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EPJ Quantum Technology

Quantum secure multiparty multiplication based on d-level single particles

Xiuli Song, Jie Yan, You-Sheng Zhou, Tao Wu

Published Dec 31, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1140/epjqt/s40507-025-00356-z

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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.
Most of the existing quantum secure multiparty multiplications use entangled states to carry secret information. However, the preparation of these quantum states is difficult. In order to solve this problem, a single-particle secure multiparty product protocol based on a d-level Lagrange unitary operator is proposed. In this protocol, a semi-honest third party (Server) and each participant share a private key. The participant first uses the private key and random number to multiply his own secret integer with module d, and then he uses Lagrange unitary operator to encode the calculation result into an unbiased basis particle. The server obtains the encoded information by measuring the particle sent back by each participant. Finally, the server uses the module d product of all the random numbers sent by the participant’s representative to calculate the product corresponding to the secret integers of multiple participants. Performance analysis shows that, compared with similar protocols, the proposed protocol requires less of the entity’s quantum computing capabilities. In terms of security, this protocol can resist both external and internal attacks. Finally, the proposed protocol uses the Q# quantum programming language combined with Python language to simulate and verify its correctness.
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.
As an important subtopic of classical cryptography, secure multiparty quantum computation allows multiple parties to jointly compute their private inputs without revealing them. Most existing secure multiparty computation protocols have the shortcomings of low computational efficiency and high resource consumption. To remedy these shortcomings, we propose a secure multiparty quantum computation protocol by using the Lagrange unitary operator and the Shamir (t, n) threshold secret sharing, in which the server generates all secret shares and distributes each secret share to the corresponding participant, in addition, he prepares a particle and sends it to the first participant. The first participant performs the Lagrange unitary operation on the received particle, and then sends the transformed particle to the next participant. Until the last participant's computation task is completed, the transformed particle is sent back to the server. The server performs Lagrange unitary operation on the received particle by using a secret message, and then measures the transformed particle to obtain the sum of the calculations of multiple participants. Security analysis shows that the proposed protocol can resist intercept-measurement attack, intercept-resend attack, entanglement-swapping attack, entanglement-measurement attack and collusion attack. Performance comparison shows that it has higher computation efficiency and lower resource consumption than other similar protocols.
Blind millionaire (BM) problem is an extended version of the initial millionaire problem required to compare the sum of the participants’ secrets between different groups. As a new topic of quantum secure multiparty computing, existing protocols with some special entangled states may not be easily achieved in practice. This study proposes a non-entangled method of solving the quantum blind millionaire (QBM) problem with special d-level single-particle states for the first time. To protect the confidentiality of transmission secrets, this protocol exploits the property of randomly generated d-level single-particle states. Furthermore, simple shift operations are used to encode the respective secrets. Detailed security analysis demonstrates that this protocol is impervious to internal and external threats. The presented methods can not only be used to solve the blind millionaire problem but also be used as a basic module to solve other secure multiparty computing problems.
With the rapid advancement of information technology, data sharing has become increasingly accessible, leading to a heightened need for robust personal data protection. One important application in privacy-preserving computing is the aggregation of information when collaboratively establishing AI models through public distributed networks. To counter the threat posed by quantum computing to encrypted data, various quantum private summation (QPS) protocols have been proposed thus far. However, some of these existing protocols operate solely under modulo 2, while other approaches for modulo d often rely on impractically high-dimensional qudits. Therefore, this study proposes an innovative multiparty QPS method that balances participant data sharing and privacy without requiring high-dimensional photons. The proposed QPS protocol enables participants to contribute aggregated information to third parties without disclosing individual data. A security analysis further demonstrates that the proposed QPS effectively counters common eavesdropping attacks, ensuring reliable protection of personal data.
Secure multiparty computing is an important class of cryptographic primitives and is widely used in electronic voting, data mining, blockchain, cloud computing and other fields. In this paper, we propose an efficient secure multiparty quantum computation protocol based on quantum entanglement and the Euler theorem. In this protocol, all participants can safely compute multivariate polynomial functions with the help of a semitrusted third party. A performance analysis shows that the protocol is correct and can resist some common external and internal attacks. Additionally, the proposed protocol not only improves particle detection efficiency but also effectively reduces the communication complexity.