## Cryptology ePrint Archive: Report 2014/147

The Multiple Number Field Sieve for Medium and High Characteristic Finite Fields

Razvan Barbulescu and Cécile Pierrot

Abstract: In this paper, we study the discrete logarithm problem in medium and high characteristic finite fields. We propose a variant of the Number Field Sieve (NFS) based on numerous number fields. Our improved algorithm computes discrete logarithms in $\mathbb{F}_{p^n}$ for the whole range of applicability of NFS and lowers the asymptotic complexity from $L_{p^n}(1/3, (128/9)^{1/3})$ to $L_{p^n}(1/3, (2^{13} /3^6)^{1/3})$ in the medium characteristic case, and from $L_{p^n} (1/3, (64/9)^{1/3})$ to $L_{p^n}(1/3,((92 + 26\sqrt{13})/27))^{1/3})$ in the high characteristic case.

Category / Keywords: public-key cryptography / discrete logarithm problem

Date: received 27 Feb 2014, last revised 27 Feb 2014

Contact author: razvan barbulescu at inria fr

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