CAJ | 학술논문

研究了现有安全多方计算几何协议,提出了安全多方计算几何的模型和框架,从数学模型、安全模型和通信模型3个维度展开描述.针对现有安全两方线段关系判定协议都忽略求解交点坐标的问题,在半诚实模型下基于 Paillier 同态加密技术提出了安全两方线段求交协议,使用 Goldreich 证明法进行了理论安全性分析,并在恶意模型下进行了推广.分析结果表明,该半诚实模型下的算法在效率上优于现有算法.作为安全两方线段求交协议的应用,结合 O’Rourke 算法提出了保护隐私的凸包求交集协议,弥补了安全计算几何领域仅实现了凸包并集算法的缺陷.
연구료현유안전다방계산궤하협의,제출료안전다방계산궤하적모형화광가,종수학모형、안전모형화통신모형3개유도전개묘술.침대현유안전량방선단관계판정협의도홀략구해교점좌표적문제,재반성실모형하기우 Paillier 동태가밀기술제출료안전량방선단구교협의,사용 Goldreich 증명법진행료이론안전성분석,병재악의모형하진행료추엄.분석결과표명,해반성실모형하적산법재효솔상우우현유산법.작위안전량방선단구교협의적응용,결합 O’Rourke 산법제출료보호은사적철포구교집협의,미보료안전계산궤하영역부실현료철포병집산법적결함.
The model and framework of secure multi-party computational geometry were presented based on the existing protocols. The new framework has three dimensions, the math model, the security model and the communication model. Using the new model and framework, a secure two-party line segments intersection protocol based on Paillier homomor-phic encryption scheme is proposed. This protocol solves the problem that the existing secure two party inter-sect-determination schemes of line segments cannot output the exact coordinates of the intersection. The security of the protocol is demonstrated using Goldreich method. The results show that this protocol has better efficiency than the exist-ing ones. In addition, the secure two-party line segments intersection in malicious model is also designed. As an applica-tion, a privacy-preserving convex hull intersection protocol is proposed based on the O’Rourke scheme. This application makes up for the gap in privacy-preserving convex hull intersection protocol in the area of secure multi-party computa-tional geometry.