Analog Secure Distributed Matrix Multiplication over Complex Numbers

Funding Information: This work has been supported by the Academy of Finland, under Grants No. 318937 and 336005. The authors would like to thank Dr. Diego Villamizar Rubiano for useful discussions. Publisher Copyright: © 2022 IEEE.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.Peer reviewe