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## Section: New Results

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

In [10], 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 ${k}_{0}$ 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 ${F}_{{q}^{{k}_{0}k}}$.