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We consider the problem of secure distributed matrix multiplication in whicha user wishes to compute the product of two matrices with the assistance ofhonest but curious servers. In this paper, we answer the following question: Isit beneficial to offload the computations if security is a concern? We answerthis question in the affirmative by showing that by adjusting the parameters ina polynomial code we can obtain a trade-off between the user's and the servers'computational time. Indeed, we show that if the computational time complexityof an operation in $\mathbb{F}_q$ is at most $\mathcal{Z}_q$ and thecomputational time complexity of multiplying two $n\times n$ matrices is$\mathcal{O}(n^\omega \mathcal{Z}_q)$ then, by optimizing the trade-off, theuser together with the servers can compute the multiplication in$\mathcal{O}(n^{4-\frac{6}{\omega+1}} \mathcal{Z}_q)$ time. We also show thatif the user is only concerned in optimizing the download rate, a commonassumption in the literature, then the problem can be converted into a simpleprivate information retrieval problem by means of a scheme we call PrivateOracle Querying. However, this comes at large upload and computational costsfor both the user and the servers.

Notes on Communication and Computation in Secure Distributed Matrix Multiplication