A Generalised Successive Resultants Algorithm

The Successive Resultants Algorithm (SRA) is a root-finding algorithm for polynomials over F-pn 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.