Faster Linear Transformations in $\textsf{HElib}$ , Revisited

HElib is a C++ library that implements fully homomorphic encryption (FHE). This supports homomorphic linear transformations on plaintext slots which consist of many rotation operations on plaintext slots, and currently, each rotation involves one or two automorphisms. In this paper, we describe a new method for linear transformations that perform only one automorphism for the rotation operation for many kinds of linear transformations. We then further investigate our new method to have algorithmic improvement, which can be understood as a generalization of the baby-step/giant-step strategy on HElib. Finally, we verify that our improvement works well by implementation, and see 2-4 times speedup than the current HElib implementation.