Haifa University - Dept. of CS Theory Seminar
Speaker : Shachar Lovett, Weizmann.
Title: "Unconditional pseudorandom generators for low degree polynomials"
Date: Thursday, Jan. 10.
Place: Haifa U. Education Building, room 570.
Time: 12:15 - 13:30
Abstract:
We give an explicit construction of pseudorandom
generators against low degree polynomials over finite fields. We
show that the sum of $2^d$ small-biased generators with error
$\epsilon^{2^{O(d)}}$ is a pseudorandom generator against degree $d$
polynomials with error $\epsilon$. This gives a generator with seed
length $2^{O(d)} \log{(n/\epsilon)}$. Our construction follows the
recent breakthrough result of Bogadnov and Viola \cite{BV}. Their
work shows that the sum of $d$ small-biased generators is a
pseudo-random generator against degree $d$ polynomials, assuming the
Inverse Gowers Conjecture. However, this conjecture is only proven
for $d=2,3$. The main advantage of our work is that it
does not rely on any unproven conjectures.