One-Way Fuctions are Essential for Non-Trivial Zero-Knowledge

  title={One-Way Fuctions are Essential for Non-Trivial Zero-Knowledge},
  author={Rafail Ostrovsky and Avi Wigderson},
It was known that if one-way functions exist, then there are zero-knowledge proofs for every language in PSPACE . We prove that unless very weak one-way functions exist, ZeroKnowledge proofs can be given only for languages in BPP. For average-case definitions of BPP we prove an analogue result under the assumption that uniform one-way functions do not exist. ∗ University of California at Berkeley and International Computer Science Institute at Berkeley. Part of this work was done at Bellcore… CONTINUE READING
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