The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions

Antoine Joux 1 Cécile Pierrot 1
1 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : In this paper, we study the discrete logarithm problem in finite fields related to pairing-based curves. We start with a precise analysis of the state-of-the-art algorithms for computing discrete logarithms that are suitable for finite fields related to pairing-friendly constructions. To improve upon these algorithms, we extend the Special Number Field Sieve to compute discrete logarithms in $\F_{p^{n}}$, where $p$ has an adequate sparse representation. Our improved algorithm works for the whole range of applicability of the Number Field Sieve.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01213666
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Submitted on : Thursday, October 8, 2015 - 5:10:41 PM
Last modification on : Thursday, March 21, 2019 - 1:04:17 PM

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Antoine Joux, Cécile Pierrot. The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions. 6th International Conference on Pairing-based Cryptography, Pairing 2013, Nov 2013, Beijing, China. pp.45-61, ⟨10.1007/978-3-319-04873-4_3⟩. ⟨hal-01213666⟩

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