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 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 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 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 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.
Quantum secure multi-party summation (QSMS) is a fundamental problem in quantum secure multi-party computation (QSMC), wherein multiple parties compute the sum of their data without revealing them. This paper proposes a novel QSMS protocol based on graph state, which offers enhanced security, usability, and flexibility compared to existing methods. The protocol leverages the structural advantages of graph state and employs random graph state structures and random encryption gate operations to provide stronger security. Additionally, the stabilizer of the graph state is utilized to detect eavesdroppers and channel noise without the need for decoy bits. The protocol allows for the arbitrary addition and deletion of participants, enabling greater flexibility. Experimental verification is conducted to demonstrate the security, effectiveness, and practicality of the proposed protocols. The correctness and security of the protocols are formally proven. The QSMS method based on graph state introduces new opportunities for QSMC. It highlights the potential of leveraging quantum graph state technology to securely and efficiently solve various multi-party computation problems.
Abstract Quantum secure multi-party computation (SMC) is a vital field in quantum cryptography. In this paper, we try to resolve SMC problems universally via graph states. Firstly, three kinds of quantum SMC protocols are investigated, which are quantum private comparison protocol, quantum millionaire protocol and quantum multi-party summation protocol. Secondly, three proposed protocols are reviewed, and then the core of them is summarized. We further find that the computation, deduced as modulo subtraction, can be resolved by using graph state. This implies that our protocols are universal in part and will be widely applicable. Thirdly, analyses show that the proposed protocols are correct and secure. Our research will promote the development of quantum secure multi-party computation.