高效的区间保密计算及应用
发布时间：2018-11-02 10:08
【摘要】：多方保密计算是目前国际密码学界的研究热点,是网络空间隐私保护与信息安全的关键技术.密码学者已经研究了很多多方保密计算问题,但更多的多方保密计算问题还有待研究.文中研究一个重要的多方保密计算问题——有理数的区间的保密计算,即保密地计算一个保密的有理数在不在另一个保密的有理数区间内.该问题在密码学中有重要的理论意义,在其他多方保密计算协议的构造中有重要的实际意义,在隐私保护方面有广泛的应用.其中包括计算几何上的点与圆环的包含问题,点与无限区域的包含问题,点与线段的包含问题等.甚至在现实的商品交易中,运用该问题的解决方案能够减少交易成本.文中基于Paillier同态加密方案,以百万富翁协议为基本思想,利用计算几何理论,将有理数区间保密计算问题输入的有理数看成过原点的直线的斜率,将区间保密计算问题归约为直线之间的位置关系,根据平面直角坐标系上三点定义的三角形面积计算公式,设计了一个高效的有理数区间保密计算协议;采用基本算术知识,将有理数的大小比较归约到算术不等式的判定,调用对称密码整数集百万富翁协议,设计了另一个高效的有理数区间保密计算协议;用模拟范例证明了两个协议的安全性;通过理论和实际编程分析了协议的效率;分析表明两个协议是正确高效的;最后给出了协议在解决其他多方保密计算问题中的应用实例.
[Abstract]:Multi-party secure computing is a research hotspot in the field of cryptography and the key technology of privacy protection and information security in cyberspace. Cryptographers have studied many multi-party secure computing problems, but more multi-party secure computing problems need to be studied. In this paper, we study an important problem of multiparty secure computation, that is, the secure computation of the interval of rational numbers, that is, the secret calculation of a secure rational number in the interval of another secure rational number. This problem has important theoretical significance in cryptography, important practical significance in the construction of other multi-party secure computing protocols, and is widely used in privacy protection. It includes the inclusion problem of point and circle in computational geometry, the inclusion problem of point and infinite region, the inclusion problem of point and line segment and so on. Even in real commodity trading, the solution to this problem can reduce transaction costs. Based on the homomorphic encryption scheme of Paillier, taking the millionaire protocol as the basic idea and using the computational geometry theory, the rational number inputted in the rational number interval security calculation problem is regarded as the slope of the straight line passing through the origin. The problem of interval security calculation is reduced to the position relation between straight lines. According to the calculation formula of triangle area defined by three points in the plane rectangular coordinate system, an efficient interval security calculation protocol for rational numbers is designed. By using basic arithmetic knowledge, the size of rational number is reduced to the judgement of arithmetic inequality, and another efficient interval secure computing protocol of rational number is designed by calling the symmetric integer set millionaire protocol. The security of the two protocols is proved by a simulation example; the efficiency of the two protocols is analyzed by theoretical and practical programming; the analysis shows that the two protocols are correct and efficient; finally, an application example of the protocol in solving other multi-party security computing problems is given.
【作者单位】： 陕西师范大学计算机科学学院;中国科学院软件研究所可信计算与信息保障实验室;陕西师范大学数学与信息科学学院;清华大学计算机科学与技术系;
【基金】：国家自然科学基金(61272435,61373020,U1536102,U1536116) 中央高校基本科研业务费专项资金(GK201504017)资助~~
【分类号】：TP309
[Abstract]:Multi-party secure computing is a research hotspot in the field of cryptography and the key technology of privacy protection and information security in cyberspace. Cryptographers have studied many multi-party secure computing problems, but more multi-party secure computing problems need to be studied. In this paper, we study an important problem of multiparty secure computation, that is, the secure computation of the interval of rational numbers, that is, the secret calculation of a secure rational number in the interval of another secure rational number. This problem has important theoretical significance in cryptography, important practical significance in the construction of other multi-party secure computing protocols, and is widely used in privacy protection. It includes the inclusion problem of point and circle in computational geometry, the inclusion problem of point and infinite region, the inclusion problem of point and line segment and so on. Even in real commodity trading, the solution to this problem can reduce transaction costs. Based on the homomorphic encryption scheme of Paillier, taking the millionaire protocol as the basic idea and using the computational geometry theory, the rational number inputted in the rational number interval security calculation problem is regarded as the slope of the straight line passing through the origin. The problem of interval security calculation is reduced to the position relation between straight lines. According to the calculation formula of triangle area defined by three points in the plane rectangular coordinate system, an efficient interval security calculation protocol for rational numbers is designed. By using basic arithmetic knowledge, the size of rational number is reduced to the judgement of arithmetic inequality, and another efficient interval secure computing protocol of rational number is designed by calling the symmetric integer set millionaire protocol. The security of the two protocols is proved by a simulation example; the efficiency of the two protocols is analyzed by theoretical and practical programming; the analysis shows that the two protocols are correct and efficient; finally, an application example of the protocol in solving other multi-party security computing problems is given.
【作者单位】： 陕西师范大学计算机科学学院;中国科学院软件研究所可信计算与信息保障实验室;陕西师范大学数学与信息科学学院;清华大学计算机科学与技术系;
【基金】：国家自然科学基金(61272435,61373020,U1536102,U1536116) 中央高校基本科研业务费专项资金(GK201504017)资助~~
【分类号】：TP309
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