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arXiv:2201.03496 · Globecom

Private Set Intersection with Delegated Blind Quantum Computing

Michele Amoretti

Published Dec 1, 2021• 3 citations
arXivHTMLPDF

Abstract

Private set intersection is an important problem with implications in many areas, ranging from remote diagnostics to private contact discovery. In this work, we consider the case of two-party PSI in the honest-but-curious setting. We propose a protocol that solves the server-aided PSI problem using delegated blind quantum computing. More specifically, the proposed protocol allows Alice and Bob (who do not have any quantum computational resources or quantum memory) to interact with Steve (who has a quantum computer) in order for Alice and Bob to obtain set intersection such that privacy is preserved. In particular, Steve learns nothing about the clients' input, output, or desired computation. The proposed protocol is correct, secure and blind against a malicious server, and characterized by a quantum communication complexity that is linear in the input size.

DOI
10.1109/globecom46510.2021.9685125

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Private set intersection is an important problem with implications in many areas, ranging from remote diagnostics to private contact discovery. In this work, we consider the case of two-party PSI in the honest-but-curious setting. We propose a protocol that solves the server-aided PSI problem using delegated blind quantum computing. More specifically, the proposed protocol allows Alice and Bob (who do not have any quantum computational resources or quantum memory) to interact with Steve (who has a quantum computer) in order for Alice and Bob to obtain set intersection such that privacy is preserved. In particular, Steve learns nothing about the clients' input, output, or desired computation. The proposed protocol is correct, secure and blind against a malicious server, and characterized by a quantum communication complexity that is linear in the input size.
Blind quantum computation (BQC) protocol allows a client having partial quantum ability to delegate his quantum computation to a remote quantum server without leaking any information about the input, the output and the intended computation to the server. Several BQC protocols have been proposed, e.g., Li et al. in [1] proposed a triple-server BQC protocol and Xu et al. in [2] proposed a single-server BQC protocol. Though both papers claimed that their protocols can satisfy the requirement of privacy, this paper points out a security loophole in their protocols. With that the server can reveal the private information of the client.
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.
Recently, we proposed a quantum solution to the problem of private set intersection cardinality (PSI-CA) (Information Sciences 370–371 (2016) 147–158). Compared to classical solutions, the proposed quantum PSI-CA protocol achieves an exponential reduction in communication complexity, since it only needsO(1)O(1)O(1)communication cost. However, this protocol requires two additional assumptions about the cardinalities of the sets, which may limit its wider applications. In this paper, we successfully discard these assumptions and present a stronger quantum PSI-CA protocol without any limitation. The new protocol ensures the parties’ private security, i.e., unconditionally secure server privacy and statistically secure client privacy, and it achieves the constant computation and communication complexities, which are independent of the size of the sets. Therefore, it is more suitable for practical applications with big data sets.
Private set intersection (PSI) is a cryptographic primitive that allows two or more parties to learn the intersection of their input sets and nothing else. In this paper, we introduce a new secure multi-party quantum computation for the greatest common divisor (GCD) and a PSI protocol based on it. The protocol extends the recent least common multiple (LCM)-based quantum private set union protocol by Liu et al. Performance analysis verifies the correctness and demonstrates the entire security of the suggested protocols in the semi-honest model. Additionally, it has been demonstrated that the complexity is efficient in terms of the input set size.
Blind quantum computing protocols enable a client, who can generate or measure single-qubit states, to delegate quantum computing to a remote quantum server protecting the client's privacy (i.e., input, output, and program). With current technologies, generations or measurements of single-qubit states are not too much burden for the client. In other words, secure delegated quantum computing is possible for ``almost classical" clients. However, is it possible for a ``completely classical" client? Here we consider a one-round perfectly-secure delegated quantum computing, and show that the protocol cannot satisfy both the correctness (i.e., the correct result is obtained when the server is honest) and the perfect blindness (i.e., the client's privacy is completely protected) simultaneously unless BQP is in NP. Since BQP is not believed to be in NP, the result suggests the impossibility of the one-round perfectly-secure delegated quantum computing.
Private Set Intersection Cardinality (PSI-CA) is one of the most concerned issues with the protection of privacy, in which two parties jointly compute the intersection cardinality without revealing their respective private sets. There are important applications of PSI-CA in real society, e.g., strongly privacy-preserving data statistics in contact tracing for health authorities to fight the outbreaks of highly contagious diseases. In this paper, we present a novel quantum PSI-CA protocol, in which we adopt oblivious quantum key distribution, secure quantum summation and quantum counting algorithm. The proposed PSI-CA protocol not only ensures the approximatively perfect security but also achieves the linear communication complexity, i.e.,O(N){O(N)}O(N). Furthermore, we define a new privacy protection problem, i.e., Privacy-preserving Condition Query (PCQ), and provide an efficient solution to the PCQ problem based on the proposed quantum PSI-CA protocol. Finally, we verify the correctness and the feasibility of the proposed quantum PSI-CA protocol by circuit simulations in IBM Qiskit.