Parallel Repetition of Zero-Knowledge Proofs and the Possibility of Basing Cryptography on NP-Hardness

Authors:
Rafael Pass
Affiliations:
CSAIL, MIT
Venue:
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Year:
2006

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Abstract

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.