Pseudorandom Generators for Group Products

@article{Kouck2010PseudorandomGF,
  title={Pseudorandom Generators for Group Products},
  author={Michal Kouck{\'y} and Prajakta Nimbhorkar and Pavel Pudl{\'a}k},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2010},
  volume={17},
  pages={113}
}
We prove that the pseudorandom generator introduced in [INW94] fools group products of a given finite group. The seed length is O(log n log 1ε ), where n the length of the word and ε is the precision. The result is equivalent to the statement that the pseudorandom generator fools read-once permutation branching programs of constant width.