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Advanced Quantum Technologies

Efficient Quantum Multi‐Party Summation Based on Shift Operations

Jason Lin, Shou‐Yu Lin

Published Oct 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT Private computation has become an increasingly important trend. It can be achieved either through traditional methods, such as homomorphic encryption, or by implementing various quantum protocols. Most existing protocols for quantum multiparty summation rely on quantum Fourier transforms and the generation of high‐dimensional entangled states. This paper presents a highly efficient quantum multiparty summation protocol that requires only shift operations applied to ‐level quantum systems (qudits), significantly simplifying its implementation. Furthermore, the number of values that each participant can express scales with the number of photons, without requiring higher‐dimensional quantum states. This study adopts a circular model for quantum transmission to ensure that no participant gains an advantage regarding information leakage based on the order of participation.

DOI
10.1002/qute.70509

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ABSTRACT Private computation has become an increasingly important trend. It can be achieved either through traditional methods, such as homomorphic encryption, or by implementing various quantum protocols. Most existing protocols for quantum multiparty summation rely on quantum Fourier transforms and the generation of high‐dimensional entangled states. This paper presents a highly efficient quantum multiparty summation protocol that requires only shift operations applied to ‐level quantum systems (qudits), significantly simplifying its implementation. Furthermore, the number of values that each participant can express scales with the number of photons, without requiring higher‐dimensional quantum states. This study adopts a circular model for quantum transmission to ensure that no participant gains an advantage regarding information leakage based on the order of participation.
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 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.
In this paper, a quantum secure multi-party summation scheme with a third party based on quantum Fourier transform (QFT) is put forward, where the third party cannot be permitted to cooperate with others but is allowed for all kinds of attacks. Under the help of third party, [Formula: see text] users can calculate the addition modulo [Formula: see text] of their private integer strings. The third party generates two-level single qubit and its product state as the initial quantum resource, produces the traveling particles with QFT and the controlled-not (CNOT) operations, and sends the traveling particles out to the first users; then, [Formula: see text] users encode their private integer sequences by performing the phase shifting operations on the travelling particles one after another; and finally, the third party decodes out the summation of the private integer sequences from [Formula: see text] users through CNOT operations and inverse quantum Fourier transform (IQFT). This protocol only adopts two-level single particle state and its product state as initial quantum resource, only needs [Formula: see text]-level single particle measurement and does not need to perform quantum entanglement swapping. Security analysis indicates that this protocol can overcome not only the outside attack but also the participant attack.
Abstract Secure multiparty quantum summation, as a critical part of secure multiparty quantum computation, plays a pivotal role in the field of quantum cryptography. In this paper, a hybrid protocol is proposed to implement secure multiparty quantum summation and anonymous ranking simultaneously, which uses ‐level two‐particle entangled states. In the designed protocol, the particles are conveyed in the way of the circle‐type transmission mode, which can compute the sum of the secret and the ranking by analyzing the distribution of participants associated with different secret values. Moreover, random number sequences can be obtained by constructing a fundamental system of solutions, which avoids the transmission of random numbers and reduces the use of quantum resources. According to the analysis, it can be seen that the protocol is secure against known attacks, and the secrets remain undisclosed throughout the protocol's implementation.
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.
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.