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ASIACRYPT
2003
Springer
14 years 1 months ago
Rotations and Translations of Number Field Sieve Polynomials
We present an algorithm that finds polynomials with many roots modulo many primes by rotating candidate Number Field Sieve polynomials using the Chinese Remainder Theorem. We also...
Jason E. Gower
JC
2008
77views more  JC 2008»
13 years 8 months ago
A numerical algorithm for zero counting, I: Complexity and accuracy
We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(log(nD(f))) iterations (grid refinements) where n is...
Felipe Cucker, Teresa Krick, Gregorio Malajovich, ...
ICALP
2010
Springer
14 years 1 months ago
On the Relation between Polynomial Identity Testing and Finding Variable Disjoint Factors
We say that a polynomial f(x1, . . . , xn) is indecomposable if it cannot be written as a product of two polynomials that are defined over disjoint sets of variables. The polynom...
Amir Shpilka, Ilya Volkovich
ICASSP
2011
IEEE
13 years 5 days ago
Rank-deficient quadratic-form maximization over M-phase alphabet: Polynomial-complexity solvability and algorithmic developments
The maximization of a positive (semi)definite complex quadratic form over a finite alphabet is NP-hard and achieved through exhaustive search when the form has full rank. Howeve...
Anastasios T. Kyrillidis, George N. Karystinos
EUROCRYPT
2012
Springer
11 years 11 months ago
Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Fields
Abstract. The goal of this paper is to further study the index calculus method that was first introduced by Semaev for solving the ECDLP and later developed by Gaudry and Diem. In...
Jean-Charles Faugère, Ludovic Perret, Chris...