Efficient Homomorphic Conversion Between (Ring) LWE Ciphertexts

Abstract

© 2021, Springer Nature Switzerland AG.In the past few years, significant progress on homomorphic encryption (HE) has been made toward both theory and practice. The most promising HE schemes are based on the hardness of the Learning With Errors (LWE) problem or its ring variant (RLWE). In this work, we present new conversion algorithms that switch between different (R)LWE-based HE schemes to take advantage of them. Specifically, we present and combine three ideas to improve the key-switching procedure between LWE ciphertexts, transformation from LWE to RLWE, as well as packing of multiple LWE ciphertexts in a single RLWE encryption. Finally, we demonstrate an application of building a secure channel between a client and a cloud server with lightweight encryption, low communication cost, and capability of homomorphic computation.