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Title:
A Simplified Approach to Rigorous Degree 2 Elimination in Discrete Logarithm Algorithms
Authors: Faruk Göloğlu, 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}}.
ePrint: https://eprint.iacr.org/2018/430
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