A Generalised Successive Resultants Algorithm [chapter]

James H. Davenport, Christophe Petit, Benjamin Pring
2016 Lecture Notes in Computer Science  
The Successive Resultants Algorithm (SRA) is a root-finding algorithm for polynomials over Fpn and was introduced at ANTS in 2014 [19] . The algorithm was designed to be 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.
doi:10.1007/978-3-319-55227-9_9 fatcat:haejcyuy6rfipiyc3bjrj3wole