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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A simplified approach to rigorous degree 2 elimination in discrete logarithm algorithms
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by Faruk Göloğlu and Antoine Joux HTML | PDF
Math. Comp. 88 (2019), 2485-2496

Abstract:

In this paper, we revisit the ZigZag strategy of Granger, Kleinjung, and Zumbrägel. In particular, we provide a new algorithm and proof for the so-called degree 2 elimination step. This allows us to provide a stronger theorem concerning discrete logarithm computations in small characteristic fields $\mathbb {F}_{q^{k_0k}}$ with $k$ close to $q$ and $k_0$ a small integer. As in the aforementioned paper, we rely on the existence of two polynomials $h_0$ and $h_1$ of degree $2$ providing a convenient representation of the finite field $\mathbb {F}_{q^{k_0k}}$.
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Additional Information
  • Faruk Göloğlu
  • Affiliation: Department of Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
  • Email: farukgologlu@gmail.com
  • Antoine Joux
  • Affiliation: Chaire de Cryptologie de la Fondation SU, Sorbonne Université, Institut de Mathématiques de Jussieu–Paris Rive Gauche, CNRS, INRIA, Univ Paris Diderot. Campus Pierre et Marie Curie, F-75005 Paris, France
  • MR Author ID: 316495
  • Email: antoine.joux@m4x.org
  • Received by editor(s): April 16, 2018
  • Received by editor(s) in revised form: April 20, 2018, and September 4, 2018
  • Published electronically: December 31, 2018
  • Additional Notes: This work was supported in part by the European Union’s H2020 Programme under grant agreement number ERC-669891. It has also been supported by GAČR Grant 18-19087S-301-13/201843.
  • © Copyright 2018 Foruk Göloğlu and Antoine Joux
  • Journal: Math. Comp. 88 (2019), 2485-2496
  • MSC (2010): Primary 11Y16, 12Y05
  • DOI: https://doi.org/10.1090/mcom/3404
  • MathSciNet review: 3957902