Homomorphic Encryption-Based LSB Substitution for High Capacity Data Hiding in the Encrypted Domain

Pauline Puteaux,William Puech,Manon Vialle

doi:10.1109/access.2020.3001385

Abstract

During the last few decades, multimedia security over the cloud has become a major issue. Public-key homomorphism is an efficient approach for data hiding in encrypted images (DHEI). An original image is encrypted using a public key and sent across a network and then processed to embed a secret message directly in the encrypted domain. During the decoding step, a private key is used to obtain a marked reconstructed image, where the secret message can be extracted. In this paper, we propose an efficient method of DHEI based on the Paillier cryptosystem. Using its homomorphic properties, pixel blocks and bits of the message are multiplied in the encrypted domain resulting in an addition in the clear domain. By applying a pre-processing step on the original image before encryption, this addition becomes a least significant bits (LSB) substitution. Experimental results show that using our proposed scheme, we obtain a high payload value ( $1~bpp$ ) without expanding a lot the original image size contrary to current state-of-the-art methods. Indeed, whatever the key size, the expansion rate is always equal to 2. In addition, the original image and the marked reconstructed image are very similar.

Highlights

With the constant evolution of the Internet and cloud services, multimedia data exchanged over the networks need to be protected against illegal access and fraudulent usage
For the ten past years, data hiding in encrypted images (DHEI) methods have been proposed [6]–[11] to achieve image annotation or authentication in the encrypted domain
We propose a new efficient method of data hiding in encrypted images using the Paillier cryptosystem

Summary

INTRODUCTION

With the constant evolution of the Internet and cloud services, multimedia data exchanged over the networks need to be protected against illegal access and fraudulent usage. Wu et al divided each unit of an original image into three parts according to the signal energy transfer principle [21] These parts are encrypted using the Paillier cryptosystem and one bit of the secret message can be embedded by processing the three encrypted parts. Xiang and Luo proposed a separable homomorphic encryption-based method of DHEI involving the mirroring ciphertext group strategy [15] Using such a technique, there is no pixel oversaturation in the clear domain after decryption, but the computational cost remains high. Using the Paillier cryptosystem and its homomorphic properties, a secret message can be embedded in an encrypted image which corresponds to a substitution of the least significant bits (LSB) of each pixel in the clear domain.

IMAGE ENCRYPTION

MESSAGE ENCRYPTION AND EMBEDDING

EXPERIMENTAL RESULTS AND DISCUSSION

CONCLUSION