Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Two Quantum Protocols for Oblivious Set-member Decision Problem

Runhua Shi, Yi Mu, Hong Zhong, Jie Cui, Shun Zhang

Published Oct 30, 2015• 12 citations
Publisher

Abstract

In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology.

DOI
10.1038/srep15914

Related papers

Quantum oblivious set-member decision protocol

Runhua Shi, Yi Mu, Hong Zhong +1 more

We present and define a privacy-preserving problem called the oblivious set-member decision problem, which allows a server to decide whether a private secret of a user is a member of his private set in an oblivious manner. Namely, if the secret belongs to his private set, he does not know which member it is. We propose a quantum solution to the oblivious set-member decision problem. Compared to classical solutions, the proposed quantum protocol achieves an exponential reduction in communication complexity, since it only needs $O(1)$ communication cost.

Physical Review A•Aug 5, 2015•38 citations

Comment on “Quantum oblivious set-member decision protocol”

Bin Liu, Di Xiao, Wei Huang +1 more

In a recent paper [Phys. Rev. A 92, 022309 (2015)], the authors proposed a quantum oblivious set-member decision protocol, which is designed to allow a server to check whether a private secret of a user is a member of his private set in an oblivious manner. Such protocols should protect the privacies of both the server and the user. However, we find that the user in their protocol can steal $l\ensuremath{-}1$ bits of information about the server's private set by sending the false decoy states.

Physical Review A•Mar 18, 2016•1 citation

Semi-quantum private set intersection and union cardinality protocol based on single-particle states

Peiyi Zhu, Chong‐Qiang Ye, Yuan Tian

Abstract Quantum private set computation plays a crucial role in secure multi-party computation and privacy-preserving data mining. However, in quantum resource-constrained scenarios, most existing semi-quantum private set computation protocols rely on entangled states, making them difficult to scale effectively to multi-party settings. To address these limitations, this paper proposes a semi-quantum protocol for private set intersection and union cardinality computation. The proposed protocol uses single-particle states as information carriers and establishes the required keys by exploiting the correlations between prepared quantum states and selected measurement bases, thus avoiding the need for entangled states and pre-shared keys. By adopting a star topology, the protocol is further extended to general multiparty scenarios, with resource costs increasing linearly rather than exponentially. Security and performance analyses show that the proposed protocol can resist typical external and internal attacks. Compared with existing protocols, it reduces quantum resource requirements while achieving advantages in qubit efficiency and scalability.

Physica Scripta•Jul 10, 2026•0 citations

Authenticated Multi-Party Quantum Private Set Intersection with Single Particles

Gongde Guo, Li Zheng, Kai Yu +1 more

As an important branch of secure multi-party computation, privacy set intersection enables multiple parties to input their private sets and jointly compute the intersection of these sets without revealing any information other than the intersection itself. With the increasing demand for privacy protection of user data, privacy set intersection has been widely used in privacy computing and other fields. In this paper, we utilize the properties of mutually unbiased bases to propose a multi-party quantum private set intersection protocol that incorporates identity authentication mechanisms. A semi-honest third party (TP) is introduced to facilitate the secure execution of this task among the multiple participating parties. The TP establishes a shared master key with each party, which serves as the basis for authenticating the identity of each participant throughout the protocol. Single-particle quantum states, prepared by the TP, act as the information carriers and are sequentially transmitted among the participating parties. Each party performs a local unitary operation on the circulating particle, thereby encoding their private data within the quantum state. At the end of the protocol, the TP announces his measurement result, by which all participants can concurrently ascertain the intersection of their private data sets. Notably, the proposed protocol eliminates the need for long-term storage of single-particle quantum states, thereby rendering it feasible with existing quantum technological capabilities. Furthermore, a comprehensive security analysis demonstrates that the protocol effectively resists some common external and internal attacks, thereby ensuring its theoretical security.

Mathematics•Jun 18, 2025•4 citations

Quantum private set intersection with correlated sum using single photons

Yaohua Lu, Gangyi Ding

Secure multi-party computation (SMC) enables multiple parties to collaboratively perform computational tasks without revealing their private data. A specific application scenario within SMC is Private Set Intersection with Correlated Sum (PSI-CS), where two participating parties compute the sum of associated elements in their intersection while preserving the privacy of their individual sets. This problem arises in various contexts, including calculating conversion amounts between suppliers and platforms, such as advertising conversion amounts and agency business conversion amounts. The paper proposes a protocol that employs quantum single-photon technology to compute the PSI-CS, provides four technical solutions suitable for various scenarios ranging from small to large data volumes, sparse to dense datasets, and without revealing the cardinality of the intersection. Additionally, the method extends to computing the union set with correlated sums. We experimentally validate the proposed protocol, conduct correctness and security analyses, and demonstrate its practical significance and application value. By utilizing single-photon technology, quantum gate operations, and measurements become more accessible, simplifying the protocol’s implementation. Notably, our approach provides unconditional security against quantum computational attacks, representing a substantial improvement in both efficiency and practical applicability compared to classical domain protocols.

Modern Physics Letters A•Dec 14, 2024•0 citations

Efficient Quantum Protocol for Private Set Intersection Cardinality

Runhua Shi

Recently, we proposed a quantum solution to the problem of private set intersection cardinality (PSI-CA) (Information Sciences 370–371 (2016) 147–158). Compared to classical solutions, the proposed quantum PSI-CA protocol achieves an exponential reduction in communication complexity, since it only needs$O(1)$communication cost. However, this protocol requires two additional assumptions about the cardinalities of the sets, which may limit its wider applications. In this paper, we successfully discard these assumptions and present a stronger quantum PSI-CA protocol without any limitation. The new protocol ensures the parties’ private security, i.e., unconditionally secure server privacy and statistically secure client privacy, and it achieves the constant computation and communication complexities, which are independent of the size of the sets. Therefore, it is more suitable for practical applications with big data sets.

IEEE Access•Jan 1, 2018•24 citations
In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology.
We present and define a privacy-preserving problem called the oblivious set-member decision problem, which allows a server to decide whether a private secret of a user is a member of his private set in an oblivious manner. Namely, if the secret belongs to his private set, he does not know which member it is. We propose a quantum solution to the oblivious set-member decision problem. Compared to classical solutions, the proposed quantum protocol achieves an exponential reduction in communication complexity, since it only needs O(1)O(1)O(1) communication cost.
In a recent paper [Phys. Rev. A 92, 022309 (2015)], the authors proposed a quantum oblivious set-member decision protocol, which is designed to allow a server to check whether a private secret of a user is a member of his private set in an oblivious manner. Such protocols should protect the privacies of both the server and the user. However, we find that the user in their protocol can steal $l\ensuremath{-}1$ bits of information about the server's private set by sending the false decoy states.
Abstract Quantum private set computation plays a crucial role in secure multi-party computation and privacy-preserving data mining. However, in quantum resource-constrained scenarios, most existing semi-quantum private set computation protocols rely on entangled states, making them difficult to scale effectively to multi-party settings. To address these limitations, this paper proposes a semi-quantum protocol for private set intersection and union cardinality computation. The proposed protocol uses single-particle states as information carriers and establishes the required keys by exploiting the correlations between prepared quantum states and selected measurement bases, thus avoiding the need for entangled states and pre-shared keys. By adopting a star topology, the protocol is further extended to general multiparty scenarios, with resource costs increasing linearly rather than exponentially. Security and performance analyses show that the proposed protocol can resist typical external and internal attacks. Compared with existing protocols, it reduces quantum resource requirements while achieving advantages in qubit efficiency and scalability.
As an important branch of secure multi-party computation, privacy set intersection enables multiple parties to input their private sets and jointly compute the intersection of these sets without revealing any information other than the intersection itself. With the increasing demand for privacy protection of user data, privacy set intersection has been widely used in privacy computing and other fields. In this paper, we utilize the properties of mutually unbiased bases to propose a multi-party quantum private set intersection protocol that incorporates identity authentication mechanisms. A semi-honest third party (TP) is introduced to facilitate the secure execution of this task among the multiple participating parties. The TP establishes a shared master key with each party, which serves as the basis for authenticating the identity of each participant throughout the protocol. Single-particle quantum states, prepared by the TP, act as the information carriers and are sequentially transmitted among the participating parties. Each party performs a local unitary operation on the circulating particle, thereby encoding their private data within the quantum state. At the end of the protocol, the TP announces his measurement result, by which all participants can concurrently ascertain the intersection of their private data sets. Notably, the proposed protocol eliminates the need for long-term storage of single-particle quantum states, thereby rendering it feasible with existing quantum technological capabilities. Furthermore, a comprehensive security analysis demonstrates that the protocol effectively resists some common external and internal attacks, thereby ensuring its theoretical security.
Secure multi-party computation (SMC) enables multiple parties to collaboratively perform computational tasks without revealing their private data. A specific application scenario within SMC is Private Set Intersection with Correlated Sum (PSI-CS), where two participating parties compute the sum of associated elements in their intersection while preserving the privacy of their individual sets. This problem arises in various contexts, including calculating conversion amounts between suppliers and platforms, such as advertising conversion amounts and agency business conversion amounts. The paper proposes a protocol that employs quantum single-photon technology to compute the PSI-CS, provides four technical solutions suitable for various scenarios ranging from small to large data volumes, sparse to dense datasets, and without revealing the cardinality of the intersection. Additionally, the method extends to computing the union set with correlated sums. We experimentally validate the proposed protocol, conduct correctness and security analyses, and demonstrate its practical significance and application value. By utilizing single-photon technology, quantum gate operations, and measurements become more accessible, simplifying the protocol’s implementation. Notably, our approach provides unconditional security against quantum computational attacks, representing a substantial improvement in both efficiency and practical applicability compared to classical domain protocols.
Recently, we proposed a quantum solution to the problem of private set intersection cardinality (PSI-CA) (Information Sciences 370–371 (2016) 147–158). Compared to classical solutions, the proposed quantum PSI-CA protocol achieves an exponential reduction in communication complexity, since it only needsO(1)O(1)O(1)communication cost. However, this protocol requires two additional assumptions about the cardinalities of the sets, which may limit its wider applications. In this paper, we successfully discard these assumptions and present a stronger quantum PSI-CA protocol without any limitation. The new protocol ensures the parties’ private security, i.e., unconditionally secure server privacy and statistically secure client privacy, and it achieves the constant computation and communication complexities, which are independent of the size of the sets. Therefore, it is more suitable for practical applications with big data sets.