Straggler-Exploiting Fully Private Distributed Matrix Multiplication With Chebyshev Polynomials

In this paper, we consider coded computation for matrix multiplication tasks in distributed computing to mitigate straggler effects. We assume that the stragglers’ computation results can be leveraged at the master by assigning multiple sub-tasks to the workers. We propose a new coded computation scheme, namely Chebyshev coded fully private matrix multiplication (CFP), to preserve the privacy of a master in a scenario where a master wants to obtain a matrix multiplication result from the libraries which are shared by the workers, while concealing both of the two indices of the desired matrices from each worker. The key idea of CFP is to introduce Chebyshev polynomials, which have commutative property, in queries sent to workers to allocate sub-tasks. We also extend CFP to keep the privacy of a master from colluding workers. In conclusion, we show that CFP can preserve the privacy of a master from each worker and efficiently mitigate straggler effects compared to existing schemes.