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arXiv · 2001.05568

Notes on Communication and Computation in Secure Distributed Matrix Multiplication

Rafael G. L. D'Oliveira·Salim El Rouayheb·Daniel Heinlein·David Karpuk
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Abstract

We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. In this paper, we answer the following question: Is it beneficial to offload the computations if security is a concern? We answer this question in the affirmative by showing that by adjusting the parameters in a 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 complexity of an operation in $\mathbb{F}_q$ is at most $\mathcal{Z}_q$ and the computational time complexity of multiplying two $n\times n$ matrices is $\mathcal{O}(n^\omega \mathcal{Z}_q)$ then, by optimizing the trade-off, the user together with the servers can compute the multiplication in $\mathcal{O}(n^{4-\frac{6}{\omega+1}} \mathcal{Z}_q)$ time. We also show that if the user is only concerned in optimizing the download rate, a common assumption in the literature, then the problem can be converted into a simple private information retrieval problem by means of a scheme we call Private Oracle Querying. However, this comes at large upload and computational costs for both the user and the servers.

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Rafael G. L. D'Oliveira, Salim El Rouayheb, Daniel Heinlein, David Karpuk. 2020-01-15. Notes on Communication and Computation in Secure Distributed Matrix Multiplication. https://arxiv.org/abs/2001.05568

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