2015/505

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