The bit extraction problem or t-resilient functions

@article{Chor1985TheBE,
  title={The bit extraction problem or t-resilient functions},
  author={Benny Chor and Oded Goldreich and Johan H{\aa}stad and Joel Friedman and Steven Rudich and Roman Smolensky},
  journal={26th Annual Symposium on Foundations of Computer Science (sfcs 1985)},
  year={1985},
  pages={396-407}
}
We consider the following adversarial situation. Let n, m and t be arbitrary integers, and let f : {0, 1}n → {0, 1}m be a function. An adversary, knowing the function f, sets t of the n input bits, while the rest (n-t input, bits) are chosen at random (independently and with uniform probability distribution) The adversary tries to prevent the outcome of f from being uniformly distributed in {0, 1}m. The question addressed is for what values of n, m and t does the adversary necessarily fail in… CONTINUE READING

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