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ICPPW
2005
IEEE
15 years 11 months ago
Factoring Solution Sets of Polynomial Systems in Parallel
We report on a £rst parallel implementation of a recent algorithm to factor positive dimensional solution sets of polynomial systems. As the algorithm uses homotopy continuation,...
Anton Leykin, Jan Verschelde
140
Voted
ISSAC
2009
Springer
123views Mathematics» more  ISSAC 2009»
16 years 11 days ago
Schemes for deterministic polynomial factoring
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 o...
Gábor Ivanyos, Marek Karpinski, Nitin Saxen...
203
Voted
PKC
2011
Springer
197views Cryptology» more  PKC 2011»
14 years 8 months ago
Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants
We investigate the security of a generalization of HFE (multivariate and odd-characteristic variants). First, we propose an improved version of the basic Kipnis-Shamir key recovery...
Luk Bettale, Jean-Charles Faugère, Ludovic ...
181
Voted
ANTS
2010
Springer
260views Algorithms» more  ANTS 2010»
15 years 9 months ago
On the Complexity of the Montes Ideal Factorization Algorithm
Let p be a rational prime and let Φ(X) be a monic irreducible polynomial in Z[X], with nΦ = deg Φ and δΦ = vp(disc Φ). In [13] Montes describes an algorithm for the decomposi...
David Ford, Olga Veres
FOCS
2008
IEEE
16 years 8 days ago
Computing the Tutte Polynomial in Vertex-Exponential Time
The deletion–contraction algorithm is perhaps the most popular method for computing a host of fundamental graph invariants such as the chromatic, flow, and reliability polynomi...
Andreas Björklund, Thore Husfeldt, Petteri Ka...