基于阈值的向量保密计算

Secure Vector Computation Based on Threshold

向量保密计算已成为安全多方计算的重要研究课题.对于向量优势与向量等分量数这类问题,现有的相关计算协议大多都是在有全集限制的条件下,通过编码方法设计的.当数据范围较大较分散时,此类方法具有一定的局限性.本文针对向量中数据没有全集限制的情形,提出并研究向量优势阈值问题以及向量等分量数阈值问题的双方保密计算.通过灵活运用加密算法的同态性质以及明文空间的有关性质,结合问题转化以及加密选择等技巧,对于向量优势阈值问题设计了安全高效的保密计算协议.当设置阈值为向量维数时,本文协议可用于解决向量优势判定问题,且与已有协议相比具有更高的效率.在向量优势阈值协议的基础上,进一步构造向量等分量数阈值问题的计算协议,并通过严格分析证明了本文协议的正确性,应用模拟范例严格证明了协议的安全性.最后,对协议的效率进行了详细的分析比较,并通过实验验证了协议的实际可行性.

Secure vector computation has become an important problem in secure multiparty computation.For vector dominance and equal problems,most of the existing computation protocols are designed by coding methods under the condition that the private data belong to a known set.When the data range is large and scattered,such methods have certain limitations.In this paper,the problem of threshold vector dominance and threshold vector problem with equal number of components under the condition that the components of the private vectors do not belong to a known set are proposed.By using the homomorphism property of some encryption algorithms,the flexibility of plaintext space,and the methods of problem transformation and encrypt-and-choose,a secure and efficient computation protocol for threshold vector dominance problem is designed.Based on this,a protocol for threshold vector problem with equal number of components is constructed,and the security of the protocol is proven using the simulation paradigm,the efficiency of the protocol is analyzed,and the practical feasibility of the protocol is verified by the experiments.