  This paper proposes a fully homomorphic encryption encapsulated difference
expansion (FHEE-DE) scheme for reversible data hiding in encrypted domain
(RDH-ED). In the proposed scheme, we use key-switching and bootstrapping
techniques to control the ciphertext extension and decryption failure. To
realize the data extraction directly from the encrypted domain without the
private key, a key-switching based least-significant-bit (KS-LSB) data hiding
method has been designed. In application, the user first encrypts the plaintext
and uploads ciphertext to the server. Then the server performs data hiding by
FHEE-DE and KS-LSB to obtain the marked ciphertext. Additional data can be
extracted directly from the marked ciphertext by the server without the private
key. The user 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. A fidelity constraint of DE is
introduced to reduce the distortion of the marked plaintext. FHEE-DE enables
the server to implement FHEE-DE recovery or extraction on the marked
ciphertext, which returns the ciphertext of original plaintext or additional
data to the user. In addition, we simplified the homomorphic operations of the
proposed universal FHEE-DE to obtain an efficient version. The Experimental
results demonstrate that the embedding capacity, fidelity, and reversibility of
the proposed scheme are superior to existing RDH-ED methods, and fully
separability is achieved without reducing the security of encryption.
