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» Permutations, hyperplanes and polynomials over finite fields
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FOCS
1998
IEEE
15 years 1 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»
14 years 10 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
103
Voted
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,...
TC
2002
14 years 9 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»
14 years 9 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...