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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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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