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 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 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.
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 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 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.
Range query in cloud-based outsourcing applications is an important data search service, but it can suffer from privacy disclosure. In this paper, we generalize and redefine privacy-preserving range query in edge-based Internet of Things (IoT). Furthermore, to enhance security and privacy of sensitive data, we introduce quantum cryptographic technologies and present a novel quantum approach to solve the problem. First, we present a feasible protocol for Quantum Secret Permutating (QSP) with single photons, which will be later utilized in the final scheme as a basic block. Second, we generalize traditional privacy-preserving range query to a secure one-sided two-party computation, i.e., specific dot product. Third, we present a synchronously grouping strategy based on Quantum Key Distribution (QKD) to reduce the complexity and improve the efficiency of solving this two-party computation, so that it can easily get the desired result by repeatedly using feasible quantum privacy query group by group. Finally, adopting our previously proposed quantum protocols, we design privacy-preserving range query quantum scheme in edge-based IoT. Compared with the classical related schemes, our proposed quantum scheme has higher security, because the security of our proposed protocols is based on the basic physical principles of quantum mechanics, instead of unproven computational difficulty assumptions.
Range query in cloud-based outsourcing applications is an important data search service, but it can suffer from privacy disclosure. In this paper, to enhance the security and privacy of sensitive data, we introduce quantum cryptographic technologies and present a feasible quantum approach to address an important range query, i.e., privacy-preserving range MAX/MIN query. First, we define a primitive protocol of secure multiparty computations, called Oblivious Set Inclusion Decision (OSID), in which two parties jointly decide whether a private set includes another private set in an oblivious way, and present an efficient OSID quantum protocol. Especially, in order to efficiently implement OSID quantum protocol, we design a single-photon-based quantum protocol for computing XOR of two private bits, which can achieve the information-theoretical security with the help of a non-colluding quantum cloud. Finally, we propose a novel quantum scheme for privacy-preserving range MAX/MIN query in edge-based Internet of Things by using OSID quantum protocols. Compared with the classical related schemes, our proposed quantum scheme has higher security (i.e., quantum security), because the security of our proposed protocols is based on the basic physical principles of quantum mechanics, instead of unproven computational difficulty assumptions.