Fully Homomorphic Encryption Encapsulated Difference Expansion for Reversible Data hiding in Encrypted Domain

This paper proposes a fully homomorphic encryption encapsulated difference expansion (FHEE-DE) scheme for reversible data hiding in encrypted domain (RDH-ED). The homomorphic circuits and ciphertext operations are elaborated. Key-switching and bootstrapping techniques are introduced to control the ciphertext extension and decryption failure of homomorphic encryption. A key-switching based least-significant-bit (KS-LSB) data hiding method has been designed to realize data extraction directly from the encrypted domain without the private key. In application, the user first encrypts the plaintext and uploads ciphertext to the server. The server embeds additional data into the ciphertext by performing FHEE-DE data hiding and KS-LSB data hiding. Additional data can be extracted directly from the marked ciphertext by the server without the private key. The user owns the private key and can decrypt the marked ciphertext to obtain the marked plaintext. Then additional data or plaintext can be obtained from the marked plaintext by using the standard DE extraction or recovery. The server could also implement FHEE-DE recovery or extraction on the marked ciphertext to return the ciphertext of original plaintext or additional data to the user. Experimental results demonstrate that the embedding capacity and reversibility of the proposed scheme are superior to existing RDH-ED methods, and fully separability is achieved without reducing the security of encryption.