Abstract
The paper is about the discrete logarithm problem for elliptic curves over characteristic 2 finite fields \({\mathbb {F}}_{2^n}\) of prime degree \(n\). We consider practical issues about index calculus attacks using summation polynomials in this setting. The contributions of the paper include: a new choice of variables for binary Edwards curves (invariant under the action of a relatively large group) to lower the degree of the summation polynomials; a choice of factor base that “breaks symmetry” and increases the probability of finding a relation; an experimental investigation of the use of SAT solvers rather than Grobner basis methods for solving multivariate polynomial equations over \({\mathbb {F}}_2\).
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