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In this paper, we revisit the ZigZag strategy of Granger, Kleinjung and Zumbragel. 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 .

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