  Recent advances in cryptography promise to enable secure statistical
computation on encrypted data, whereby a limited set of operations can be
carried out without the need to first decrypt. We review these homomorphic
encryption schemes in a manner accessible to statisticians and machine
learners, focusing on pertinent limitations inherent in the current state of
the art. These limitations restrict the kind of statistics and machine learning
algorithms which can be implemented and we review those which have been
successfully applied in the literature. Finally, we document a high performance
R package implementing a recent homomorphic scheme in a general framework.
