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Simpósio Brasileiro de Cibersegurança (SBSeg)

Non-Interactive Quantum Zero-Knowledge: Scope, Limits, and the Cost of Shared Entanglement in Authentication Protocols

Éricles Antônio Aquiles Barbosa Lima

Published Sep 1, 2026• 0 citations
Publisher

Abstract

Non-interactive quantum statistical zero-knowledge (NIQSZK), introduced by Kobayashi in 2002 via shared EPR pairs replacing a classical common reference string, is often invoked as a general tool for quantum-native authentication, but the term spans results of very different scope. We give an account of what Kobayashi’s model actually establishes – non-interactive proofs for one promise problem, Quantum State Closeness to Identity, and, by reduction, Graph Non-Automorphism – and contrast it with the independent, more recent line achieving non-interactive zero-knowledge arguments for all of QMA from quantum-hardness of Learning With Errors (LWE). Using a Software-Defined Quantum Network (SDQN) control-plane authentication case study, we compare the realistically available proof systems along a resource-cost model grounded in published entanglement-distribution benchmarks and lattice-parameter estimation, and argue classical post-quantum NIZK dominates unless the credential itself is an inherently quantum object.

DOI
10.5753/sbseg_estendido.2026.32870

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Non-interactive quantum statistical zero-knowledge (NIQSZK), introduced by Kobayashi in 2002 via shared EPR pairs replacing a classical common reference string, is often invoked as a general tool for quantum-native authentication, but the term spans results of very different scope. We give an account of what Kobayashi’s model actually establishes – non-interactive proofs for one promise problem, Quantum State Closeness to Identity, and, by reduction, Graph Non-Automorphism – and contrast it with the independent, more recent line achieving non-interactive zero-knowledge arguments for all of QMA from quantum-hardness of Learning With Errors (LWE). Using a Software-Defined Quantum Network (SDQN) control-plane authentication case study, we compare the realistically available proof systems along a resource-cost model grounded in published entanglement-distribution benchmarks and lattice-parameter estimation, and argue classical post-quantum NIZK dominates unless the credential itself is an inherently quantum object.
We study non-interactive zero-knowledge proofs (NIZKs) for NP satisfying: 1) statistical soundness, 2) computational zero-knowledge (ZK) and 3) certified-everlasting zero-knowledge (CE-ZK). The CE-ZK property allows a verifier of a quantum proof to revoke the proof in a way that can be checked (certified) by the prover. Conditioned on successful certification, the verifier's state can be efficiently simulated with only the statement, in a statistically indistinguishable way. Our contributions regarding these certified-everlasting NIZKs (CE-NIZKs) are as follows: - We identify a barrier to obtaining CE-NIZKs in the CRS model via generalizations of known interactive ZK proofs that satisfy CE-ZK. - We circumvent this by constructing CE-NIZK using non-black-box use of NIZK for NP satisfying certain properties, along with OWFs. As a result, we obtain CE-NIZKs for NP in the CRS model, based on polynomial hardness of the learning with errors (LWE) assumption. - In addition, we observe that the aforementioned barrier does not apply to the shared EPR model. We leverage this to construct CE-NIZK for NP in this model based on any statistical binding hidden bits generator, which is known from LWE. The only quantum computation here involves single-qubit measurements of the EPR pairs.
We initiate the study of non-interactive zero-knowledge (NIZK) arguments for languages in QMA. Our first main result is the following: if Learning With Errors (LWE) is hard for quantum computers, then any language in QMA has an NIZK argument with preprocessing. The preprocessing in our argument system consists of (i) the generation of a CRS and (ii) a single (instance-independent) quantum message from verifier to prover. The instance-dependent phase of our argument system involves only a single classical message from prover to verifier. Importantly, verification in our protocol is entirely classical, and the verifier needs not have quantum memory; its only quantum actions are in the preprocessing phase. Our second contribution is to extend the notion of a classical proof of knowledge to the quantum setting. We introduce the notions of arguments and proofs of quantum knowledge (AoQK/PoQK), and we show that our non-interactive argument system satisfies the definition of an AoQK. In particular, we explicitly construct an extractor which can recover a quantum witness from any prover which is successful in our protocol. Finally, we show that any language in QMA has an (interactive) proof of quantum knowledge.
We present the first non-interactive zero-knowledge argument system for QMA with multi-theorem security. Our protocol setup constitutes an additional improvement and is constructed in the malicious designated-verifier (MDV-NIZK) model (Quach, Rothblum, and Wichs, EUROCRYPT 2019), where the setup consists of a trusted part that includes only a common uniformly random string and an untrusted part of classical public and secret verification keys, which even if sampled maliciously by the verifier, the zero knowledge property still holds. The security of our protocol is established under the Learning with Errors Assumption. Our main technical contribution is showing a general transformation that compiles any sigma protocol into a reusable MDV-NIZK protocol, using NIZK for NP. Our technique is classical but works for quantum protocols and allows the construction of a reusable MDV-NIZK for QMA.
We propose the first generalization of the famous Non-Interactive Zero-Knowledge (NIZK) proofs to quantum languages (NIZKoQS) and we provide a protocol to prove advanced properties on a received quantum state non-destructively and non-interactively (a single message being sent from the prover to the verifier). In our second orthogonal contribution, we improve the costly Remote State Preparation protocols [Cojocaru et al. 2019 ; Gheorghiu and Vidick 2019 ] that can classically fake a quantum channel (this is at the heart of our NIZKoQS protocol) by showing how to create a multi-qubit state from a single superposition. Finally, we generalize these results to a multi-party setting and prove that multiple parties can anonymously distribute a GHZ state in such a way that only participants knowing a secret credential can share this state, which could have applications to quantum anonymous transmission, quantum secret sharing, quantum onion routing and more.
In a proof of knowledge (PoK), a verifier becomes convinced that a prover possesses privileged information. In combination with zero-knowledge proof systems, PoKs play an important role in security protocols such as in digital signatures and authentication schemes, as they enable a prover to demonstrate possession of certain information (such as a private key or a credential), without revealing it. A PoK is formally defined via the existence of an extractor, which is capable of reconstructing the key information that makes a verifier accept, given oracle access to any accepting prover. We extend this concept to the setting of a single classical verifier and multiple quantum provers and present the first statistical zero-knowledge (ZK) PoK proof system for problems in QMA. To achieve this, we establish the PoK property for the ZK protocol of Broadbent, Mehta, and Zhao (TQC 2024), which applies to the local Hamiltonian problem. More specifically, we construct an extractor which, given oracle access to a provers' strategy that leads to high acceptance probability, is able to reconstruct the ground state of a local Hamiltonian. Our result can be seen as a new form of self-testing, where, in addition to certifying a pre-shared entangled state, the verifier also certifies that provers have access to a quantum system, in particular, a ground state; this indicates a new level of verification for a proof of quantumness.
We propose the first generalization of the famous Non-Interactive Zero-Knowledge (NIZK) proofs to quantum languages (NIZKoQS) and we provide a protocol to prove advanced properties on a received quantum state non-destructively and non-interactively (a single message being sent from the prover to the verifier). In our second orthogonal contribution, we improve the costly Remote State Preparation protocols [CCKW18,CCKW19,GV19] that can classically fake a quantum channel (this is at the heart of our NIZKoQS protocol) by showing how to create a multi-qubits state from a single superposition. Finally, we generalize these results to a multi-party setting and prove that multiple parties can anonymously distribute a GHZ state in such a way that only participants knowing a secret credential can share this state, which could have applications to quantum anonymous transmission, quantum secret sharing, quantum onion routing and more.