Noisy Interpolation of Multivariate Sparse Polynomials in Finite Fields

Authors:
Álvar Ibeas;Arne Winterhof
Affiliations:
University of Cantabria, Santander, Spain E-39071;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria 4040
Venue:
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2009

Citing 2
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Noisy interpolation of sparse polynomials in finite fields

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Abstract

We consider the problem of recovering an unknown sparse multivariate polynomial $f\in \mathbb{F}_p[X_1,\ldots,X_m]$ over a finite field $\mathbb{F}_p$ of prime order p from approximate values of f (t 1 ,...,t m ) at polynomially many points $(t_1,\ldots,t_m)\in \mathbb{F}_p^m$ selected uniformly at random. Our result is based on a combination of bounds on exponential sums with the lattice reduction technique.