基于云计算的安全高效矩阵求逆方案

Secure and Efficient Computing Matrix Inversion in Cloud

摘要: 本文研究了基于云计算的矩阵求逆安全外包问题。针对现有方案安全性较弱等问题，我们提出了一种新的矩阵安全变换机制，可以使用随机的稠密矩阵对用户输入矩阵进行安全乘法变换，能够有效提升用户输入输出的安全性。同时，我们设计了一种新的稠密随机矩阵生成方法，可以支持快速的矩阵乘法，从而能够大幅降低用户的计算复杂度。我们通过理论分析证明了所提方案的安全性。最后，我们通过模拟实验验证了所提方案的运行效率。

Abstract: This paper studies secure matrix inversion outsourcing in cloud. We point out the security weakness of the existing scheme, and then propose a new solution which perturbs the private matrix by multiplying two random dense matrices and thus can improve the security. Besides, we present a new method to generate random dense matrices and achieve fast matrix multiplication, by which we can dramatically reduce users’ computation cost. We theoretically prove the security of our proposed scheme, and confirm the high efficiency of our proposed scheme by simulation experiments.