Welcome to the resource topic for 2014/506
Title:
Finding Roots in GF(p^n) with the Successive Resultant Algorithm
Authors: Christophe Petit
Abstract:The problem of solving polynomial equations over finite fields has many applications in cryptography and coding theory. In this paper, we consider polynomial equations over a large'' finite field with a small’’ characteristic. We introduce a new algorithm for solving this type of equations, called the \emph{Successive Resultants Algorithm} (SRA) in the sequel. SRA is radically different from previous algorithms for this problem, yet it is conceptually simple. A straightforward implementation using Magma was able to beat the built-in function \emph{Roots} for some parameters. These preliminary results encourage a more detailed study of SRA and its applications. Moreover, we point out that an extension of SRA to the multivariate case would have an importa
ePrint: https://eprint.iacr.org/2014/506
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