Limits on Low-Degree Pseudorandom Generators (Or: Sum-of-Squares Meets Program Obfuscation)

An m output pseudorandom generator G: ({+/- 1}(b))(n) -> {+/- 1}(m) that takes input n blocks of b bits each is said to be l-block local if every output is a function of at most l blocks. We show that such l-block local pseudorandom generators can have output length at most (O) over tilde (2(lb)n(inverted right) (perpendicularl/2inverted ...More