Secure Distributed Matrix Computation With Discrete Fourier Transform

We consider the problem of secure distributed matrix computation (SDMC), where a user queries function data matrices generated at xmlns:xlink="http://www.w3.org/1999/xlink">source nodes. assume availability $N$ honest but curious servers, which are connected to sources, user, and each other through orthogonal reliable communication links. Our goal is minimize amount that must be transmitted from sources called xmlns:xlink="http://www.w3.org/1999/xlink">upload cost , while guaranteeing no notation="LaTeX">$T$ colluding servers can learn any information about source matrices, user cannot beyond result. first focus on multiplication (SDMM), considering two propose novel polynomial coding scheme using properties finite field discrete Fourier transform, achieves an upload cost significantly lower than existing results in literature. then generalize proposed include straggler mitigation, multiple keeping input intermediate results, as well final result against servers. also special case, with own data, used for belong user. In this we drop security requirement show minimal cost. methods performing common computations securely including changing parameters secret sharing, transpose, exponentiation, solving linear system, inversion, how arbitrary polynomials computed procedure.