Locally Encoded Secure Distributed Batch Matrix Multiplication.

We study the problem of locally encoded secure distributed batch matrix multiplication (LESDBMM), where M pairs of sources each encode their respective batches of massive matrices and distribute the generated shares to a subset of N worker nodes. Each worker node computes a response from the received shares and sends the result to a sink node, which must be able to recover all M batches of pairwise matrix products in the presence of up to S stragglers. Additionally, any set of up to X colluding workers cannot learn any information about the matrices. Based on the idea of cross-subspace (CSA) codes and CSA null shaper, we propose the first LESDBMM scheme for batch processing. When the problem reduces to the coded distributed batch matrix multiplication (CDBMM) setting where M=1,X=0 and every source distributes its share to all worker nodes, the proposed scheme achieves performance matching that of the cross-subspace alignment (CSA) codes for CDBMM in terms of the maximum number of tolerable stragglers, communication cost, and computational complexity. Therefore, our scheme can be viewed as a generalization of CSA codes for CDBMM to the LESDBMM setting.