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A simplified approach to rigorous degree 2 elimination in discrete logarithm algorithms

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 F q k 0 k with k close to q and k0 a small integer. As in the aforementioned paper, we rely on the existence of two polynomi-als h0 and h1 of degree 2 providing a convenient representation of the finite field F q k 0 k .
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Submitted on : Friday, July 12, 2019 - 12:30:16 PM
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  • HAL Id : hal-01960765, version 1

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Faruk Göloğlu, Antoine Joux. A simplified approach to rigorous degree 2 elimination in discrete logarithm algorithms. Mathematics of Computation, American Mathematical Society, 2019, pp.1. ⟨hal-01960765⟩

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