This paper proves that several interactive proof systems are zero-knowledge against general quantum attacks. This includes the well-known Goldreich–Micali–Wigderson classical zero-knowledge protocols for graph isomorphism and graph 3-coloring (assuming the existence of quantum computationally concealing commitment schemes in the second case). Also included is a quantum interactive proof system for a complete problem for the complexity class of problems having honest verifier quantum statistical zero-knowledge proofs, which therefore establishes that honest verifier and general quantum statistical zero-knowledge are equal: $\mathrm{QSZK}= \mathrm{QSZK}_{\mathrm{HV}}$. Previously no nontrivial interactive proof systems were known to be zero-knowledge against quantum attacks, except in restricted settings such as the honest verifier and common reference string models. This paper therefore establishes for the first time that true zero-knowledge is indeed possible in the presence of quantum information and computation.
This paper proves that several interactive proof systems are zero-knowledge against general quantum attacks. This includes the well-known Goldreich–Micali–Wigderson classical zero-knowledge protocols for graph isomorphism and graph 3-coloring (assuming the existence of quantum computationally concealing commitment schemes in the second case). Also included is a quantum interactive proof system for a complete problem for the complexity class of problems having honest verifier quantum statistical zero-knowledge proofs, which therefore establishes that honest verifier and general quantum statistical zero-knowledge are equal: QSZK=QSZKHV. Previously no nontrivial interactive proof systems were known to be zero-knowledge against quantum attacks, except in restricted settings such as the honest verifier and common reference string models. This paper therefore establishes for the first time that true zero-knowledge is indeed possible in the presence of quantum information and computation.
This paper proves that several interactive proof systems are zero-knowledge against general quantum attacks. This includes the well-known Goldreich-Micali-Wigderson classical zero-knowledge protocols for Graph Isomorphism and Graph 3-Coloring (assuming the existence of quantum computationally concealing commitment schemes in the second case). Also included is a quantum interactive protocol for a complete problem for the complexity class of problems having "honest verifier" quantum statistical zero-knowledge proofs, which therefore establishes that honest verifier and general quantum statistical zero-knowledge are equal: QSZK = QSZKHV. Previously no non-trivial proof systems were known to be zero-knowledge against quantum attacks, except in restricted settings such as the honest-verifier and common reference string models. This paper therefore establishes for the first time that true zero-knowledge is indeed possible in the presence of quantum information and computation.
This paper proves that several interactive proof systems are zero-knowledge against quantum attacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class HVQSZK, which comprises all problems having "honest verifier" quantum statistical zero-knowledge proofs. It is also proved that zero-knowledge proofs for every language in NP exist that are secure against quantum attacks, assuming the existence of quantum computationally concealing commitment schemes. Previously no non-trivial proof systems were known to be zero-knowledge against quantum attacks, except in restricted settings such as the honest-verifier and common reference string models. This paper therefore establishes for the first time that true zero-knowledge is indeed possible in the presence of quantum information and computation.
This paperprovesthat several interactiveproofsystems are zero-knowledgeagainstquantumattacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class QSZK HV , which comprises all problems having “honest verifier” quantum statistical zero-knowledge proofs. It is also proved that zero-knowledge proofs for every languagein NP exist that are secure against quantumattacks, assuming the existence of quantumcomputationally concealing commitment schemes. Previously no non-trivial problems were known to be zeroknowledge against quantum attacks, except in restricted settings such as the honest-verifierand common reference string models. This paper therefore establishes for the first time that true zero-knowledge is indeed possible in the presence of quantum information.
The concept of zero-knowledge (ZK) has become of fundamental importance in cryptography. However, in a setting where entities are modeled by quantum computers, classical arguments for proving ZK fail to hold since, in the quantum setting, the concept of rewinding is not generally applicable. Moreover, known classical techniques that avoid rewinding have various shortcomings in the quantum setting. We propose new techniques for building quantum zero-knowledge (QZK) protocols, which remain secure even under (active) quantum attacks. We obtain computational QZK proofs and perfect QZK arguments for any NP language in the common reference string model. This is based on a general method converting an important class of classical honest-verifier ZK (HVZK) proofs into QZK proofs. This leads to quite practical protocols if the underlying HVZK proof is efficient. These are the first proof protocols enjoying these properties, in particular the first to achieve perfect QZK. As part of our construction, we propose a general framework for building unconditionally hiding (trapdoor) string commitment schemes, secure against quantum attacks, as well as concrete instantiations based on specific (believed to be) hard problems. This is of independent interest, as these are the first unconditionally hiding string commitment schemes withstanding quantum attacks. Finally, we give a partial answer to the question whether QZK is possible in the plain model. We propose a new notion of QZK, non-oblivious verifier QZK, which is strictly stronger than honest-verifier QZK but weaker than full QZK, and we show that this notion can be achieved by means of efficient (quantum) protocols.
Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result representing a further quantum generalization of this fact, which is that every problem in the complexity class QMA has a quantum zero-knowledge proof system. More specifically, assuming the existence of an unconditionally binding and quantum computationally concealing commitment scheme, we prove that every problem in the complexity class QMA has a quantum interactive proof system that is zero-knowledge with respect to efficient quantum computations. Our QMA proof system is sound against arbitrary quantum provers, but only requires an honest prover to perform polynomial-time quantum computations, provided that it holds a quantum witness for a given instance of the QMA problem under consideration.
Interactive proof systems with a laconic prover, studied by Goldreich, Vadhan, and Wigderson (CC, 2002), capture problems verifiable with logarithmic prover communication in the classical setting. For two-message quantum analogs, even a single-bit prover response contains quantum statistical zero-knowledge (QSZK), introduced by Watrous (FOCS 2002). However, restricting the verifier's question to classical public coins collapses the corresponding class to BQP, as shown by Beigi, Shor, and Watrous (ToC, 2011).
We further study two-message quantum interactive proof systems with a laconic prover. To this end, we introduce the class QIPℓ-bit(2), where ℓ is the length of the prover's response, and establish:
1. A natural complete characterization of QIPℓ-bit(2) by Multi-State Distinguishability. In particular, Quantum State Distinguishability (QSD) is QIPbit-complete. Since QSD is QSZK-hard, our result places QIPℓ-bit(2), for ℓ≥2, in a landscape "just above" QSZK.
2. Easy regimes for QIPℓ-bit(2) collapsing to QSZK. We prove that QSD[a,b] (and thus QIPbit[a,b]) is in QSZK when a(n)−b(n)≥1/O(logn), and combine this with an answer compression from QIPℓ-bit[2,c,s] to QIPbit to obtain another easy regime when 2c>(1+2ℓ/2)s. Remarkably, our improved polarization applies to SD and SZK, resolving an open problem in Sahai and Vadhan (JACM, 2003).
3. Quantum public coins also make the interaction useless: qc-QAM[O(logn)] with constant gap is in BQP, where qc-QAM[ℓ] is a subclass of QIPℓ-bit(2) in which the verifier's question is exactly halves of EPR pairs.