On the Round Complexity of Zero-Knowledge Proofs Based on One-Way Permutations

We consider the following problem: can we construct constant-round zero-knowledge proofs (with negligible soundness) for NP assuming only the existence of one-way permutations? We answer the question in the negative for fully black-box constructions (using only black-box access to both the underlying primitive and the cheating verifier) that satisfy a natural restriction on the “adaptivity” of the simulator’s queries. Specifically, we show that only languages in coAM have constant-round zero-knowledge proofs of this kind. ∗ Dept. of Computer Science, University of Maryland. † Queens College, CUNY. Most of this research was completed while a post-doc at Columbia University. ‡ LRI, Universit´e Paris-Sud. This reseach was completed while the author was a student at Princeton University. 1 

• Type: Journal
• Year: 2010
• Where: LATINCRYPT
• Authors: S. Dov Gordon, Hoeteck Wee, David Xiao, Arkady Yerukhimovich
• Keywords: Black-box Constructions, Constant-round Zero-knowledge, Constant-round Zero-knowledge Proofs, Cryptology, LATINCRYPT 2010