Faster Homomorphic Linear Transformations in HElib.

HElib is a software library that implements homomorphic encryption (HE), with a focus on effective use of "packed" ciphertexts. An important operation is applying a known linear map to a vector of encrypted data. In this paper, we describe several algorithmic improvements that significantly speed up this operation: in our experiments, our new algorithms are 30-75 times faster than those previously implemented in HElib for typical parameters. One application that can benefit from faster linear transformations is bootstrapping (in particular, "thin bootstrapping" as described in [Chen and Han, Eurocrypt 2018]). In some settings, our new algorithms for linear transformations result in a 6x speedup for the entire thin bootstrapping operation. Our techniques also reduce the size of the large public evaluation key, often using 33%-50% less space than the previous HElib implementation. We also implemented a new tradeoff that enables a drastic reduction in size, resulting in a 25x factor or more for some parameters, paying only a penalty of a 2-4x times slowdown in running time (and giving up some parallelization opportunities).