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Physica Scripta

A three-party verifiable blind quantum computing protocol with separated input and function ownership

Yinqi Feng, Ri‐Gui Zhou, Ran Guo, Jun-Kai Shan, Run-Han Zhao

Published Aug 28, 2026• 0 citations
Publisher

Abstract

Abstract Blind quantum computing enables quantum-limited clients to securely access untrusted quantum servers. This paper proposes a three-party verifiable blind quantum computing protocol with separated input and function ownership, where Alice holds the private input, Bob holds the target function, and Charlie performs the delegated quantum computation, with the result released only to Alice. Alice and Bob first establish a shared key using BB84. Under the measurement-based quantum computing framework, a secure two-party computation protocol is then used to jointly generate adaptive blinded measurement instructions, eliminating the need for Bob to transmit quantum states to Charlie. A hidden dummy-trap mechanism is further incorporated to verify malicious server behavior. Under the honest-but-curious client model without client-server collusion, the protocol protects input and function privacy while ensuring computation blindness, shared-key security, and verifiability. Most quantum operations are performed by Charlie, while the clients require only limited quantum capabilities.

DOI
10.1088/1402-4896/aea030

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Abstract Blind quantum computing enables quantum-limited clients to securely access untrusted quantum servers. This paper proposes a three-party verifiable blind quantum computing protocol with separated input and function ownership, where Alice holds the private input, Bob holds the target function, and Charlie performs the delegated quantum computation, with the result released only to Alice. Alice and Bob first establish a shared key using BB84. Under the measurement-based quantum computing framework, a secure two-party computation protocol is then used to jointly generate adaptive blinded measurement instructions, eliminating the need for Bob to transmit quantum states to Charlie. A hidden dummy-trap mechanism is further incorporated to verify malicious server behavior. Under the honest-but-curious client model without client-server collusion, the protocol protects input and function privacy while ensuring computation blindness, shared-key security, and verifiability. Most quantum operations are performed by Charlie, while the clients require only limited quantum capabilities.
Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness), and the correctness of the computation is verifiable by the client despite her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum computing. If the input of the client's quantum computing is a quantum state, whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a protocol of measurement-only verifiable blind quantum computing where the correctness of the quantum input is also verifiable.
The characteristics of BQC is that it enables a client with less quantum abilities to delegate her quantum computation to a server with strong quantum computablities while keeping the client's privacy. In this article, we study single client-server BQC based on measurement which is verifiable. In detail, the verifiability is that the client Alice can obtain the correct measurement results if the server Bob is honest, while Bob does not get nothing of Alice's secret information if he is malicious. We construct a latticed state, composed of six-qubit cluster states and eight-qubit entangled states, to realize Alice's quantum computing. In this proposed protocol, the cilent Alice prepares and sends initial single-qubit states to Bob, where the initial states include useful qubits and trap qubits. And then Bob performs controlled-Z gate to produce the entanglement and returns them to Alice. Alice will send trap qubits and useful qubits to Bob randomly and Bob returns all measurement results to her. Alice makes a comparison for trap qubits between true results and Bob's results to check the honesty of Bob. In a word, the trap qubtis have two purposes: 1) confusing Bob to keep the blindness; 2)verifying the honesty of Bob and correctness of Bob's quantum computing. There has an important feature that Alice does not need to encrypt the computing angles by rπr\pirπ (r∈{0,1}\in\{0,1\}∈{0,1}), meanwhile the blindness and correctness can also be ensured. That is, Alice's computing results don't need to flipped since Bob is not impossible know anything about the quantum computation. Our work gives a better understanding for verifiable BQC based on measurement.
Abstract Most existing blind quantum computation protocols involve a client and a server or multiple servers. The case of multiple clients needs to be explored as well, but it becomes less secure as more people are involved. Authentication helps to solve the problem by enabling clients and servers to verify each other’s identity. In this paper, a multi-party verifiable blind quantum computation protocol with mutual authenti-cation is proposed which consists of three phases. Firstly, we improve the method for generating keys. Based on this, a deterministic method is proposed to generate authentication keys. Then, the client and the server perform mutual authentication. Finally, the only requirement for the client is to perform the gate S to accomplish the quantum computing task. The proposed protocol can resist both insider and outsider attacks, ensuring the legitimacy of clients and servers in a quantum network. The protocol further also limits the client’s quantum power and allows the client to verify the accuracy of the calculation results.
Blind quantum computation (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computational tasks to remote quantum servers while keeping their own data private. In this paper, we first propose three multi-party verifiable blind quantum computation (MPVBQC) protocols, each of which can handle one type of clients with certain simple quantum capabilities such as making single-qubit measurements, preparing single qubits, or performing a few single-qubit gates. Then a flexible and hybrid MPVBQC framework for multi-type clients in quantum networks is given by combining the three proposed MPVBQC protocols. It simultaneously allows at least three types of clients in quantum networks to achieve BQC depending on their own quantum devices. Furthermore, all the proposed protocols can achieve identity authentication, resist both insider and outsider attacks, and be verifiable which means that the clients can verify the correctness of their computational results.
We construct a multi-Client verifiable blind delegated quantum computing (VBDQC) protocol in which M classical Verifier Clients jointly delegate a public quantum circuit acting on their combined private inputs to two quantum-capable Provers sharing entanglement but having no direct communication channel. We begin by modifying the single-Client, entanglement-based CGJV Verifier-on-a-Leash protocol. We then prove simulator-based blind verifiability for the modified protocol using the abstract/constructive cryptography framework. We adapt the DFPR upward-reduction chain to the two-Prover setting, constructing a no-direct-communication simulator architecture. We then extend the CGJV protocol to M Clients using classical multiparty computation techniques, preserving the single-Client guarantees of completeness, soundness, and blindness while additionally guaranteeing input privacy between Clients. Security is analyzed under a threat model that allows a subset of Clients to collude with one but not both of the Provers, which do not communicate even after the protocol execution.
Quantum computing has considerable advantages in solving some problems over its classical counterpart. Currently various physical systems are developed to construct quantum computers but it is still challenging and the first use of quantum computers may adopt the cloud style. Blind quantum computing (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computation to remote quantum servers while keeping input, output, and even algorithm private. In this paper, we propose three multi-party verifiable blind quantum computing (VBQC) protocols with identity authentication to handle clients with varying quantum capabilities in quantum networks, such as those who can just make measurements, prepare single qubits, or perform a few single-qubit gates. They are client-friendly and flexible since the clients can achieve BQC depending on their own quantum devices and resist both insider outsider attacks in quantum networks. Furthermore, all the three proposed protocols are verifiable, namely that the clients can verify the correctness of their calculations.