General Properties of Quantum Zero-Knowledge Proofs

@inproceedings{Kobayashi2008GeneralPO,
  title={General Properties of Quantum Zero-Knowledge Proofs},
  author={Hirotada Kobayashi},
  booktitle={TCC},
  year={2008}
}
  • H. Kobayashi
  • Published in TCC 8 May 2007
  • Mathematics, Computer Science
This paper studies general properties of quantum zeroknowledge proof systems. Among others, the following properties are proved on quantum computational zero-knowledge proofs: - Honest-verifier quantum zero-knowledge equals general quantum zero-knowledge. - Public-coin quantum zero-knowledge equals general quantum zeroknowledge. - Quantum zero-knowledge with perfect completeness equals general quantum zero-knowledge with imperfect completeness. - Any quantum zero-knowledge proof system can be… 
Analysis of Quantum Multi-Prover Zero-Knowledge Systems: Elimination of the Honest Condition and Computational Zero-Knowledge Systems for QMIP
TLDR
The LHI protocol makes previous research for Local Hamiltonians applicable to check the history state of interactive proofs, and Broadbent et al.'s zero-knowledge protocol for QMA \cite{BJSW} to quantum multi-prover systems in order to obtain the second result.
Complete Problem for Perfect Zero-Knowledge Quantum Proof
  • Jun Yan
  • Computer Science, Mathematics
    SOFSEM
  • 2012
TLDR
This paper proves that (promise) problem Quantum State Identicalness (abbreviated QSI) is essentially complete for perfect zero-knowledge quantum interactive proof (QPZK).
Increasing the power of the verifier in Quantum Zero Knowledge
TLDR
This paper studies what happens when an honest verifier is allowed to flip some coins in addition to using unitary operations, and shows that Quantum Statistical Zero Knowledge where the verifier applies any non-unitary operation is equal to Quantum Zero-Knowledge where theVerifier uses only unitaries.
Making Classical Honest Verifier Zero Knowledge Protocols Secure against Quantum Attacks
We show that any problem that has a classical zero-knowledge protocol against the honest verifier also has, under a reasonable condition, a classical zero-knowledge protocol which is secure against
Quantum Bit Commitment with Application in Quantum Zero-Knowledge Proof (Extended Abstract)
TLDR
This paper showed that plugging quantum bit commitment scheme into the GMW-type construction of zero- knowledge also gives a quantum zero-knowledge proof, as one expects, and proposed a formalization of non-interactive quantum bit commit scheme, which may come in handy in other places.
Witness-Indistinguishability Against Quantum Adversaries 6 . 845 Quantum Complexity Theory – Project Report
TLDR
This report characterize witness-indistinguishability against quantum adversaries and surveys the main results of research aimed at characterizing what happens to zero-knowledge when quantum adversaries are possible.
Quantum Proofs
TLDR
An overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define is provided.
Quantum Information and Variants of Interactive Proof Systems
TLDR
The expressive power of quantum interactiveProof systems is exactly PSPACE, the class of problems that can be solved by a polynomial-space deterministic Turing machines and that also admit a classical interactive proof systems, and both the models are equivalent in terms of complexity-theoretic characterization.
General Properties of Quantum Bit Commitments
  • Jun Yan
  • Computer Science, Physics
  • 2022
TLDR
The question of whether canonical quantum bit commitment schemes exist is interesting in its own right in quantum complexity theory and may serve as an alternative foundation of complexity-based quantum cryptography.
Witness indistinguishability and witness hiding against quantum attacks
  • Huiqin Xie, Li Yang
  • Computer Science, Mathematics
    IET Inf. Secur.
  • 2019
TLDR
The authors study the witness indistinguishability (WI) and witness hiding (WH) of proof systems against quantum adversaries and construct a quantum-secure signature scheme in the CRS model that remains secure even if a common random string is used to sign polynomially many messages.
...
...

References

SHOWING 1-10 OF 59 REFERENCES
Zero-knowledge against quantum attacks
  • J. Watrous
  • Mathematics, Computer Science
    STOC '06
  • 2006
TLDR
This paper proves that several interactive proof systems are zero-knowledge against general quantum attacks and establishes for the first time that true zero- knowledge is indeed possible in the presence of quantum information and computation.
Limits on the power of quantum statistical zero-knowledge
  • J. Watrous
  • Computer Science, Mathematics
    The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
TLDR
A definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems is proposed and the resulting complexity class is studied, which is denote QSZK/sub HV/.
Non-interactive Quantum Perfect and Statistical Zero-Knowledge
TLDR
It is shown that sharing randomness or entanglement is necessary for non-trivial protocols of non-interactive quantum perfect and statistical zero-knowledge proof systems and the Graph Non-Automorphism problem is shown to have a non-Interactive quantumperfect zero- knowledge proof system.
Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge
We show how to transform any interactive proof system which is statistical zero-knowledge with respect to the honest-verifier, into a proof system which is statistical zero-knowledgewith respect to
An unconditional study of computational zero knowledge
  • S. Vadhan
  • Mathematics, Computer Science
    45th Annual IEEE Symposium on Foundations of Computer Science
  • 2004
TLDR
To enable this combination, it is proved that every problem in CZK can be decomposed into a problem in SZK together with a set of instances from which a one-way function can be constructed.
Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems
In this paper the generality and wide applicability of Zero-knowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs
Parallelization, amplification, and exponential time simulation of quantum interactive proof systems
TLDR
It is proved that any polynomial-round quan tum interactiveProof system with two-sided bounded error can be parallelized to a quantum interactive proof system with exponentially small one-sided error, in which the prover and verifier exchange only 3 messages.
The complexity of perfect zero-knowledge
  • L. Fortnow
  • Computer Science, Mathematics
    Adv. Comput. Res.
  • 1989
TLDR
It is shown that knowledge complexity can be used to show that a language is easy to prove and that there are not any perfect zero-knowledge protocols for NP-complete languages unless the polynomial time hierarchy collapses.
Comparing entropies in statistical zero knowledge with applications to the structure of SZK
  • Oded Goldreich, S. Vadhan
  • Mathematics, Computer Science
    Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
  • 1999
TLDR
An alternative proof of Okamoto's result by which HVSZK: (i.e., honest-verifier statistical zero knowledge) equals public-coin HVSzK is obtained, and an equivalence of a weak notion of statisticalzero knowledge to the standard one is obtained.
Zero-Knowledge twenty years after its invention
  • Oded Goldreich
  • Computer Science, Mathematics
    Electron. Colloquium Comput. Complex.
  • 2002
TLDR
The main deenitions and results regarding zero-knowledge proofs are surveyed, the basic deenitional approach and its variants are presented, results regarding the power of zero- knowledge proofs are presented as well as recent results regarding questions such as the composeability of Zero Knowledge proofs.
...
...