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

Advanced Quantum Technologies

Quantum Secure Geometric Computation via Semi‐Quantum Computation

Jia Hao, Yu‐Guang Yang, Guang‐Bao Xu, Dong‐Huan Jiang

Published Dec 22, 2025• 1 citation
Publisher

Abstract

ABSTRACT Quantum secure geometric computation is a vital branch in secure multiparty quantum computation, aiming to collaborate to complete secure geometric computation tasks without compromising participants’ respective secrets. In this paper, four semi‐quantum cryptographic protocols are first proposed for key distribution, private comparison, summation, and multiplication, respectively. Building upon them, it is further presented five semi‐quantum secure geometric computation protocols for point‐point distance computation, point‐line distance computation, line‐circle intersection, circle‐circle intersection, and circle‐polygon intersection, respectively. It is the first time that quantum secure geometric computation protocols are designed under a semi‐quantum framework to the best of our knowledge. Furthermore, all the proposed protocols are proven to resist both insider and outsider attacks. Simulation studies conducted on the IBM quantum cloud platform validate the correctness and feasibility of the proposed protocols.

DOI
10.1002/qute.202500936

Related papers

Quantum‐Secure Point‐Circle, Circle‐Circle Relation Determination Protocol With Application to Privacy‐Preserving Geometric Range Query

Yi Zhou, Yao‐Fei Wu, Xiang-Rui Li +2 more

ABSTRACT As an important branch of quantum‐secure multi‐party computation, quantum‐secure multi‐party computational geometry aims to solve geometric computation problems without revealing the parties' geometric inputs. Privacy‐preserving point‐circle and circle‐circle positional relationships are classic problems in secure multi‐party computational geometry, with broad applications in privacy‐preserving queries, collision detection, and clustering. Building on the quantum two‐party summation and multiplication protocols proposed by Sutradhar and Om, this paper presents the first quantum‐secure protocols for determining point‐circle and circle‐circle positional relationships, enabling accurate relationship determination without disclosing private geometric parameters. Security analysis and simulation experiments on the IBM Qiskit platform demonstrate the security and feasibility of the proposed protocols. Furthermore, since existing quantum privacy‐preserving range query protocols are limited to one‐dimensional linear spaces, we build on the proposed protocols to present the first quantum‐secure privacy‐preserving geometric range query protocol, which enables arbitrary geometric range search for private coordinates in the two‐dimensional space while protecting the privacy of the query range and data points.

Advanced Quantum Technologies•May 1, 2026•0 citations

An Enhanced QFT‐Based Quantum‐Secure Multi‐Party Protocol for Geometric Relation Determination Involving Ellipses

Yi‐Hua Zhou, Xin‐Rong He, Yi Yang +2 more

ABSTRACT Quantum‐secure multi‐party computational geometry (QSMCG) aims to determine geometric relations without revealing the private spatial parameters of the participants. Existing QFT‐based secure multiparty quantum summation and multiplication protocols provide useful arithmetic primitives, but they still involve single‐initiator trust dependence and insufficient protocol‐level verification of channel disturbance and abnormal quantum‐state evolution. This paper proposes enhanced QFT‐based secure multi‐party summation and multiplication protocols. The protocols combine ‐threshold secret sharing with two complementary verification layers. Decoy‐particle detection monitors the quantum channel during transmission and is designed to catch eavesdropping, interception‐resend, delayed‐photon, invisible‐photon, or other transmission disturbances. Zero‐check verification is executed after the accumulated state is disentangled; it checks whether the target register returns to , so it tests whether the internal computation flow is consistent with the intended protocol. Based on these protocols, three modular QSMCG protocols are constructed for point‐ellipse, line‐ellipse, and circle‐ellipse relation determination under a TP‐assisted blinded‐comparison architecture. Correctness and security analyses show that the proposed protocols obtain the intended arithmetic and geometric results while improving resistance to representative external and internal attacks. Moreover, Qiskit simulations further verify the correctness and circuit‐level feasibility of the core quantum operations.

Advanced Quantum Technologies•Oct 1, 2026•0 citations

A secure two-party polygon intersection area computation protocol based on quantum homomorphic encryption

B Y Liu, Xin-Guo Wang

Abstract Secure Multi-party Geometric Computation(SMGC) is an important field in Secure Multi-party Computation(SMC). It aims to enable multiple mutually distrustful parties to collaboratively perform geometric computation tasks while protecting their respective private information. As an important branch of this field, the secure two-party polygon intersection area computation focuses on enabling two untrusted parties to securely compute the overlapping area between their polygons without revealing their private coordinate information. This paper introduces a semi-honest third party and leverages quantum homomorphic encryption technology to first achieve secure two-party segment intersection computation. Subsequently, by integrating a quantum protocol for point inclusion verification within arbitrary regions, it proposes an exact method for calculating the intersection area of polygons. Finally, through comprehensive analysis, it has been demonstrated that this protocol is secure and reliable, offering new insights for future regional collaborative computing in quantum environments.

Chinese Physics B•May 26, 2026•0 citations

Semi‐Quantum Secure Multiparty Summation and its Applications to Anonymous Auction and Ranking

Chong‐Qiang Ye, J. Li, Xiu‐Bo Chen +4 more

Abstract Semi‐quantum secure summation allows multiple parties with limited quantum capabilities to perform collective calculations under the premise of protecting privacy. However, current approaches are confined to low‐dimensional quantum states as information carriers and are restricted to scenarios involving two or three parties. This limitation hinders their universality and ability to fulfill the requirements of practical secure multiparty computations. To address these challenges, a novel semi‐quantum secure multiparty summation (SQSMS) protocol is proposed based on high‐dimensional entangled states and single‐particle states. The protocol leverages the entanglement correlation to guarantee the security of the transmission, enabling resistance against various potential attacks. Then, by utilizing the IBM Qiskit platform, corresponding quantum circuits and simulation results are presented to validate the feasibility and correctness of the protocol. Furthermore, building upon the foundation of the SQSMS protocol, semi‐quantum anonymous auction and anonymous ranking protocols are further constructed. Compared with previous approaches, the designed protocols cater to the requirements of their respective counterparts. Consequently, the approach may have broad applications in semi‐quantum secure multiparty computation scenarios.

Advanced Quantum Technologies•Jan 8, 2024•14 citations

Quantum secure multi-party computational geometry based on multi-party summation and multiplication

Zhao Dou, Yifei Wang, Zhaoqian Liu +3 more

Abstract Secure multi-party computational geometry is a branch of secure multi-party computation, which is applied in many important fields. But up to now, the research on how to solve this problem with quantum methods has just started. Therefore, we study the design of quantum secure multi-party computational geometry (QSMCG) protocols in this paper. As the foundation, we extend the two-party summation and multiplication protocols proposed by Sutradhar and Om to multi-party protocols. Then we propose three new QSMCG protocols. Our proposed quantum secure two-party distance computation protocol has improvement in efficiency and accuracy. And the proposed quantum secure multi-party polytope volume computation protocol as well as the quantum secure circle–circle intersection area computation protocol are designed for the first time. Moreover, these protocols are designed to use multi-third parties, which solves the problem of intermediate value leakage in computation. The correctness, security and performance of all these protocols are analyzed.

Quantum Science and Technology•Mar 18, 2024•8 citations

Novel quantum solutions to privacy-preserving point-line relation determination

Zhenwan Peng, Runhua Shi, Ran Ding +1 more

Abstract Secure multiparty computational geometry is an essential field of secure multiparty computation. It involves solving geometric problems without disclosing any private geometric information from each participating party. Privacy-preserving point-line relation determination, a pivotal branch of secure multiparty computational geometry, holds significant potential for applications in various domains, including business, engineering, and military. In this paper, leveraging the assistance of a third party, we introduce a quantum solution to privacy-preserving point-line relation determination. This approach incorporates quantum key distribution and one-time pad encryption. Under the condition that the third party does not conspire with any participant, our protocol ensures heightened security and enhanced privacy protection compared to classical methods. This superiority is attributed to the underlying principles of quantum mechanics and the utilization of one-time pad encryption. Furthermore, we extend our protocol to involve multiple third parties, employing the technology of quantum secret sharing. In scenarios where these third parties refrain from colluding with any single participant, no information is divulged to the other participant. Consequently, the protocol becomes more rational and secure when multiple third parties are involved.

Physica Scripta•Mar 4, 2024•4 citations
ABSTRACT Quantum secure geometric computation is a vital branch in secure multiparty quantum computation, aiming to collaborate to complete secure geometric computation tasks without compromising participants’ respective secrets. In this paper, four semi‐quantum cryptographic protocols are first proposed for key distribution, private comparison, summation, and multiplication, respectively. Building upon them, it is further presented five semi‐quantum secure geometric computation protocols for point‐point distance computation, point‐line distance computation, line‐circle intersection, circle‐circle intersection, and circle‐polygon intersection, respectively. It is the first time that quantum secure geometric computation protocols are designed under a semi‐quantum framework to the best of our knowledge. Furthermore, all the proposed protocols are proven to resist both insider and outsider attacks. Simulation studies conducted on the IBM quantum cloud platform validate the correctness and feasibility of the proposed protocols.
ABSTRACT As an important branch of quantum‐secure multi‐party computation, quantum‐secure multi‐party computational geometry aims to solve geometric computation problems without revealing the parties' geometric inputs. Privacy‐preserving point‐circle and circle‐circle positional relationships are classic problems in secure multi‐party computational geometry, with broad applications in privacy‐preserving queries, collision detection, and clustering. Building on the quantum two‐party summation and multiplication protocols proposed by Sutradhar and Om, this paper presents the first quantum‐secure protocols for determining point‐circle and circle‐circle positional relationships, enabling accurate relationship determination without disclosing private geometric parameters. Security analysis and simulation experiments on the IBM Qiskit platform demonstrate the security and feasibility of the proposed protocols. Furthermore, since existing quantum privacy‐preserving range query protocols are limited to one‐dimensional linear spaces, we build on the proposed protocols to present the first quantum‐secure privacy‐preserving geometric range query protocol, which enables arbitrary geometric range search for private coordinates in the two‐dimensional space while protecting the privacy of the query range and data points.
ABSTRACT Quantum‐secure multi‐party computational geometry (QSMCG) aims to determine geometric relations without revealing the private spatial parameters of the participants. Existing QFT‐based secure multiparty quantum summation and multiplication protocols provide useful arithmetic primitives, but they still involve single‐initiator trust dependence and insufficient protocol‐level verification of channel disturbance and abnormal quantum‐state evolution. This paper proposes enhanced QFT‐based secure multi‐party summation and multiplication protocols. The protocols combine ‐threshold secret sharing with two complementary verification layers. Decoy‐particle detection monitors the quantum channel during transmission and is designed to catch eavesdropping, interception‐resend, delayed‐photon, invisible‐photon, or other transmission disturbances. Zero‐check verification is executed after the accumulated state is disentangled; it checks whether the target register returns to , so it tests whether the internal computation flow is consistent with the intended protocol. Based on these protocols, three modular QSMCG protocols are constructed for point‐ellipse, line‐ellipse, and circle‐ellipse relation determination under a TP‐assisted blinded‐comparison architecture. Correctness and security analyses show that the proposed protocols obtain the intended arithmetic and geometric results while improving resistance to representative external and internal attacks. Moreover, Qiskit simulations further verify the correctness and circuit‐level feasibility of the core quantum operations.
Abstract Secure Multi-party Geometric Computation(SMGC) is an important field in Secure Multi-party Computation(SMC). It aims to enable multiple mutually distrustful parties to collaboratively perform geometric computation tasks while protecting their respective private information. As an important branch of this field, the secure two-party polygon intersection area computation focuses on enabling two untrusted parties to securely compute the overlapping area between their polygons without revealing their private coordinate information. This paper introduces a semi-honest third party and leverages quantum homomorphic encryption technology to first achieve secure two-party segment intersection computation. Subsequently, by integrating a quantum protocol for point inclusion verification within arbitrary regions, it proposes an exact method for calculating the intersection area of polygons. Finally, through comprehensive analysis, it has been demonstrated that this protocol is secure and reliable, offering new insights for future regional collaborative computing in quantum environments.
Abstract Semi‐quantum secure summation allows multiple parties with limited quantum capabilities to perform collective calculations under the premise of protecting privacy. However, current approaches are confined to low‐dimensional quantum states as information carriers and are restricted to scenarios involving two or three parties. This limitation hinders their universality and ability to fulfill the requirements of practical secure multiparty computations. To address these challenges, a novel semi‐quantum secure multiparty summation (SQSMS) protocol is proposed based on high‐dimensional entangled states and single‐particle states. The protocol leverages the entanglement correlation to guarantee the security of the transmission, enabling resistance against various potential attacks. Then, by utilizing the IBM Qiskit platform, corresponding quantum circuits and simulation results are presented to validate the feasibility and correctness of the protocol. Furthermore, building upon the foundation of the SQSMS protocol, semi‐quantum anonymous auction and anonymous ranking protocols are further constructed. Compared with previous approaches, the designed protocols cater to the requirements of their respective counterparts. Consequently, the approach may have broad applications in semi‐quantum secure multiparty computation scenarios.
Abstract Secure multi-party computational geometry is a branch of secure multi-party computation, which is applied in many important fields. But up to now, the research on how to solve this problem with quantum methods has just started. Therefore, we study the design of quantum secure multi-party computational geometry (QSMCG) protocols in this paper. As the foundation, we extend the two-party summation and multiplication protocols proposed by Sutradhar and Om to multi-party protocols. Then we propose three new QSMCG protocols. Our proposed quantum secure two-party distance computation protocol has improvement in efficiency and accuracy. And the proposed quantum secure multi-party polytope volume computation protocol as well as the quantum secure circle–circle intersection area computation protocol are designed for the first time. Moreover, these protocols are designed to use multi-third parties, which solves the problem of intermediate value leakage in computation. The correctness, security and performance of all these protocols are analyzed.
Abstract Secure multiparty computational geometry is an essential field of secure multiparty computation. It involves solving geometric problems without disclosing any private geometric information from each participating party. Privacy-preserving point-line relation determination, a pivotal branch of secure multiparty computational geometry, holds significant potential for applications in various domains, including business, engineering, and military. In this paper, leveraging the assistance of a third party, we introduce a quantum solution to privacy-preserving point-line relation determination. This approach incorporates quantum key distribution and one-time pad encryption. Under the condition that the third party does not conspire with any participant, our protocol ensures heightened security and enhanced privacy protection compared to classical methods. This superiority is attributed to the underlying principles of quantum mechanics and the utilization of one-time pad encryption. Furthermore, we extend our protocol to involve multiple third parties, employing the technology of quantum secret sharing. In scenarios where these third parties refrain from colluding with any single participant, no information is divulged to the other participant. Consequently, the protocol becomes more rational and secure when multiple third parties are involved.