TY - JOUR

T1 - Noisy interpolation of sparse polynomials in finite fields

AU - Shparlinski, Igor

AU - Winterhof, Arne

PY - 2005/12

Y1 - 2005/12

N2 - We consider a polynomial analogue of the hidden number problem introduced by Boneh and Venkatesan, namely the sparse polynomial noisy interpolation problem of recovering an unknown polynomial f(X) [InlineMediaObject not available: see fulltext.][X] with at most w non-zero terms from approximate values of f(t) at polynomially many points t [InlineMediaObject not available: see fulltext.] 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.

AB - We consider a polynomial analogue of the hidden number problem introduced by Boneh and Venkatesan, namely the sparse polynomial noisy interpolation problem of recovering an unknown polynomial f(X) [InlineMediaObject not available: see fulltext.][X] with at most w non-zero terms from approximate values of f(t) at polynomially many points t [InlineMediaObject not available: see fulltext.] 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.

UR - http://www.scopus.com/inward/record.url?scp=33645282569&partnerID=8YFLogxK

U2 - 10.1007/s00200-005-0180-1

DO - 10.1007/s00200-005-0180-1

M3 - Article

AN - SCOPUS:33645282569

VL - 16

SP - 307

EP - 317

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

SN - 0938-1279

IS - 5

ER -