Abstract The quantum blind millionaires’ (QBM) problem is an expanded version of the millionaires’ problem in a quantum environment. For any two sets with different members, the QBM problem represents the quantum solution of the private summation in each set and the private comparison of the results simultaneously. During it, the secrets of any participant should be protected. As a new topic in quantum secure multiparty computation (QSMC), current solutions to QBM problems usually require an honest third party to resist some potential attack strategies. However, the assumptions will affect their applicability in practical cooperative security systems. In this paper, we propose a new solution to the quantum blind millionaires’ (QBM) problem without the help of an honest third party for the first time. In our solution, the shift operations are applied to the d -dimensional 2-particle entangled states to encode the secrets of the participants. According to our analysis, the proposed solution can effectively resist typical internal and external attacks by applying the detection methods generated by the participants. We hope that the research will make positive developments for QSMC.Abstract The quantum blind millionaires’ (QBM) problem is an expanded version of the millionaires’ problem in a quantum environment. For any two sets with different members, the QBM problem represents the quantum solution of the private summation in each set and the private comparison of the results simultaneously. During it, the secrets of any participant should be protected. As a new topic in quantum secure multiparty computation (QSMC), current solutions to QBM problems usually require an honest third party to resist some potential attack strategies. However, the assumptions will affect their applicability in practical cooperative security systems. In this paper, we propose a new solution to the quantum blind millionaires’ (QBM) problem without the help of an honest third party for the first time. In our solution, the shift operations are applied to the d -dimensional 2-particle entangled states to encode the secrets of the participants. According to our analysis, the proposed solution can effectively resist typical internal and external attacks by applying the detection methods generated by the participants. We hope that the research will make positive developments for QSMC.

EPJ Quantum TechnologyNov 25, 20246 citations

Quantum protocols for secure multi-party summation

Zhaoxu Ji, Huanguo Zhang, Houzhen Wang +3 more

Quantum Information ProcessingApr 20, 201966 citations

Improvement of Quantum Protocols for Secure Multi-Party Summation

Zhi-Gang Gan

International Journal of Theoretical PhysicsAug 16, 20206 citations

On the generic structures of the protocols for quantum auction and quantum summation and their relation

Kabir Sandhu, Sandeep Mishra, Anirban Pathak

Secure multi-party computation (SMC) addresses the problem of jointly computing global functions of private inputs while revealing minimal information about individual data. Two prominent examples of SMC tasks are sealed-bid auction and secure multi-party summation. Existing schemes for quantum auction and quantum summation have largely been developed independently, motivated by distinct applications and employing different computational primitives. In this work, mutual reductions between the two tasks are established for single-item sealed-bid auctions with first-price payment. In one direction, an auction used as a black box computes a secure sum: each party bids a private random key drawn from its input, so the clearing price depends on the inputs only through their sum $S$ . The reduction is perfectly private against colluding semi-honest parties and uses $O(S^2\log(1/δ))$ auction rounds, which is optimal, or $O(S\log(1/δ))$ under coherent access. It can be instantiated with an existing auctioneer-free quantum auction after a one-line change to its disjunction subroutine, which as published leaks occupancy counts. In the other direction, summation with randomized inputs yields threshold disjunctions, and a single search over composite keys locates the highest bid and a winner, revealing nothing else. Because each query consumes the bidders' encodings, a bidder can adapt its effective bid undetected, while a fixed query set restores sealed bidding. Combinatorial auctions and general payment rules lie outside this framework. On a superconducting processor, one instance of each direction is executed, recovering the winner for four-bidder instances with ties and the sum of private inputs from repeated auctions.Secure multi-party computation (SMC) addresses the problem of jointly computing global functions of private inputs while revealing minimal information about individual data. Two prominent examples of SMC tasks are sealed-bid auction and secure multi-party summation. Existing schemes for quantum auction and quantum summation have largely been developed independently, motivated by distinct applications and employing different computational primitives. In this work, mutual reductions between the two tasks are established for single-item sealed-bid auctions with first-price payment. In one direction, an auction used as a black box computes a secure sum: each party bids a private random key drawn from its input, so the clearing price depends on the inputs only through their sum $S$. The reduction is perfectly private against colluding semi-honest parties and uses $O(S^2\log(1/δ))$ auction rounds, which is optimal, or $O(S\log(1/δ))$ under coherent access. It can be instantiated with an existing auctioneer-free quantum auction after a one-line change to its disjunction subroutine, which as published leaks occupancy counts. In the other direction, summation with randomized inputs yields threshold disjunctions, and a single search over composite keys locates the highest bid and a winner, revealing nothing else. Because each query consumes the bidders' encodings, a bidder can adapt its effective bid undetected, while a fixed query set restores sealed bidding. Combinatorial auctions and general payment rules lie outside this framework. On a superconducting processor, one instance of each direction is executed, recovering the winner for four-bidder instances with ties and the sum of private inputs from repeated auctions.

quant-pharXiv:2606.27693Jun 29, 20260 citations

Robust Semi-Quantum Summation over a Collective-Dephasing Noise Channel

Chun‐Wei Yang, Chia‐Wei Tsai, Chi‐An Chen +1 more

Quantum summation is one of the various applications in secure multi-party computation. However, most of the existing quantum summation protocols assume that the participants possess all the quantum devices. Considering future applications, the capability of the participants must be adjusted before it can be put into practical use. Although Boyer et al. proposed that the semi-quantum environment could be used to solve this problem; another practical problem is the interference by noise. In 2022, Ye et al. proposed a two-party semi-quantum summation (SQS) protocol resistant to the interference of collective noise, in which two classical participants can accomplish the summation of their private binary sequences with the assistance of a quantum semi-honest third party. They proved that their SQS protocol is resistant to various eavesdropping attacks. This paper unveils two risks of information leakage in Ye et al.’s SQS protocol. If the aforementioned security issues are not resolved, Ye et al.’s SQS protocol may not be able to perform private quantum computations securely. Fortunately, the SQS protocol against the collective-dephasing noise proposed in this study is free from the issue of information leakage as well as resistant to various quantum attacks. In addition, the quantum efficiency of the SQS protocol proposed in this study is four times higher than that of Ye et al.’s SQS protocol, which can effectively improve the quantum utilization rate.Quantum summation is one of the various applications in secure multi-party computation. However, most of the existing quantum summation protocols assume that the participants possess all the quantum devices. Considering future applications, the capability of the participants must be adjusted before it can be put into practical use. Although Boyer et al. proposed that the semi-quantum environment could be used to solve this problem; another practical problem is the interference by noise. In 2022, Ye et al. proposed a two-party semi-quantum summation (SQS) protocol resistant to the interference of collective noise, in which two classical participants can accomplish the summation of their private binary sequences with the assistance of a quantum semi-honest third party. They proved that their SQS protocol is resistant to various eavesdropping attacks. This paper unveils two risks of information leakage in Ye et al.’s SQS protocol. If the aforementioned security issues are not resolved, Ye et al.’s SQS protocol may not be able to perform private quantum computations securely. Fortunately, the SQS protocol against the collective-dephasing noise proposed in this study is free from the issue of information leakage as well as resistant to various quantum attacks. In addition, the quantum efficiency of the SQS protocol proposed in this study is four times higher than that of Ye et al.’s SQS protocol, which can effectively improve the quantum utilization rate.

MathematicsMar 14, 202313 citations

S

. The reduction is perfectly private against colluding semi-honest parties and uses

O(S^2\log(1/δ))

auction rounds, which is optimal, or

O(S\log(1/δ))

under coherent access. It can be instantiated with an existing auctioneer-free quantum auction after a one-line change to its disjunction subroutine, which as published leaks occupancy counts. In the other direction, summation with randomized inputs yields threshold disjunctions, and a single search over composite keys locates the highest bid and a winner, revealing nothing else. Because each query consumes the bidders' encodings, a bidder can adapt its effective bid undetected, while a fixed query set restores sealed bidding. Combinatorial auctions and general payment rules lie outside this framework. On a superconducting processor, one instance of each direction is executed, recovering the winner for four-bidder instances with ties and the sum of private inputs from repeated auctions.