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» Finding roots of polynomials over finite fields
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103
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ICISC
2000
126views Cryptology» more  ICISC 2000»
14 years 11 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,...
62
Voted
COCO
2008
Springer
79views Algorithms» more  COCO 2008»
14 years 11 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»
14 years 9 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
15 years 9 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»
15 years 9 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