Secure Batch Matrix Multiplication From Grouping Lagrange Encoding

In this letter, the problem of distributed Secure Batch Matrix Multiplication (SBMM) is studied, where a user wishes to compute the pairwise products of two batches of massive matrices $\mathbf {A}$ and $\mathbf {B}$ generated by two external source nodes, with the aid of $N$ distributed servers. The security for data matrices $\mathbf {A}$ (resp. $\mathbf {B}$ ) is guaranteed against any group of up to $X_{\mathbf {A}}$ (resp. $X_{\mathbf {B}}$ ) colluding servers. As a result, a computation strategy is presented to characterize the trade-off between recovery threshold, system cost and system complexity, based on grouping Lagrange encoding, which unifies and improves the previous strategies for SBMM.