A Generalised Successive Resultants Algorithm

The Successive Resultants Algorithm (SRA) is a root-finding algorithm for polynomials over \(\mathbb {F}_{p^n}\) and was introduced at ANTS in 2014 [19]. The algorithm is efficient when the characteristic p is small and \(n > 1\). In this paper, we abstract the core SRA algorithm to arbitrary finite fields and present three instantiations of our general algorithm, one of which is novel and makes use of a series of isogenies derived from elliptic curves with sufficiently smooth order.

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