  In this work, we propose a method for speeding up linear regression
distributively, while ensuring security. We leverage randomized sketching
techniques, and improve straggler resilience in asynchronous systems.
Specifically, we apply a random orthonormal matrix and then subsample in
\textit{blocks}, to simultaneously secure the information and reduce the
dimension of the regression problem. In our setup, the transformation
corresponds to an encoded encryption in an \textit{approximate} gradient coding
scheme, and the subsampling corresponds to the responses of the non-straggling
workers; in a centralized coded computing network. We focus on the special case
of the \textit{Subsampled Randomized Hadamard Transform}, which we generalize
to block sampling; and discuss how it can be used to secure the data. We
illustrate the performance through numerical experiments.
