Paper 2021/918

The Round Complexity of Quantum Zero-Knowledge

Orestis Chardouvelis and Giulio Malavolta


We study the round complexity of zero-knowledge for QMA (the quantum analogue of NP). Assuming the quantum quasi-polynomial hardness of the learning with errors (LWE) problem, we obtain the following results: - 2-Round statistical witness indistinguishable (WI) arguments for QMA. - 4-Round statistical zero-knowledge arguments for QMA in the plain model, additionally assuming the existence of quantum fully homomorphic encryption. This is the first protocol for constant-round statistical zero-knowledge arguments for QMA. - 2-Round computational (statistical, resp.) zero-knowledge for QMA in the timing model, additionally assuming the existence of post-quantum non-parallelizing functions (time-lock puzzles, resp.). All of these protocols match the best round complexity known for the corresponding protocols for NP with post-quantum security. Along the way, we introduce and construct the notions of sometimes-extractable oblivious transfer and sometimes-simulatable zero-knowledge, which might be of independent interest.

Available format(s)
Cryptographic protocols
Publication info
Preprint. MINOR revision.
quantum cryptographyzero-knowledgetiming model
Contact author(s)
orestischar @ gmail com
giulio malavolta @ hotmail it
2021-09-17: last of 2 revisions
2021-07-08: received
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      author = {Orestis Chardouvelis and Giulio Malavolta},
      title = {The Round Complexity of Quantum Zero-Knowledge},
      howpublished = {Cryptology ePrint Archive, Paper 2021/918},
      year = {2021},
      note = {\url{}},
      url = {}
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