dorsal/arxiv
View SchemaNon-Interactive Quantum Statistical and Perfect Zero-Knowledge
| Authors | Hirotada Kobayashi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207158 |
| URL | https://arxiv.org/abs/quant-ph/0207158 |
Abstract
This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of non-interactive quantum perfect and statistical zero-knowledge. It is also shown that, with sharing EPR pairs a priori, the class of languages having one-sided bounded error non-interactive quantum perfect zero-knowledge proof systems has a natural complete problem. Non-triviality of such a proof system is based on the fact proved in this paper that the Graph Non-Automorphism problem, which is not known in BQP, can be reduced to our complete problem. Our results may be the first non-trivial quantum zero-knowledge proofs secure even against dishonest quantum verifiers, since our protocols are non-interactive, and thus the zero-knowledge property does not depend on whether the verifier in the protocol is honest or not. A restricted version of our complete problem derives a natural complete problem for BQP.
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"abstract": "This paper introduces quantum analogues of non-interactive perfect and\nstatistical zero-knowledge proof systems. Similar to the classical cases, it is\nshown that sharing randomness or entanglement is necessary for non-trivial\nprotocols of non-interactive quantum perfect and statistical zero-knowledge. It\nis also shown that, with sharing EPR pairs a priori, the class of languages\nhaving one-sided bounded error non-interactive quantum perfect zero-knowledge\nproof systems has a natural complete problem. Non-triviality of such a proof\nsystem is based on the fact proved in this paper that the Graph\nNon-Automorphism problem, which is not known in BQP, can be reduced to our\ncomplete problem. Our results may be the first non-trivial quantum\nzero-knowledge proofs secure even against dishonest quantum verifiers, since\nour protocols are non-interactive, and thus the zero-knowledge property does\nnot depend on whether the verifier in the protocol is honest or not. A\nrestricted version of our complete problem derives a natural complete problem\nfor BQP.",
"arxiv_id": "quant-ph/0207158",
"authors": [
"Hirotada Kobayashi"
],
"categories": [
"quant-ph",
"cs.CC"
],
"title": "Non-Interactive Quantum Statistical and Perfect Zero-Knowledge",
"url": "https://arxiv.org/abs/quant-ph/0207158"
},
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