摘要 利用格上LWE (Leaning With Error)困难性假设，将保密地比较两个数是否相等转化为判断对随机串加密后的解密是否正确，有效地解决了数和集合关系的判定、求集合交集和集合相等安全多方计算问题，并利用模拟范例证明该协议在半诚实模型下是安全的。与传统的基于数论的协议相比，该方案由于不需要模指数运算，因而具有较低的计算复杂度，同时因其基于格中困难问题，因而能抵抗量子攻击。
Abstract：Using Learning With Errors (LWE) in the lattice, the equation test is converted to a decryption ability of a random string. It solves the secure two-party computation such as the relationship of an element and a set, set intersection, and set equation etc. The simulations in the semi-honest model show that these two-party solutions are secure and efficient. Compared with protocols based on security assumptions in number theory, the proposed protocols not only have lower computational complexity without exponential operations but can also resist quantum attack because of the assumption on lattice problem.
夏峰, 杨波, 张明武, 马莎, 雷涛. 基于LWE的集合相交和相等的两方保密计算[J]. 电子与信息学报, 2012, 34(2): 462-467.
Xia Feng, Yang Bo, Zhang Ming-Wu, Ma Sha, Lei Tao. Secure Two-party Computation for Set Intersection and Set Equality Problems Based on LWE. , 2012, 34(2): 462-467.
2012, Vol. 34 
