Paper 2018/167

On the Existence of Three Round Zero-Knowledge Proofs

Nils Fleischhacker, Vipul Goyal, and Abhishek Jain


We study the round complexity of zero-knowledge (ZK) proof systems. While five round ZK proofs for NP are known from standard assumptions [Goldreich-Kahan, J. Cryptology'96], Katz [TCC'08] proved that four rounds are insufficient for this task w.r.t. black-box simulation. In this work, we study the feasibility of ZK proofs using non-black-box simulation. Our main result is that three round private-coin ZK proofs for NP do not exist (even w.r.t. non-black-box simulation), under certain assumptions on program obfuscation. Our approach builds upon the recent work of Kalai et al. [Crypto'17] who ruled out constant round public-coin ZK proofs under the same assumptions as ours.

Available format(s)
Publication info
Published by the IACR in EUROCRYPT 2018
zero-knowledgeround complexitylower bound
Contact author(s)
mail @ nilsfleischhacker de
abhishek @ cs jhu edu
goyal @ cs cmu edu
2018-02-11: received
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Creative Commons Attribution


      author = {Nils Fleischhacker and Vipul Goyal and Abhishek Jain},
      title = {On the Existence of Three Round Zero-Knowledge Proofs},
      howpublished = {Cryptology ePrint Archive, Paper 2018/167},
      year = {2018},
      note = {\url{}},
      url = {}
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