Rotation Key Reduction for Client-Server Systems of Deep Neural Network on Fully Homomorphic Encryption

In this paper, we propose a new concept of hierarchical rotation key for homomorphic encryption to reduce the burdens of the clients and the server running on the fully homomorphic encryption schemes such as Cheon-Kim-Kim-Song (CKKS) and Brakerski/Fan-Vercauteran (BFV) schemes. Using this concept, after the client generates and transmits only a small set of rotation keys to the server, the server can generate any required rotation keys from the public key and the smaller set of rotation keys that the client sent. This proposed method significantly reduces the communication cost of the client and the server, and the computation cost of the client. For example, if we implement the standard ResNet-18 network for the ImageNet dataset with the CKKS scheme, the server requires 617 rotation keys. It takes 145.1 s for the client with a personal computer to generate whole rotation keys and the total size is 115.7GB. If we use the proposed two-level hierarchical rotation key system, the size of the rotation key set generated and transmitted by the client can be reduced from 115.7GB to 2.91GB (x1/39.8), and the client-side rotation key generation runtime is reduced from 145.1 s to 3.74 s (x38.8 faster) without any changes in any homomorphic operations to the ciphertexts. If we use the three-level hierarchical rotation key system, the size of the rotation key set generated and transmitted by the client can be further reduced from 1.54GB (x1/75.1), and the client-side rotation key generation runtime is further reduced to 1.93 s (x75.2 faster) with a slight increase in the key-switching operation to the ciphertexts and further computation in the offline phase.