Algorithms in HElib.

HElib is a software library that implements homomorphic encryption (HE), specifically the Brakerski-Gentry-Vaikuntanathan (BGV) scheme, focusing on effective use of the Smart-Vercauteren ciphertext packing techniques and the Gentry-Halevi-Smart optimizations. The underlying cryptosystem serves as the equivalent of a "hardware platform" for HElib, in that it defines a set of operations that can be applied homomorphically, and specifies their cost. This "platform" is a SIMD environment (somewhat similar to Intel SSE and the like), but with unique cost metrics and parameters. In this report we describe some of the algorithms and optimization techniques that are used in HElib for data movement, linear algebra, and other operations over this "platform."