Irreducibility of multivariate polynomials
Journal of Computer and System Sciences
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Interpolation of sparse multivariate polynomials over large finite fields with applications
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Efficient Multivariate Factorization over Finite Fields
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
Modern Computer Algebra
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Improved dense multivariate polynomial factorization algorithms
Journal of Symbolic Computation
Lifting and recombination techniques for absolute factorization
Journal of Complexity
Interpolation of polynomials given by straight-line programs
Theoretical Computer Science
Faster Combinatorial Algorithms for Determinant and Pfaffian
Algorithmica - Special Issue: Algorithms and Computation; Guest Editor: Takeshi Tokuyama
New recombination algorithms for bivariate polynomial factorization based on Hensel lifting
Applicable Algebra in Engineering, Communication and Computing
Practical polynomial factoring in polynomial time
Proceedings of the 36th international symposium on Symbolic and algebraic computation
An improved algorithm for computing logarithms over and its cryptographic significance (Corresp.)
IEEE Transactions on Information Theory
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In this paper we present a new algorithm for extracting sparse factors from multivariate integral polynomials. The method hinges on a new type of substitution, which reduces multivariate integral polynomials to bivariate polynomials over finite fields and keeps the sparsity of the polynomial. We retrieve the multivariate sparse factors, term by term, using discrete logarithms. We show that our method is really effective when used for factoring multivariate polynomials that have only sparse factors and when used to extract sparse factors of multivariate polynomials that may also have dense factors.