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arXiv:2309.15856 · IEEE Transactions on Circuits and Systems I Regular Papers

Secure and Efficient Two-Party Quantum Scalar Product Protocol With Application to Privacy-Preserving Matrix Multiplication

Wenjie Liu, Zixian Li

Published Jul 21, 2023• 18 citations
arXivHTMLPDF

Abstract

Secure two-party scalar product (S2SP) is a promising research area within secure multiparty computation (SMC), which can solve a range of SMC problems, such as intrusion detection, data analysis, and geometric computations. However, existing quantum S2SP protocols are not efficient enough, and the complexity is usually close to exponential level. In this paper, a novel secure two-party quantum scalar product (S2QSP) protocol based on Fourier entangled states is proposed to achieve higher efficiency. Firstly, the definition of unconditional security under malicious models is given. And then, an honesty verification method called Entanglement Bondage is proposed, which is used in conjunction with the modular summation gate to resist malicious attacks. The property of Fourierentangled states is used to calculate the scalar product with polynomial complexity. The unconditional security of our protocol is proved, which guarantees the privacy of all parties. In addition, we design a privacy-preserving quantum matrix multiplication protocol based on S2QSP protocol. By transforming matrix multiplication into a series of scalar product processes, the product of two private matrices is calculated without revealing any privacy. Finally, we show our protocol’s feasibility in IBM Qiskit simulator.

DOI
10.1109/tcsi.2023.3295891

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Abstract With the rapid development of distributed collaborative computing, privacy leakage risks in multi-source data joint analysis are increasing, and classical secure scalar product (SSP) protocols are vulnerable to quantum attacks. Existing quantum secure scalar product schemes mostly rely on complex quantum resources or third parties, only support two-party computation, and have poor scalability. To address these issues, this paper proposes a secure multi-party quantum scalar product protocol based on single-photon resources without a third party. The protocol adopts a two-layer architectural design, integrating pairwise secure product operation and privacy-preserving aggregation mechanism. It realizes result blinding via data splitting and reconstruction to fully guarantee data confidentiality. By adopting ring interaction structure and lightweight secure computing modes, it completes collaborative computation of multi-party private data and effectively prevents information leakage in interactive processes. Performance analysis shows that the protocol requires no more than single-photon and single-particle measurements, with complexity within a reasonable range, making it feasible with current quantum technology. This protocol provides an efficient and secure primitive for multi-party privacy-preserving collaborative computing in quantum-resistant scenarios.
With the rapid expansion of the digital economy and smart grids, secure and fair pricing mechanisms have become essential for data trading. However, existing approaches remain vulnerable to quantum attacks, exhibit poor scalability in multi-party settings, and demand high resource consumption. To overcome these limitations, we introduce, for the first time, a Quantum Secure Joint Pricing (QSJP) mechanism, which supports multi-party joint pricing and ensures fair and privacy-preserving pricing in power data trading while protecting participants’ sensitive information and incentivizing their active participation. At the core of QSJP, we propose a novel Secure Multi-Party Quantum Scalar Product (SMQSP) protocol, supported by a Secure Multi-Party Quantum Summation (SMQS) scheme that enables privacy-preserving and efficient aggregation of intermediate results. The SMQSP protocol leverages Fourier entangled states and GHZ states to achieve scalable and efficient scalar product computation with polynomial complexity. We further validate the correctness and practicality of the proposed framework through circuit simulations on IBM Qiskit.
The quantum secure multiparty multiplication (QSMM) protocol aims to leverage the advantages of quantum computing to ensure data privacy and security in multiparty computation, preventing information from being leaked and protecting privacy against malicious attacks. However, current QSMM protocols suffer from high resource consumption and computation complexity in particle preparation and participant computation stages. In view of this, a QSMM protocol based on single particles is proposed in this paper. The proposed protocol utilizes high-dimensional single particles as information carriers, and the optimized quantum multiplication circuit is employed to embed the participants’ secret message and perform the multiplication. All participants collaboratively generate a blind matrix, and each column product of the blind matrix acts as the participant’s private key for the blinding of the secret value. Unlike other protocols that use decoy particles for eavesdropping detection, the proposed protocol leverages the properties of mutually unbiased basis particles to ensure its security, while reducing quantum resource consumption and the quantum capabilities required from the participants. Security analysis demonstrates that the proposed protocol can effectively resist attacks from external eavesdroppers and internal participants, and performance analysis shows that the proposed protocol achieves superior execution efficiency compared to other similar protocols.
Abstract Secure multiparty computation (SMC) provides collaboration among multiple parties, ensuring the confidentiality of their private information. However, classical SMC implementations encounter significant security and efficiency challenges. Resorting to the entangled Greenberger–Horne–Zeilinger (GHZ) state, we propose a quantum-based two-party protocol to compute binary Boolean functions, with the help of a third party. We exploit a technique in which a random Z-phase rotation on the GHZ state is performed to achieve higher security. The security and complexity analyses demonstrate the feasibility and improved security of our scheme compared to other SMC Boolean function computation methods. Additionally, we implemented the proposed protocol on the IBM QisKit and found consistent outcomes that validate the protocol’s correctness.
Secure multiparty computation is a very important research topic in cryptography. The sub-problem of secure multiparty computation that has received special attention by researchers because of its close relation to many cryptographic tasks is secure two-party computation. This area of research is concerned with the question: ldquoCan two party computation be achieved more efficiently and under weaker security assumptions than general multiparty computation?rdquo Yaopsilas protocol provided security against passive adversaries, while Lindell and Pinkas proposed secure two party protocols that are secure against active adversaries. In this paper, we would like to propose a set of information theoretically secure protocols based on scalar product protocol. The detailed complexity analysis is also provided.
Abstract Quantum secure multiparty computation occupies an important place in quantum cryptography. Based on access structure and linear secret sharing, we propose a new general quantum secure multiparty computation protocol for simultaneous summation and multiplication in a high-dimensional quantum system. In our protocol, each participant within any authorized sets only needs to perform local Pauli operation once on the generalized Bell state, then the summation and multiplication results can be output simultaneously, which improves the practicality of the protocol. Moreover, in the privacy computation phase, the decoy particle detection technique as well as the addition of random numbers are applied to blind the privacy information, making our protocol higher privacy protection. Security analysis shows that our protocol is resistant to a series of typical external attacks and dishonest internal participant attacks such as individual attack and collusion attack. Finally, compared with the existing protocols, our protocol not only has higher efficiency but also lower consumption.