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» On the subset sum problem over finite fields
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ANTS
2006
Springer
118views Algorithms» more  ANTS 2006»
15 years 1 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
15 years 6 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»
14 years 11 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»
14 years 11 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»
15 years 1 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