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» Testing Low-Degree Polynomials over Prime Fields
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JCT
2011
85views more  JCT 2011»
13 years 6 days ago
Relatively prime polynomials and nonsingular Hankel matrices over finite fields
Mario García-Armas, Sudhir R. Ghorpade, Sam...
STOC
2010
ACM
228views Algorithms» more  STOC 2010»
14 years 2 months ago
On the Structure of Cubic and Quartic Polynomials
In this paper we study the structure of polynomials of degree three and four that have high bias or high Gowers norm, over arbitrary prime fields. In particular we obtain the foll...
Elad Haramaty and Amir Shpilka
ISSAC
1997
Springer
138views Mathematics» more  ISSAC 1997»
13 years 9 months ago
Fast Polynomial Factorization Over High Algebraic Extensions of Finite Fields
New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number. When log q = n1+a , where a ...
Erich Kaltofen, Victor Shoup
EUROCRYPT
2004
Springer
13 years 10 months ago
Construction of Secure Random Curves of Genus 2 over Prime Fields
For counting points of Jacobians of genus 2 curves defined over large prime fields, the best known method is a variant of Schoof’s algorithm. We present several improvements on...
Pierrick Gaudry, Éric Schost
JCT
2008
67views more  JCT 2008»
13 years 5 months ago
On the number of directions determined by a pair of functions over a prime field
A three-dimensional analogue of the classical direction problem is proposed and an asymptotically sharp bound for the number of directions determined by a nonplanar set in AG(3, p)...
Simeon Ball, András Gács, Pét...