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Journal of Physics A Mathematical and Theoretical

Verifiable quantum protocol for dynamic secure multiparty summation based on homomorphic encryption *

Mei Luo, Feixiang Li, Li Liu, Shixin Zhu

Published Feb 21, 2024• 1 citation
Publisher

Abstract

Abstract The research of quantum secure multiparty computation is a subject of great importance in modern cryptography. In this study, we construct a verifiable quantum protocol for dynamic secure multiparty summation based on the cyclic property of d-level MUBs. Our protocol can realize dynamic parameter update in the aspect of members and secret inputs, improving the practicality of the protocol. Moreover, a verification mechanism for result checking by applying ElGamal homomorphic encryption is given, and further enables the detectability of cheating behaviors, making our protocol safer. The security analysis proves the proposed protocol not only can resist a range of typical attacks from outside and inside, but also is secure against dishonest revoked participant attack which has been neglected in previous dynamic quantum summation protocols. From a theoretical perspective, compared with existing summation protocols, the protocol provides better practicability, higher privacy protection, and higher efficiency.

DOI
10.1088/1751-8121/ad2b88

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Abstract The research of quantum secure multiparty computation is a subject of great importance in modern cryptography. In this study, we construct a verifiable quantum protocol for dynamic secure multiparty summation based on the cyclic property of d-level MUBs. Our protocol can realize dynamic parameter update in the aspect of members and secret inputs, improving the practicality of the protocol. Moreover, a verification mechanism for result checking by applying ElGamal homomorphic encryption is given, and further enables the detectability of cheating behaviors, making our protocol safer. The security analysis proves the proposed protocol not only can resist a range of typical attacks from outside and inside, but also is secure against dishonest revoked participant attack which has been neglected in previous dynamic quantum summation protocols. From a theoretical perspective, compared with existing summation protocols, the protocol provides better practicability, higher privacy protection, and higher efficiency.
Secure multi-party computation has been playing a fundamental role in terms of classical cryptography. Quantum homomorphic encryption (QHE) could compute the encrypted data without decryption. At present, most protocols use a semi-honest third party (TP) to protect participants’ secrets. We use a quantum homomorphic encryption scheme instead of TP to protect the privacy of parties. Based on quantum homomorphic encryption, a secure multi-party quantum summation scheme is proposed in which N participants can delegate a server with strong quantum computing power to assist computation. By delegating the computation and key update processes to a server and a semi-honest key center, participants encrypt their private information data using Pauli operators to get the sum. Besides, the server can design and optimize the summation lines itself, and the correct results can be obtained even if the secret information is negative. The correctness analysis showed that the participants could correctly obtain the results of the calculation. The security analysis proves the scheme is resistant to both outside attack and participant’s attack, and is secure against collusive attack by up to N-2 participants. From the theoretical point of view, our protocol can extend to other secure multi-party computing problems.
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.
In this paper, a novel quantum secure multiparty summation protocol is proposed based on the mutually unbiased bases of d-level quantum systems. The quantum states of mutually unbiased bases, which are transmitted in a circular pattern, are imposed with the transformation operations of n secrecy owners to encode their secrecies. Security analysis reveals that the proposed protocol can resist outside attacks as well as participant attacks. The proposed protocol is suitable for d-level quantum systems and can calculate the modulo d addition using the integer-by-integer technique. Compared with the quantum secure summation protocols with bit-by-bit calculations, the proposed protocol has a higher calculation efficiency and has more extensive applications compared with the protocols with smaller modulo. Moreover, this protocol can be successfully used for quantum multiparty private comparison and quantum multiparty anonymous voting.
The significant advantage of the quantum homomorphic encryption scheme is to ensure the perfect security of quantum private data. In this paper, a novel secure multiparty quantum homomorphic encryption scheme is proposed, which can complete arbitrary quantum computation on the private data of multiple clients without decryption by an almost dishonest server. Firstly, each client obtains a secure encryption key through the measurement device independent quantum key distribution protocol and encrypts the private data by using the encryption operator and key. Secondly, with the help of the almost dishonest server, the non-maximally entangled states are pre-shared between the client and the server to correct errors in the homomorphic evaluation of T gates, so as to realize universal quantum circuit evaluation on encrypted data. Thirdly, from the perspective of the application scenario of secure multi-party computation, this work is based on the probabilistic quantum homomorphic encryption scheme, allowing multiple parties to delegate the server to perform the secure homomorphic evaluation. The operation and the permission to access the data performed by the client and the server are clearly pointed out. Finally, a concrete security analysis shows that the proposed multiparty quantum homomorphic encryption scheme can securely resist outside and inside attacks.
Abstract Secure Multiparty Computation (MPC) is a cryptography technique that allows multiple parties to securely perform operations on their private inputs without revealing them. It is used in various applications, such as data aggregation in the cloud, IoT, etc., where data privacy is the prime concern. Many researchers have explored ways to develop secure protocols with minimal risk of data leakage. Many of these classical secure MPC protocols depend on classical random number generators. However, advances in quantum information processing are putting classical key distribution methods at risk. Traditional summation protocols adopt an ((n,n))((n, n))((n,n)) threshold approach, requiring the participation of all (n)(n)(n) players to compute the sum securely. However, the proposed quantum secure multiparty computation based on secure summation and QKD (QSMPC-SSQKD) introduces a generalised quantum secure multiparty summation protocol. The proposed protocol utilises entanglement, a fundamental property of quantum mechanics, to facilitate safe key exchange, thereby ensuring robust security measures. We use a quantum random number generator (QRNG) to generate true random numbers, ensuring privacy preservation. The protocol achieves a per-bit entropy level of 0.708 through QRNG, which provides strong randomness. The security of the proposed protocol is validated using the CHSCH test ((B≈2.8)(\mathcal{B}\approx2.8)(B≈2.8)), ensuring that any attempt to eavesdrop on the system can be detected, and the complete process will be rescheduled. Compared to some similar protocols, the proposed QSMPC-SSQKD protocol provides higher randomness and lower quantum circuit cost without using any trusted third party (TTP). This improvement enhances the protocol’s efficiency and practicality in preventing data leakage during computation.
As a particular area of quantum security multiparty computation, quantum secure multiparty summation plays a critical role in modern cryptography. It is widely known that most of the existing quantum summation protocols are based on an honest or semi-honest third party (TP). However, the introduced TP makes the protocol difficult to implement in practice, as it may face a single-point-of-failure attack on TP. Although some TP-free protocols are proposed to mitigate this risk, the increased cost of communication reduces its efficiency. To address these issues, a novel quantum-secure multiparty summation protocol based on a cooperative random number distribution mechanism (QMS-CRM) is proposed in this paper for the first time. During it, this mechanism is designed using Shamir’s secret sharing scheme. Furthermore, this approach eliminates the requirement for random number exchange between participants without the help of TP, enhancing the efficiency of the protocol. The security analysis demonstrates that the proposed protocol can resist both external attacks and collusion attacks by up to n−2n - 2n−2 participants. Finally, we simulated the protocol on the IBM Quantum Cloud platform, confirming its feasibility.