Cryptology ePrint Archive: Report 2018/430

A Simplified Approach to Rigorous Degree 2 Elimination in Discrete Logarithm Algorithms

Faruk Göloğlu and Antoine Joux

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 $\mathbb{F}_{q^{k_0k}}$.

Category / Keywords: foundations / discrete logarithm problem

Date: received 6 May 2018, last revised 11 May 2018

Contact author: farukgologlu at gmail com

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Version: 20180511:113534 (All versions of this report)

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