论文标题
从MDS编码的存储中，信息从理论上私有矩阵乘法
Information-Theoretically Private Matrix Multiplication From MDS-Coded Storage
论文作者
论文摘要
我们研究了由主节点组成的分布式计算系统的私有矩阵乘法的两个问题，以及多个使用最大距离分离（MDS）代码共同存储公共矩阵家族的服务器。 In the first problem of Private and Secure Matrix Multiplication (PSMM) from colluding servers, the master intends to compute the product of its confidential matrix $\mathbf{A}$ with a target matrix stored on the servers, without revealing any information about $\mathbf{A}$ and the index of target matrix to some colluding servers.在第二个问题的第二个问题中，还从MDS形式以MDS形式存储在服务器上的另一个公共矩阵家族中选择了矩阵$ \ mathbf {a} $。在这种情况下，两个目标矩阵的索引均应使串谋服务器私密。我们为两个PSMM和FPMM问题开发了新颖的策略，这些策略同时保证了信息理论数据/指数隐私和计算正确性。我们将提出的PSMM策略与以前的PSMM策略和较弱的隐私保证（非批量服务器）进行了比较，并就通信和计算开销方面证明了对先前策略的实质性改进。此外，与基线FPMM策略相比，该策略使用私人信息检索（PIR）直接检索所需的矩阵乘法的概念，提出的FPMM策略大大减少了开销的存储空间，但略微造成了大型的通信和计算开销。
We study two problems of private matrix multiplication, over a distributed computing system consisting of a master node, and multiple servers that collectively store a family of public matrices using Maximum-Distance-Separable (MDS) codes. In the first problem of Private and Secure Matrix Multiplication (PSMM) from colluding servers, the master intends to compute the product of its confidential matrix $\mathbf{A}$ with a target matrix stored on the servers, without revealing any information about $\mathbf{A}$ and the index of target matrix to some colluding servers. In the second problem of Fully Private Matrix Multiplication (FPMM) from colluding servers, the matrix $\mathbf{A}$ is also selected from another family of public matrices stored at the servers in MDS form. In this case, the indices of the two target matrices should both be kept private from colluding servers. We develop novel strategies for the two PSMM and FPMM problems, which simultaneously guarantee information-theoretic data/index privacy and computation correctness. We compare the proposed PSMM strategy with a previous PSMM strategy with a weaker privacy guarantee (non-colluding servers), and demonstrate substantial improvements over the previous strategy in terms of communication and computation overheads. Moreover, compared with a baseline FPMM strategy that uses the idea of Private Information Retrieval (PIR) to directly retrieve the desired matrix multiplication, the proposed FPMM strategy significantly reduces storage overhead, but slightly incurs large communication and computation overheads.
