{"title":"Quantum Secure Clockwise Sorting","authors":"Guixin Jiang, Zixian Li, Haibin Wang, Sunil Kumar Jha","doi":"10.1007/s10773-024-05676-x","DOIUrl":null,"url":null,"abstract":"<p>Secure computational geometry (SCG) is an important type of secure multi-party computation (SMC) problem, which studies how to calculate the relationship of several geometric objects securely. Quantum SCG (QSCG) can achieve higher security than classical SCG protocols, but the achievements of QSCG are still limited at present. In this paper, we define a new SCG problem: the secure clockwise sorting (SCS) problem, and propose a quantum protocol to solve it. We first propose a quantum secure clockwise comparison subprotocol, where the cross and scalar products of two vectors are calculated by using a quantum secure two-party scalar product protocol, and then the relative clockwise order of two points is determined. Based on the subprotocol, we then give a quantum SCS protocol to determine the clockwise order of a series of points. Finally, we show the correctness, security, and efficiency of our protocol through detailed performance analysis.</p>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10773-024-05676-x","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Secure computational geometry (SCG) is an important type of secure multi-party computation (SMC) problem, which studies how to calculate the relationship of several geometric objects securely. Quantum SCG (QSCG) can achieve higher security than classical SCG protocols, but the achievements of QSCG are still limited at present. In this paper, we define a new SCG problem: the secure clockwise sorting (SCS) problem, and propose a quantum protocol to solve it. We first propose a quantum secure clockwise comparison subprotocol, where the cross and scalar products of two vectors are calculated by using a quantum secure two-party scalar product protocol, and then the relative clockwise order of two points is determined. Based on the subprotocol, we then give a quantum SCS protocol to determine the clockwise order of a series of points. Finally, we show the correctness, security, and efficiency of our protocol through detailed performance analysis.
期刊介绍:
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.