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» Permutations, hyperplanes and polynomials over finite fields
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FOCS
1998
IEEE
13 years 11 months ago
Unsatisfiable Systems of Equations, Over a Finite Field
The properties of any system of k simultaneous equations in n variables over GF(q), are studied, with a particular emphasis on unsatisfiable systems. A general formula for the num...
Alan R. Woods
SODA
1992
ACM
90views Algorithms» more  SODA 1992»
13 years 8 months ago
Self-Testing Polynomial Functions Efficiently and Over Rational Domains
In this paper we give the first self-testers and checkers for polynomials over rational and integer domains. We also show significantly stronger bounds on the efficiency of a simp...
Ronitt Rubinfeld, Madhu Sudan
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,...
TC
2002
13 years 7 months ago
A Deterministic Multivariate Interpolation Algorithm for Small Finite Fields
We present a new multivariate interpolation algorithm over arbitrary fields which is primarily suited for small finite fields. Given function values at arbitrary t points, we show ...
Zeljko Zilic, Zvonko G. Vranesic
COMBINATORICS
2006
124views more  COMBINATORICS 2006»
13 years 7 months ago
A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics
A "hybrid method", dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singulari...
Philippe Flajolet, Éric Fusy, Xavier Gourdo...