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Chinese Physics B

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

B Y Liu, Xin-Guo Wang

Published May 26, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ae7275

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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 With the growing demand for location privacy protection and collaborative computing in spatial crowdsourcing (SC) tasks, traditional encryption methods based on computational complexity face threats from quantum computing and efficiency bottlenecks. To address this, this paper proposes a secure multi-party quantum comparison (SMQC) protocol based on quantum homomorphic encryption. By utilizing a quantum comparator and a key update mechanism, this protocol enables secure comparison of numerical values among multiple parties while maintaining encryption. Building on this foundation, the SMQC protocol is further applied to the SC environment to construct a single-point collaborative convex hull computation protocol. Through extreme point determination and convex hull boundary verification, this protocol efficiently performs multi-party collaborative convex hull computation while protecting the location privacy of participants. Analysis indicates that the convex hull computation framework built on this protocol is reliable and secure, further expanding the application of quantum-secure solutions in SC scenarios such as single-point collaborative obstacle avoidance and collaborative spatial protection.
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.
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 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.
Secure multi-party computation (SMC) allows multiple parties to jointly and securely compute a function while preserving the privacy of the involved parties. In this regard, homomorphic cryptosystems allow users to perform addition or multiplication operations on encrypted values without having to decrypt the input values. In this paper, we propose both a cryptographic and a non-cryptographic privacy-preserving protocols that allow one party to collaboratively compute a private polynomial function with at least two other parties using semantically secure cryptosystems. In this respect, the function to be evaluated is kept private to the party in question. In addition, we assume that there is no fully trusted party and that all parties are semi-honest. Moreover, we assume that there is no collusion between the different parties. We present the two protocols in question and report on the underlying performance through the presentation of our implementation results. The proposed protocols are relevant in many applications such as evidence sharing in multi-party forensic investigations, situation awareness through the secure sharing in distributed monitoring of plan execution, etc.
In spatial crowdsourcing tasks, the risk of privacy leakage regarding task and workers’ locations has always been a critical issue. Although many scholars have proposed solutions based on classical computing, these methods cannot withstand potential future quantum computing attacks. This paper presents a quantum-secure protocol for selecting workers in spatial crowdsourcing, which utilizes a two-stage filtering process combining quantum multi-party geometric intersection and quantum homomorphic encryption. The protocol ensures that workers are selected without disclosing the privacy information of any participants. Compared to traditional classical protocols, our solution offers significantly higher security. The correctness analysis validates the feasibility and effectiveness of the protocol.