Abstract Secure semi-quantum summation entails the collective computation of the sum of private secrets by multi-untrustworthy and resource-limited participants, facilitated by a quantum third-party. This paper introduces three semi-quantum summation protocols based on single photons, where eliminating the need for classical users to possess measurement capabilities. Two-party protocol 1 and protocol 2 are structured upon different models: star and ring, respectively. The security analysis extensively evaluates the protocols' resilience against outside and inside attacks, demonstrating protocols are asymptotically secure. Protocol 3 extends two-party protocol 1 to multi-party scenarios, broadening its applicability. Comparison reveals a reduction in the workload for classical users compared to previous similar protocols, and the protocols' correctness are visually validated through simulation by Qiskit.
Abstract Secure semi-quantum summation entails the collective computation of the sum of private secrets by multi-untrustworthy and resource-limited participants, facilitated by a quantum third-party. This paper introduces three semi-quantum summation protocols based on single photons, where eliminating the need for classical users to possess measurement capabilities. Two-party protocol 1 and protocol 2 are structured upon different models: star and ring, respectively. The security analysis extensively evaluates the protocols' resilience against outside and inside attacks, demonstrating protocols are asymptotically secure. Protocol 3 extends two-party protocol 1 to multi-party scenarios, broadening its applicability. Comparison reveals a reduction in the workload for classical users compared to previous similar protocols, and the protocols' correctness are visually validated through simulation by Qiskit.
Tian et al. (EPJ Quantum Technol 11(1):35, 2024 ) proposed three semi-quantum summation protocols that enable resource-limited participants to securely compute the sum of their private inputs with assistance from a semi-honest third party (TP). In these protocols, participants do not need quantum measurement devices to achieve secure computation. Although the protocols have been analyzed against common attacks to demonstrate their robustness, this study identifies two significant issues in Tian et al.’s work: a security loophole and a design flaw. The security loophole permits a malicious participant to steal another participant’s private input without detection, while the design flaw prevents participants from obtaining the correct summation result when the number of participants is odd. To address these issues, this study proposes improved semi-quantum summation protocols under the same assumptions and environment.
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.
Semi-quantum protocols construct connections between quantum users and ``classical'' users who can only perform certain ``classical'' operations. In this paper, we present a new semi-quantum private comparison protocol based on entangled states and single particles, which does not require pre-shared keys between the ``classical'' users to guarantee the security of their private data. By utilizing multi-particle entangled states and single particles, our protocol can be easily extended to multi-party scenarios to meet the requirements of multiple ``classical'' users who want to compare their private data. The security analysis shows that the protocol can effectively prevent attacks from outside eavesdroppers and adversarial participants. Besides, we generalize the proposed protocol to other semi-quantum protocols such as semi-quantum key agreement, semi-quantum summation, and semi-quantum anonymous ranking protocols. We compare and discuss the proposed protocols with previous similar protocols. The results show that our protocols satisfy the demands of their respective counterparts separately. Therefore, our protocols have a wide range of application scenarios.
participants can simultaneously obtain the summation result without revealing their secret inputs. Our protocol uses single photon states as the information carriers. In addition, each participant with secret input only performs simple single-particle operators rather than particle preparation and any complex quantum measurements. These features make our protocol more feasible to implement. We demonstrate the correctness and security of the proposed protocol, which is resistant to participant attack and outside attack. In the end, we compare in detail the performance of the quantum summation protocol in this paper with other schemes in terms of different indicators. By comparison, our protocol is efficient and easy to implement.
In quantum secure multi-party summation protocols, some attackers can impersonate legitimate participants in the summation process, and easily steal the summation results from the participants. This is often overlooked for existing secure multi-party summation protocols, thus rendering them insecure. Based on commutative encryption, a quantum secure multi-party summation protocol with identity authentication is proposed in this paper. In the protocol, each participant encodes a secret integer on photons via unitary operations. At the same time, a one-way hash function technique with a key is utilized to perform identity authentication operations for each participant. Finally, the summation is calculated with the help of a semi-trusted third party. The analysis of the protocol shows that the proposed protocol is correct and resistant to common and impersonation attacks. Compared to related protocols, the use and measurement of single photons makes the protocol easier to implement into existing technology. Furthermore, the simulation experiments on the IBM Q Experience cloud platform demonstrate the effectiveness of the presented protocol.
Quantum Secure Multi-party Summation (QSMS) is a fundamental primitive of Quantum Secure Multi-party Computation (QSMC), enabling multiple participants to jointly compute the sum of their private inputs without disclosing individual data. However, most existing QSMS protocols require all participants to possess full quantum capabilities and often rely on pre-shared keys, auxiliary mask transmission, or multiple trusted third parties, resulting in high communication overhead and limited practicality. To address these limitations, we propose an efficient Semi-Quantum Secure Multi-party Summation (SQSMS) protocol based on d-dimensional n-particle entangled states. By exploiting the global correlation properties of high-dimensional entangled states, the proposed protocol generates correlated random masks directly from quantum measurement outcomes. These masks cancel automatically during the aggregation process, eliminating the need for additional mask distribution and transmission. Compared with existing QSMS schemes, the proposed protocol reduces communication overhead, improves quantum efficiency, and avoids reliance on pre-shared keys or multiple trusted third parties. Moreover, only simple measurement operations are required from classical participants, making the protocol more practical for semi-quantum environments. We further provide formal correctness and security analyses of the proposed protocol and conduct quantum circuit simulations using the IBM Qiskit platform to demonstrate its feasibility. Moreover, based on the proposed summation protocol, we design several extended application protocols, including anonymous voting, anonymous auction, and anonymous ranking, which further illustrate the scalability and practical applicability of the proposed scheme.