The prospect of outsourcing an increasing amount of data storage and management to cloud services raises many new privacy concerns that can be satisfactorily addressed if users encrypt the data they send to the cloud. If the encryption scheme is homomorphic, the cloud can still perform meaningful computations on the data even if it is encrypted. In fact, we now know a number of constructions of fully homomorphic encryption schemes that allow arbitrary computations on encrypted data. Over the past two years, solutions for fully homomorphic encryption have been proposed and improved, but all currently available options seem to be too inefficient to be used in practice. For many applications, however, it is sufficient to implement reasonably homomorphic encryption schemes that support a limited number of homomorphic operations. They can be much faster and more compact than fully homomorphic schemes. This talk focuses on describing the recent reasonably homomorphic encryption scheme by Brakerski and Vaikuntanathan, whose security is based on the ring learning with errors (RLWE) problem.

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