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Unconditional pseudorandom generators for low degree
Shachar Lovett
Sunday, 25.11.2007, 10:30
Room 337-8 Taub Bld.
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.