基于分布式线性方程组求解的安全多方计算协议

Secure Protocols for Resolving Distributed System of Linear Equations

不同组织之间的合作关系常用求解线性方程组或线性不等式组等线性代数问题来建模。当合作过程中涉及到数据的隐私保护时,一般直接求解线性方程组的方法将不再适用。文章为解决此类问题,基于同态加密方式设计了求解分布式线性方程组的安全两方计算协议和安全多方计算协议。与以往基于茫然传输协议设计的安全计算协议相比,降低了协议的通信复杂度。文章给出了协议的正确性、安全性和复杂度分析。

The cooperation between different organizations is often modeled as solving linear algebra problems, such as linear system of equations or linear inequalities. If participants concern about the data privacy in the process of cooperation, common method of directly solving linear system of equations will no longer apply. This paper designs a secure two-party protocol and a secure multi-party protocol based on homomorphic encryption scheme for solving distributed linear system of equations. Compared to the protocols based on oblivious transfer protocol, the communication complexity is reduced. This paper also gives the correctness, security and complexity analysis.