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 $F_{q^{k_{0}k}}$.