Efficient reversible data hiding in encrypted image with public key cryptosystem

Abstract

This paper proposes a new reversible data hiding scheme for encrypted images by using homomorphic and probabilistic properties of Paillier cryptosystem. The proposed method can embed additional data directly into encrypted image without any preprocessing operations on original image. By selecting two pixels as a group for encryption, data hider can retrieve the absolute differences of groups of two pixels by employing a modular multiplicative inverse method. Additional data can be embedded into encrypted image by shifting histogram of the absolute differences by using the homomorphic property in encrypted domain. On the receiver side, legal user can extract the marked histogram in encrypted domain in the same way as data hiding procedure. Then, the hidden data can be extracted from the marked histogram and the encrypted version of original image can be restored by using inverse histogram shifting operations. Besides, the marked absolute differences can be computed after decryption for extraction of additional data and restoration of original image. Compared with previous state-of-the-art works, the proposed scheme can effectively avoid preprocessing operations before encryption and can efficiently embed and extract data in encrypted domain. The experiments on the standard image files also certify the effectiveness of the proposed scheme.

Reversible Data Hiding Algorithm in Fully Homomorphic Encrypted Domain

“…Figure 1 plots the sketch of the proposed scheme, which is composed of four main phases: image encryption, data hiding, data extraction and image restoration. For the data hiding algorithm, refer to [ 23 ]. Reversible data hiding is an effective authentication or content integrity verification technique in which hidden data can be completely extracted and the original carrier can be recovered non-destructively after data extraction [ 30 ].…”

“…In [ 22 ], the authors proposed another algorithm based on discrete fourier transform and compressive sensing in encrypted domain. In [ 23 , 24 ], the authors proposed two methods for reversible data hiding by using Paillier cryptosystem. In [ 23 ], two adjacent pixels as a group are encrypted and then the differences of the two adjacent pixels in each group are computed to generate a difference histogram.…”

“…In [ 23 , 24 ], the authors proposed two methods for reversible data hiding by using Paillier cryptosystem. In [ 23 ], two adjacent pixels as a group are encrypted and then the differences of the two adjacent pixels in each group are computed to generate a difference histogram. The information can be hiding into the histogram by using histogram shifting technique and the homomorphic properties of Paillier system.…”

“…In addition, the additional data can be extracted from the directly decrypted image and the original image can be restored. Compared with the the work in [ 23 , 24 ], the proposed scheme has no preprocessing operations and has lower computational cost.…”

A Speech Homomorphic Encryption Scheme with Less Data Expansion in Cloud Computing

“…It is because the homomorphic encryption data can be processed by the third party, a few researches on image homomorphic encryption [16][17][18][19][20][21] and speech homomorphic encryption [22][23] are proposed. In [16][17][18], the original images are encrypted by Paillier homomorphic cryptosystem, and secret data is embedded in the encrypted images by using homomorphic and probabilistic properties of Paillier cryptosystem. They efficiently embed and extract secret data to perform reversible data hiding in encrypted domain.…”