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arXiv · 1408.0718

Improvements to the number field sieve for non-prime finite fields

Razvan Barbulescu·Pierrick Gaudry·Aurore Guillevic·François Morain
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Abstract

We propose various strategies for improving the computation of discrete logarithms in non-prime fields of medium to large characteristic using the Number Field Sieve. This includes new methods for selecting the polynomials; the use of explicit automorphisms; explicit computations in the number fields; and prediction that some units have a zero virtual logarithm. On the theoretical side, we obtain a new complexity bound of $L_{p^n}(1/3,\sqrt[3]{96/9})$ in the medium characteristic case. On the practical side, we computed discrete logarithms in $F_{p^2}$ for a prime number $p$ with $80$ decimal digits.Warning: This unpublished version contains some inexact statements.

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Razvan Barbulescu, Pierrick Gaudry, Aurore Guillevic, François Morain. 2014-08-04. Improvements to the number field sieve for non-prime finite fields. https://arxiv.org/abs/1408.0718

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