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| 数轴上保密关系测定协议 |
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巩林明1,2, 李顺东3, 邵连合1, 薛涛1, 王道顺4
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1.西安工程大学 计算机科学学院 新型网络智能信息服务国家地方联合工程研究中心, 陕西 西安 710048;2.陕西省功能性服装面料重点实验室(西安工程大学), 陕西 西安 710048;3.陕西师范大学 计算机科学学院, 陕西 西安 710119;4.清华大学 计算机科学与技术系, 北京 100084
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| 摘要: |
| 近些年来，安全多方计算一直是信息安全领域的热点问题之一，已经成为分布式网络用户在协同计算中用于隐私保护的关键技术.信息安全学者已经提出若干安全多方计算问题的解决方案，但更多的安全多方计算问题还有待研究.研究数轴上的保密关系测定问题，着重探讨3个子问题：（1）面向有理数的点（或数）与区间保密关系测定问题；（2）面向有理数的多维点与区间保密关系测定问题；（3）面向有理数的区间与区间保密关系测定问题.数轴上的保密关系测定问题在隐私保护领域有着广泛的应用，可以作为基础模块用于构造其他安全多方计算协议.基于由加密方计算（或选取）加密底数的Paillier变体同态加密方案，设计了3个数轴上的保密关系测定协议：面向有理数的数与区间保密关系测定协议、面向有理数的多维点与区间保密关系测定协议以及面向有理数的区间与区间保密关系测定协议.并在标准模型下，采用模拟范例（ideal/real）分析了3个协议的安全性.这3个协议中的保密比值计算思想直接可以用于解决有理数范围内的百万富翁问题.更广泛地，这3个协议还可以作为基础模块用于解决保密点与圆环区域关系判定问题、点与凸多边型位置关系判定问题、保密近感探测问题等安全多方计算问题. |
| 关键词: 保密关系测定 隐私保护 安全多方计算 分布式协同计算 |
| DOI：10.13328/j.cnki.jos.005858 |
| 分类号: |
| 基金项目:西安工程大学博士科研启动基金（107020331）；陕西省教育厅重点科学研究计划（20JS052）；陕西省2020年技术创新引导专项计划（2020CGXNG-012）；国家自然科学基金（61972225） |
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| Protocols for Secure Test on Relationship on Number Axis |
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GONG Lin-Ming1,2, LI Shun-Dong3, SHAO Lian-He1, XUE Tao1, WANG Dao-Shun4
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1.The National and Local Joint Engineering Research Center for Advanced Networking & Intelligent Information Service, School of Computer Science, Xi'an Polytechnic University, Xi'an 710048, China;2.Shaanxi Key Laboratory on Functional Cloths(Xi'an Polytechnic University), Xi'an 710048, China;3.School of Computer Science, Shaanxi Normal University, Xi'an 710062, China;4.Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
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| Abstract: |
| In recent years, secure multiparty computation (SMC) is one of research focuses in the field of information security, and a key technology of privacy protecting for distributed users in their jointly evaluating. Researchers have proposed many schemes for SMC problem, however, there are many other secure multi-computation problems needed to be investigated. This study involves private relationship test on number axis, which covers three subproblems: (1) secure test on the relationship between a confidential number and a private interval; (2) multi-dimensional secure test on the relationship between multi-number and multi-interval; (3) secure test on the relationship between two confidential intervals. Private relationship test on number axis has an extensive application in the field of privacy protection, and it can be employed as a basic block to construct other SMC protocols. Based on a variant encryption scheme of Paillier’s homomorphic encryption (in which, who encrypts message who evaluates the base), three protocols for private relationship test on number axis are designed. They are secure test on the relationship between a confidential number and a private interval, multi-dimension secure test on the relationship between multi-number and multi-interval, and secure test on the relationship between two confidential intervals. And their security is analyzed using simulation framework (idea/real) in the standard model. The idea of private ratio calculation in these three protocols can be directly used to solve the millionaire problem within the range of rational numbers. More widely, these three protocols can be employed as a basic block to solve the following SMC problems: private test on relationship between a point and an annulus, private test on relationship between a point and a convex polygon, and private proximity test. |
| Key words: private relationship test privacy protection multiparty secure computation distributed and collaborative computation |
