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» Finding roots of polynomials over finite fields
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ICISC
2000
126views Cryptology» more  ICISC 2000»
13 years 8 months ago
Cryptographic Applications of Sparse Polynomials over Finite Rings
Abstract. This paper gives new examples that exploit the idea of using sparse polynomials with restricted coefficients over a finite ring for designing fast, reliable cryptosystems...
William D. Banks, Daniel Lieman, Igor Shparlinski,...
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
CORR
2010
Springer
74views Education» more  CORR 2010»
13 years 7 months ago
Scalar-linear Solvability of Matroidal Networks Associated with Representable Matroids
We study matroidal networks introduced by Dougherty et al., who showed that if a network is scalar-linearly solvable over some finite field, then the network is a matroidal network...
Anthony Kim, Muriel Médard
DCC
2008
IEEE
14 years 7 months ago
On solving sparse algebraic equations over finite fields
A system of algebraic equations over a finite field is called sparse if each equation depends on a small number of variables. Finding efficiently solutions to the system is an unde...
Igor Semaev
STOC
2007
ACM
133views Algorithms» more  STOC 2007»
14 years 7 months ago
Interpolation of depth-3 arithmetic circuits with two multiplication gates
In this paper we consider the problem of constructing a small arithmetic circuit for a polynomial for which we have oracle access. Our focus is on n-variate polynomials, over a fi...
Amir Shpilka