A multilevel reversible data hiding scheme in encrypted domain based on LWE

This paper proposes a multilevel reversible data hiding scheme in encrypted domain by utilizing the controllable redundancy of learning with error public key cryptography. Messages can be embedded into multilevel sub-regions of ciphertext by quantifying the encrypted domain and recoding its redundancy. We recode redundancy based on the characteristics of cipher's distribution. Extraction and decryption processes are separated by dividing the encrypted domain into multilevel sub-regions and introducing different quantification standards. Original plaintext can be losslessly recovered from the marked ciphertext by using the decryption key; with a specific level data-hiding key, only the message hiding in the corresponding level can be extracted, while plaintext and other messages remain secret. We provide theoretical analysis and experimental results on the feasibility, reversibility, and security of the proposed scheme. The capacity and encryption blow up factor are discussed. The experimental results demonstrate the maximum embedding rate can exceed 0.3000 bpb of ciphertext.