In secure distributed matrix multiplication (SDMM) the multiplication $\bm A\bm B$ from two private matrices $\bm A$ and $\bm B$ is outsourced by a user to $N$ distributed servers. In $\ell$-SDMM, the goal is to design a joint communication-computation procedure that optimally balances conflicting communication and computation metrics without leaking any information on both $\bm A$ and $\bm B$ to any set of $\ell\leq N$ servers. To this end, the user applies coding with $\tilde{\bm A}_i$ and $\tilde{\bm B}_i$ representing encoded versions of $\bm A$ and $\bm B$ destined to the $i$-th server. Now, SDMM involves multiple tradeoffs. One such tradeoff is the tradeoff between uplink (UL) and downlink (DL) costs. To find a good balance between these two metrics, we propose two schemes which we term USCSA and GSCSA that are based on secure cross subspace alignment (SCSA). We implement schemes from the literature, in addition to USCSA and GSCSA, and test their performance on Amazon EC2. Our numerical results show that USCSA and GSCSA establish a good balance between the time spend on the communication and computation in SDMMs. This is because they combine advantages of polynomial codes, namely low time for the upload of $\left(\tilde{\bm A}_i,\tilde{\bm B}_i\right)_{i=1}^{N}$ and the computation of $\bm O_i=\tilde{\bm A}_i\tilde{\bm B}_i$, with those of SCSA, being a low timing overhead for the download of $\left(\bm O_i\right)_{i=1}^{N}$ and the decoding of $\bm A\bm B$.


Jaber Kakar

Ruhr University Bochum

Anton Khristoforov

Ruhr University Bochum

Seyedhamed Ebadifar

Ruhr University Bochum

Aydin Sezgin

Ruhr University Bochum

Session Chair

Yuval Kochman

Hebrew University of Jerusalem