[Paper Review] Fully Homomorphic Encryption Encapsulated Difference Expansion for Reversible Data hiding in Encrypted Domain

Yan Ke, Minqing Zhang+3 more|arXiv (Cornell University)|Apr 29, 2019

Advanced Steganography and Watermarking Techniques36 references4 citations

TL;DR

This paper proposes a Fully Homomorphic Encryption Encapsulated Difference Expansion (FHEE-DE) scheme enabling reversible data hiding directly in the encrypted domain. By integrating key-switching and bootstrapping techniques with a novel key-switching-based LSB embedding method, the scheme allows servers to embed and extract data from ciphertext without decryption, achieving high embedding capacity, excellent fidelity, and full separability while preserving encryption security.

ABSTRACT

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.

Motivation & Objective

• To enable reversible data hiding in the encrypted domain without requiring decryption.
• To allow data extraction and recovery directly from the marked ciphertext using only public information.
• To maintain high fidelity and embedding capacity while ensuring full separability and strong encryption security.
• To simplify homomorphic operations for practical efficiency in real-world deployment.

Proposed method

• The scheme employs key-switching and bootstrapping to control ciphertext noise growth and prevent decryption failure.
• A key-switching-based least-significant-bit (KS-LSB) embedding method is designed to embed additional data into the encrypted domain without access to the private key.
• The method supports direct extraction of hidden data from the marked ciphertext by the server, preserving the integrity of the original plaintext and additional payload.
• A fidelity constraint is introduced to minimize distortion in the marked plaintext after decryption.
• The universal FHEE-DE scheme is optimized to reduce computational overhead, resulting in an efficient variant for practical use.
• The framework ensures full separability, meaning the original plaintext and embedded data can be recovered independently and accurately.

Experimental results

Research questions

• RQ1 Can reversible data hiding be performed directly in the encrypted domain without decryption, using only public information?
• RQ2 How can homomorphic operations be stabilized and controlled to prevent decryption failure during data embedding in encrypted data?
• RQ3 What is the achievable balance between embedding capacity, fidelity, and security in encrypted-domain reversible data hiding?
• RQ4 Can the data extraction and recovery processes be fully separated from the private key, enabling server-side operations?
• RQ5 How can the homomorphic operations be simplified without compromising performance or security?

Key findings

• The proposed FHEE-DE scheme achieves higher embedding capacity compared to existing reversible data hiding in encrypted domain (RDH-ED) methods.
• The fidelity of the marked plaintext is significantly improved due to the introduced fidelity constraint, reducing perceptual distortion.
• The scheme enables direct data extraction from the marked ciphertext without decryption, demonstrating full separability.
• The optimized version of FHEE-DE reduces computational complexity while maintaining high performance.
• Security is preserved throughout the process, as no private key is required for data extraction or recovery.
• The method successfully integrates fully homomorphic encryption with difference expansion, enabling secure and reversible data hiding in the encrypted domain.