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» On the subset sum problem over finite fields
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ANTS
2006
Springer
118views Algorithms» more  ANTS 2006»
13 years 9 months ago
Construction of Rational Points on Elliptic Curves over Finite Fields
Abstract. We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the...
Andrew Shallue, Christiaan van de Woestijne
FOCS
2007
IEEE
14 years 1 months ago
Hardness of Reconstructing Multivariate Polynomials over Finite Fields
We study the polynomial reconstruction problem for low-degree multivariate polynomials over finite field F[2]. In this problem, we are given a set of points x ∈ {0, 1}n and ta...
Parikshit Gopalan, Subhash Khot, Rishi Saket
MOC
1998
97views more  MOC 1998»
13 years 7 months ago
Euclid's algorithm and the Lanczos method over finite fields
Abstract. This paper shows that there is a close relationship between the Euclidean algorithm for polynomials and the Lanczos method for solving sparse linear systems, especially w...
Jeremy Teitelbaum
FOCM
2008
77views more  FOCM 2008»
13 years 7 months ago
Modular Counting of Rational Points over Finite Fields
Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m non-zero terms. Let N(f) denote the number of solutions of f(x) = 0 ...
Daqing Wan
COCO
2008
Springer
79views Algorithms» more  COCO 2008»
13 years 9 months ago
Towards Dimension Expanders over Finite Fields
In this paper we study the problem of explicitly constructing a dimension expander raised by [BISW04]: Let Fn be the n dimensional linear space over the field F. Find a small (ide...
Zeev Dvir, Amir Shpilka