Noisy interpolation of sparse polynomials in finite fields

9 years 16 hour ago
Noisy interpolation of sparse polynomials in finite fields
Abstract We consider a polynomial analogue of the hidden number problem introduced by Boneh andVenkatesan, namely the sparse polynomial noisy interpolation problem of recovering an unknown polynomial f (X) IFp[X] with at most w non-zero terms from approximate values of f (t) at polynomially many points t IFp selected uniformly at random. We extend the polynomial time algorithm of the first author for polynomials f (X) of sufficiently small degree to polynomials of almost arbitrary degree. Our result is based on a combination of some number theory tools such as bounds of exponential sums and the number of solutions of congruences with the lattice reduction technique. The new idea is motivated by Waring's problem and uses a recent bound on exponential sums of Cochrane, Pinner, and Rosenhouse. Keywords Noisy interpolation
Igor Shparlinski, Arne Winterhof
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2005
Authors Igor Shparlinski, Arne Winterhof
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