Factoring polynomials and primitive elements for special primes
Theoretical Computer Science
Factoring polynomials over finite fields
Journal of Algorithms
Generalized Riemann hypothesis and factoring polynomials over finite fields
Journal of Algorithms
Galois groups and factoring polynomials over finite fields
SIAM Journal on Discrete Mathematics
Association schemes, superschemes, and relations invariant under permutation groups
European Journal of Combinatorics
Subquadratic-time factoring of polynomials over finite fields
Mathematics of Computation
On the determinitic complexity of factoring polynomials
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the second Magma conference
Factorization of polynominals over finite fields in subexponential time under GRH
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Factoring Polynominals over Finite Fields and Stable Colorings of Tournaments
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Algebraic structure of association schemes of prime order
Journal of Algebraic Combinatorics: An International Journal
A computation of some multiply homogeneous superschemes from transitive permutation groups
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On taking roots in finite fields
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Factoring Polynomials over Special Finite Fields
Finite Fields and Their Applications
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In this work we relate the deterministic complexity of factoring polynomials (over finite fields) to certain combinatorial objects, we call m-schemes, that are generalizations of permutation groups. We design a new generalization of the known conditional deterministic subexponential time polynomial factoring algorithm to get an underlying m-scheme. We then demonstrate how progress in understanding m-schemes relate to improvements in the deterministic complexity of factoring polynomials, assuming the Generalized Riemann Hypothesis (GRH). In particular, we give the first deterministic polynomial time algorithm (assuming GRH) to find a nontrivial factor of a polynomial of prime degree n where (n-1) is a constant-smooth number. We use a structural theorem about association schemes on a prime number of points, which Hanaki and Uno (2006) proved by representation theory methods.