P-schemes and Deterministic Polynomial Factoring over Finite Fields

06/30/2017

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by   Zeyu Guo, et al.

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We introduce a family of mathematical objects called P-schemes, where P is a poset of subgroups of a finite group G. A P-scheme is a collection of partitions of the right coset spaces H G, indexed by H∈P, that satisfies a list of axioms. These objects generalize the classical notion of association schemes as well as the notion of m-schemes (Ivanyos et al. 2009). Based on P-schemes, we develop a unifying framework for the problem of deterministic factoring of univariate polynomials over finite fields under the generalized Riemann hypothesis (GRH).