%0 Journal Article %J Journal of cryptology %D 2012 %T Which Languages Have 4-Round Zero-Knowledge Proofs? %A Katz, Jonathan %X We show that if a language L has a 4-round, black-box, computational zero-knowledge proof system with negligible soundness error, then . Assuming the polynomial hierarchy does not collapse, this means in particular that NP-complete languages do not have 4-round zero-knowledge proofs with black-box simulation. %B Journal of cryptology %V 25 %P 41 - 56 %8 2012/// %G eng %N 1 %R 10.1007/s00145-010-9081-y