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.
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.
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 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.
The advent of quantum computing presents a paradigm shift in modern cybersecurity, threatening the foundations of classical cryptographic systems such as RSA, ECC, and Diffie–Hellman key exchange. Quantum algorithms like Shor’s and Grover’s can efficiently break these schemes, rendering existing encryption mechanisms vulnerable and obsolete. This growing risk necessitates the development of quantum-resilient or post-quantum cryptographic (PQC) solutions that can safeguard data and computation in the era of quantum networks. Secure Multi-Party Computation (SMPC), a cornerstone of privacy-preserving computation, enables multiple entities to jointly compute a function over their private inputs without revealing them. However, its traditional security assumptions are also undermined by quantum threats. This research aims to explore and evaluate quantum-safe cryptographic protocols for integrating PQC into SMPC frameworks, thereby ensuring both confidentiality and correctness even in the presence of quantum-capable adversaries. The study focuses on lattice-based, hash-based, and code-based cryptographic primitives, analyzing their resilience, efficiency, and scalability when applied to distributed systems. A comparative framework is proposed to assess the performance and security trade-offs of different post-quantum SMPC implementations under realistic network conditions. The findings are expected to contribute to the design of a new class of cryptographic protocols capable of resisting quantum attacks, supporting the secure functioning of next-generation networks, and guiding policymakers and technologists toward practical post-quantum standardization. Ultimately, this research strengthens the bridge between theoretical cryptography and real-world cybersecurity readiness in the post-quantum era.
At present, research on secure multi-party computation is of great interest in modern cryptography. It should be acknowledged that if any function can be computed securely, then it results in a very powerful tool. In fact, all natural protocols are, or can be rephrased to be, special cases of the multi-party computation problems. Design and analysis of the special multi-party computation protocols is meaningful and has attracted much interest in this field. Based on the combination of a public-key cryptosystem of the homomorphic encryption and on the theoretic construction relying on the F-hiding assumption, a protocol for comparing information of equality is proposed. The protocol needs only a single round of interaction and ensures fairness, efficiency and security. The protocol is fair, which means that one party knows the sound result of the comparison if and only if the other one knows the result. The protocol is efficient with the help of an oblivious third party for calculating. However, the third party cannot learn any information about the participant抯 private inputs and even about the comparison result, and cannot collude with any participant. The protocol is secure for the two participants, that is, any information about their secret input will not leak except the final computation result. A precise proof of security of the protocol is presented. Applications of this protocol may include private bidding and auctions, secret ballot elections, commercial business, identification in a number of scenarios and so on. It is believed that the protocol may be of practical significance for electronic transaction.
This paper investigates the application of quantum-inspired cryptographic principles to enhance the security and efficiency of secure multi-party computation (SMC) protocols. Traditional SMC protocols, such as Shamir's Secret Sharing, rely on classical cryptographic assumptions that are increasingly vulnerable to advancements in computing power, particularly with the rise of quantum computers. We propose a framework leveraging concepts from quantum mechanics, specifically superposition and probabilistic approaches, to construct novel SMC protocols. These protocols aim to achieve comparable security levels to existing methods while potentially offering improved performance characteristics and resilience against attacks exploiting classical vulnerabilities. The core of our approach involves replacing deterministic operations with probabilistic ones, mimicking the inherent uncertainty in quantum systems. This reduces the reliance on hard mathematical problems and introduces a layer of complexity that is more difficult for adversaries to analyze. The paper details the design of a modified Shamir Secret Sharing scheme incorporating these quantum-inspired elements and provides a theoretical analysis of its security properties. Ultimately, this work contributes to the exploration of a new paradigm in cryptography, adapting quantum-inspired techniques to bolster the security of distributed computing environments.