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.
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Ibeas, Á., Winterhof, A. (2009). Noisy Interpolation of Multivariate Sparse Polynomials in Finite Fields. In: Bras-Amorós, M., Høholdt, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02181-7_18
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DOI: https://doi.org/10.1007/978-3-642-02181-7_18
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