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Physica Scripta

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

Zhenwan Peng, Runhua Shi, Ran Ding, Feifan Zhang

Published Mar 4, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ad3028

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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 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.
With the rapid advancement of information technology, data sharing has become increasingly accessible, leading to a heightened need for robust personal data protection. One important application in privacy-preserving computing is the aggregation of information when collaboratively establishing AI models through public distributed networks. To counter the threat posed by quantum computing to encrypted data, various quantum private summation (QPS) protocols have been proposed thus far. However, some of these existing protocols operate solely under modulo 2, while other approaches for modulo d often rely on impractically high-dimensional qudits. Therefore, this study proposes an innovative multiparty QPS method that balances participant data sharing and privacy without requiring high-dimensional photons. The proposed QPS protocol enables participants to contribute aggregated information to third parties without disclosing individual data. A security analysis further demonstrates that the proposed QPS effectively counters common eavesdropping attacks, ensuring reliable protection of personal data.
Convex hull computation is a fundamental problem in secure multi-party computational geometry (SMCG), classified under secure multi-party computation (SMC) for finding the convex hull of a set of points. Existing quantum solutions largely depend on quantum homomorphic encryption (QHE), which introduces significant computational overhead due to frequent key updates by a trusted third party (TTP). Furthermore, most current protocols lack a mechanism for input commitment, making them vulnerable to post-computation input tampering or denial by the TTP. To overcome these limitations, we propose an efficient convex hull protocol that utilizes quantum secret commitment (QSC) as a more secure alternative to QHE. Our protocol enables a designated party (the committer) to securely commit to input values in a manner that guarantees both binding (no post-hoc alteration) and hiding (input secrecy). We introduce a novel value comparison protocol within an Ideal Quantum K-Party model, ensuring privacy-preserving convex hull computation without reliance on QHE. Rigorous security analysis demonstrates significant improvements in computational efficiency and resilience against quantum adversaries. Our protocol represents a pivotal advancement for quantum-secure multi-party computations and lays the groundwork for scalable, future-proof privacy-preserving geometry in quantum computing contexts.
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.
This paper presents a multiparty quantum private comparison (MQPC) protocol that facilitates multiple users to compare the equality of their private inputs while preserving the confidentiality of each input through the principles of quantum mechanics. In our approach, users initially convert their secret integers into binary representations, which are then encoded into single photons that act as carriers of the information. These encoded single-photon states undergo encryption via rotational operations, effectively obscuring the original inputs before transmission to a semi-honest third party (TP). The TP decrypts the quantum states and conducts Z-basis measurements to derive the comparison results. To enhance security, the protocol incorporates decoy photons, enabling participants to detect potential eavesdropping on the quantum channel. Importantly, even if the TP or other participants attempt to glean insights into each other’s inputs, the encryption via rotational operations ensures that private information remains inaccessible. This protocol demonstrates significant advancements in practicality compared to existing MQPC frameworks that rely on complex quantum technologies, such as entanglement swapping and multi-particle entanglement. By leveraging the simplicity of single photons, rotation operations, and Z-basis measurements, our protocol is more accessible for implementation.
Quantum private comparison (QPC) is a quantum cryptographic protocol designed to enable two mutually distrustful parties to securely compare sensitive data without disclosing their private information to each other or any external entities. This study proposes a novel QPC protocol that leverages Bell states to ensure data privacy, utilizing the fundamental principles of quantum mechanics. Within this framework, two participants, each possessing a secret integer, encode the binary representation of their values using Pauli-X and Pauli-Z operators applied to quantum states transmitted from a semi-honest third party (TP). The TP, which is bound to protocol compliance and prohibited from colluding with either participant, measures the received sequences to determine the comparison result without accessing the participants’ original inputs. Theoretical analyses and simulations validate the protocol’s strong security, high efficiency, and practical feasibility in quantum computing environments. An advantage of the proposed protocol lies in its optimized utilization of Bell states, which enhances qubit efficiency and experimental practicality. Moreover, the proposed protocol outperforms several existing Bell-state-based QPC schemes in terms of efficiency.