Which Languages Have 4-Round Zero-Knowledge Proofs?

We show that if a language L has a 4-round, black-box, computational zero-knowledge proof system with negligible soundness error, then $\bar{L}\in \mathsf{MA}$. 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.

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