可验证安全外包矩阵计算及其应用

Verifiable and secure outsourcing of matrix calculation and its application

矩阵计算在科学计算和密码学领域中都有着重要的作用.许多密码协议、科学和数值计算问题都涉及到了矩阵计算.然而,对那些计算能力有限的用户来说,独立完成矩阵计算并不是件容易的事情.云计算拥有强大的计算资源,它使得用户的计算能力不再受限于他们的资源约束型设备,他们可以外包工作量给云.本文围绕矩阵计算展开研究,针对矩阵乘积、矩阵的行列式以及矩阵的逆这3种运算,分别设计了切实可行的可验证安全外包协议.与已有的关于这3种可验证外包计算的协议相比,我们的协议在效率和安全性方面都有了改进,而且我们的协议不需要任何的密码学假设.本文中,还为我们的协议给出两个具体应用,即为"大型线性方程组的求解"以及"基于纠错码的密码体制的实现"这两个问题分别构造了高效的可验证外包计算协议.

Matrix calculation plays an important role in both scientific computation and cryptography. Many cryptographic protocols, scientific computations, and numerical computations are based on matrix calculation. However, it is difficult to finish matrix calculation independently for these customers whose computation abilities are limited. Cloud Computing has a great deal of computational resources, which enable customers with limited computational resources to outsource their mass computing to the cloud. In this paper we design secure, verifiable, and practical outsourcing protocols for matrix calculation, including matrix multiplication, computing the deter- minant and inverse of a matrix. Compared with those existing outsourcing protocols, our protocols have obvious improvement concerning both efficiency and security. ~rthermore, no cryptographic assumption is needed in our protocols. Finally, we give two applications for our outsourcing protocols; one is to construct an outsourcing protocol for solving the large-scale systems of linear equations, and the other is to design an outsourcing protocol for realizing a cryptosystem based on error-correction code.