Double Batch for RLWE-Based Leveled Fully Homomorphic Encryption

To further improve the efficiency of Fully homomorphic encryption (FHE), a leveled FHE scheme based on the Ring learning with errors (RLWE) problem is put forward by simultaneously applying both batch techniques available. Our scheme therefore allows double packing many plaintext values into each ciphertext to support single-instruction-multiple-data-type operations, which effectively reduces the ciphertext expansion ratio. An efficient evolutionary method for achieving arbitrary homomorphic permutation operations on a packed ciphertext is also provided by using several given key-switching hints. Further, a few new operations are introduced, with which not only to describe the key switching process in our batch setting clearly, but also to analyze the noise growth conveniently.