Analog Secure Distributed Matrix Multiplication over Complex Numbers

Abstract

This work considers the problem of distributing matrix multiplication over the real or complex numbers to helper servers, such that the information leakage to these servers is close to being information-theoretically secure. These servers are assumed to be honest-but-curious, i.e., they work according to the protocol, but try to deduce information about the data. The problem of secure distributed matrix multiplication (SDMM) has been considered in the context of matrix multiplication over finite fields, which is not always feasible in real world applications. We present two schemes, which allow for variable degree of security based on the use case and allow for colluding and straggling servers. We analyze the security and the numerical accuracy of the schemes and observe a trade-off between accuracy and security.• Encoding phase: The user partitions the matrices to smaller submatrices and draws random matrices of the same size. These smaller matrices are encoded using some code and the encoded pieces ˜︁ A i , ˜︁ B i are sent to server i. This part can be seen as a secret sharing phase, where the secret matrices are shared among the servers.