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ECCC
2010

Pseudorandom generators for CC0[p] and the Fourier spectrum of low-degree polynomials over finite fields

13 years 11 months ago
Pseudorandom generators for CC0[p] and the Fourier spectrum of low-degree polynomials over finite fields
In this paper we give the first construction of a pseudorandom generator, with seed length O(log n), for CC0[p], the class of constant-depth circuits with unbounded fan-in MODp gates, for some prime p. More accurately, the seed length of our generator is O(log n) for any constant error > 0. In fact, we obtain our generator by fooling distributions generated by low degree polynomials, over Fp, when evaluated on the Boolean cube. This result significantly extends previous constructions that either required a long seed [LVW93] or that could only fool the distribution generated by linear functions over Fp, when evaluated on the Boolean cube [LRTV09, MZ09]. Enroute of constructing our PRG, we prove two structural results for low degree polynomials over finite fields that can be of independent interest.
Shachar Lovett, Partha Mukhopadhyay, Amir Shpilka
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2010
Where ECCC
Authors Shachar Lovett, Partha Mukhopadhyay, Amir Shpilka
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