Notes on Communication and Computation in Secure Distributed Matrix Multiplication
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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. We 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. In contrast, we show that for the right choice of parameters, polynomial codes can lower the computational time of the system, e.g. if the computational time complexity of an operation in F_q is at most Z_q and the computational time complexity of multiplying two n× n matrices is O(n^ωZ_q) then the user together with the servers can compute the multiplication in O(n^4-6/ω+1Z_q) time.
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