Objective

2

In recent years

reversible data hiding (RDH) of encrypted images has attracted considerable attention. The data hider embeds hidden information into a digital image for covert transmission. However

data embedding often causes damage to the original image

which might not be fully recovered after covert transmission. Thus

effectively combining encryption technology and RDH technology for covert transmission of data is necessary. This combinatorial method ensures that images are encrypted and recoverable. Therefore

RDH technology in the ciphertext domain has become a research focus. The algorithms can be roughly divided into two categories: vacating room after encryption(VRAE) and reserving room before encryption(RRBE). The general method of RDH is typically to encrypt a cover image first

then embed hidden information into the encrypted image

and send it to the receiver. The receiver extracts the secret information and decrypts the encrypted image by using the data hiding key and encryption key

respectively. In previous RDH methods

encrypted images have little redundant space

the bit plane utilization of images is low

the embedding capacity is small

and some flipped pixels may lead to image distortion.

Method

2

In this work

the proposed scheme is mainly divided into the following steps: image preprocessing

block tag embedding

image rearrangement

image encryption

data embedding

data extraction

and image decryption. The content owner divides a grayscale image into eight bit planes

each of which is used for data embedding. The pixel value on each bit plane can be viewed as a binary number

and each bit plane is divided into non-overlapping blocks (such as 4×4)

which are divided into discontinuous blocks (with pixel values of 0 and 1) and continuous blocks (with pixel values of 0 or 1). An image is rearranged by blocks

and the original order of block labels is embedded in the rearranged image. At the same time

the content owner makes pixel prediction on all discontinuous blocks of all bit planes and obtains the prediction map. Images after arrangement are encrypted with a stream cipher. The content owner sends the encrypted image along with the prediction map to the data hider. In the data embedding phase

the data hider embeds the data according to a pixel prediction method. For a continuous block

the bottom right pixel is kept unchanged for the recovery of the block

and data are embedded in other positions. As a result

the embedding space of each continuous block is very large. For a discontinuous block

a prediction map is generated

and then a pixel prediction model is used. When the prediction is correct

the corresponding value of the prediction map is 1; otherwise

it is 0. In the discontinuous block

only when the prediction map value is 1

data is embedded at the predicted pixel; otherwise

the predicted pixel remains unchanged without embedding data. Of note

all secret data should be encrypted before embedding. Due to the above data embedding phase

cover images can be restored completely later. The embedding capacity of the discontinuous block is less than that of the continuous block. However

due to the large number of discontinuous blocks in the low bit planes

the embedding capacity of discontinuous blocks is considerable in the whole image. However

in some state-of-the-art schemes

the utilization of low bit planes is not sufficient. The proposed scheme solves the problem by using the pixel prediction model with correction information. The data hider sends marked and encrypted images to the receiver. In the image decryption and data extraction stage

the receiver performs image decryption and data extraction according to different keys.

Result

2

In the experimental process

various RDH algorithms in the ciphertext domain were used

and a large number of comparison experiments were conducted on the eight grayscale test images to comprehensively compare the two aspects of complete reversibility and embedding efficiency. At the same time

a verification experiment was conducted on the BOSSbase and BOWS-2 dataset. Compared with some state-of-the-art schemes

the embedding rate of the scheme in this study was improved by 42.1% on the BOSSbase dataset and 43.3% on the BOWS-2 dataset. The embedding rate of the proposed scheme reached 3.089 5 and 2.932 0 bit per pixel on the BOSSbase and BOWS-2 dataset

respectively. Compared with other schemes

the proposed scheme embeds data on all bit planes. Unlike other state-of-the-art schemes

the proposed scheme can embed data in the low bit planes because of the pixel prediction method with correction information. Other schemes ignore the contribution of low bit planes to data embedding.

Conclusion

2

The proposed scheme provides a large space for embedding additional information and ensures its security. Moreover

it can achieve higher embedding rate

and the image recovery is quite correct by embedding data in different blocks with different ways and using all bit planes of images

which shows the effectiveness of the proposed scheme. The experimental results show that the embedding performance of the proposed scheme is superior to that of other state-of-the-art schemes for the RDH of encrypted images. In future work

we will focus on improving the embedding efficiency of discontinuous blocks and improving the algorithm so as to increase the embedding capacity of low bit planes.