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Journal of Convergence Information Technology

Improvement of a Secure Convex Hull Two-Party Computation Protocol

Zhao Wenjie -, Mingxing He

Published May 26, 2010• 2 citations
Publisher
DOI
10.4156/jcit.vol5.issue3.4

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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.