Paper 2021/1315

Certified Everlasting Zero-Knowledge Proof for QMA

Taiga Hiroka, Tomoyuki Morimae, Ryo Nishimaki, and Takashi Yamakawa

Abstract

In known constructions of classical zero-knowledge protocols for NP, either of zero-knowledge or soundness holds only against computationally bounded adversaries. Indeed, achieving both statistical zero-knowledge and statistical soundness at the same time with classical verifier is impossible for NP unless the polynomial-time hierarchy collapses, and it is also believed to be impossible even with a quantum verifier. In this work, we introduce a novel compromise, which we call the certified everlasting zero-knowledge proof for QMA. It is a computational zero-knowledge proof for QMA, but the verifier issues a classical certificate that shows that the verifier has deleted its quantum information. If the certificate is valid, even unbounded malicious verifier can no longer learn anything beyond the validity of the statement. We construct a certified everlasting zero-knowledge proof for QMA. For the construction, we introduce a new quantum cryptographic primitive, which we call commitment with statistical binding and certified everlasting hiding, where the hiding property becomes statistical once the receiver has issued a valid certificate that shows that the receiver has deleted the committed information. We construct commitment with statistical binding and certified everlasting hiding from quantum encryption with certified deletion by Broadbent and Islam [TCC 2020] (in a black box way), and then combine it with the quantum sigma-protocol for QMA by Broadbent and Grilo [FOCS 2020] to construct the certified everlasting zero-knowledge proof for QMA. Our constructions are secure in the quantum random oracle model. Commitment with statistical binding and certified everlasting hiding itself is of independent interest, and there will be many other useful applications beyond zero-knowledge.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint. Minor revision.
Keywords
bit commitmentquantum cryptographyzero knowledgecertified deletion
Contact author(s)
taiga hiroka @ yukawa kyoto-u ac jp
tomoyuki morimae @ yukawa kyoto-u ac jp
ryo nishimaki @ gmail com
takashi yamakawa obf @ gmail com
History
2021-09-30: received
Short URL
https://ia.cr/2021/1315
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2021/1315,
      author = {Taiga Hiroka and Tomoyuki Morimae and Ryo Nishimaki and Takashi Yamakawa},
      title = {Certified Everlasting Zero-Knowledge Proof for QMA},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1315},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/1315}},
      url = {https://eprint.iacr.org/2021/1315}
}
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