Two long-standing open problems exist on the fringe of complexity theory and cryptography: (1) Does there exist a reduction from an NP-complete problem to a one-way function? (2) Do parallelized versions of classical constant-round zero-knowledge proofs for NP conceal every "hard" bit of the witness to the statement proved? We show that, unless the polynomial-hierarchy collapses, black-box reductions cannot be used to provide positive answers to both questions.
['Rafael Pass']
Parallel repetition of zero-knowledge proofs and the possibility of basing cryptography on NP-hardness