Reversible data hiding in encrypted image (RDHEI) is a widely used technique for privacy protection, which has been developed in many applications that require high confidentiality, authentication and integrity. Proposed RDHEI methods do not allow high embedding rate while ensuring losslessly recover the original image. Moreover, the ciphertext form of encrypted image in RDHEI framework is easy to cause the attention of attackers. This paper proposes a reversible data hiding algorithm based on image camouflage encryption and bit plane compression. A camouflage encryption algorithm is used to transform a secret image into another meaningful target image, which can cover both secret image and encryption behavior based on “plaintext to plaintext” transformation. An edge optimization method based on prediction algorithm is designed to improve the image camouflage encryption quality. The reversible data hiding based bit-plane level compression, which can improve the redundancy of the bit plane by Gray coding, is used to embed watermark in the camouflage image. The experimental results also show the superior performance of the method in terms of embedding capacity and image quality.

Reversible data hiding (RDH) plays a significant role in data hiding field, and RDH scheme has demonstrated its strong potential in different applications. In many application scenarios, however, it is desirable to carry out RDH scheme directly on encrypted images. Such an approach is called reversible data hiding in encrypted images (RDHEI). RDHEI can embed secret information into encrypted images, with a reversible manner that the original covers can be losslessly decrypted and recovered after the embedded information are extracted. RDHEI can find many applications, e.g., for military communications, medical systems and cloud storage.

The RDHEI mainly includes three-party roles: content owner, information hider, and receiver. Some RDHEI schemes are vacating room after encryption (VRAE) schemes, which create redundancy after encryption process. VRAE schemes have the disadvantage that the embedding rate is low and errors may be occurred during image reconstructing phase. On the other hand, there are reserving room before encryption (RRBE) schemes, which reserve redundancy space before encryption. Although RRBE can achieve a high embedding rate, it might be impractical as the content owner needs to do an extra workload to create the space for the information hider.

For both VRAE and RRBE, the content owner will make encryption process on the secret image and send the encrypted image to the information hider. Although encryption can protect the secret image in a certain extent, but the messy codes of the encrypted image are easy to cause the attention of attackers who may try to dig out information on the content owner. In this paper, we propose a novel RDHEI schemes based on image camouflage and bit-plane compression. A camouflage encryption algorithm is used to transfer the original secret image into another meaningful image. The “plaintext to plaintext” transformation can cover both secret image and encryption behavior. Because the encrypted camouflage image is still a meaningful image that has different semantic content from original secret image, it will avoid the attention of the attacker while protecting the original secret image. Compared to exist image camouflage, an edge optimization method based on prediction algorithm is designed to improve the image encryption quality. The reversible data hiding based bit-plane level compression, which can improve the redundancy of the bit plane by Gray coding, is used to embed watermark in the camouflage image.

The RRBE scheme preserves the embedded space by extracting compressible features in the plaintext domain of the carrier image. It requires the content owner to perform additional operations to obtain the embedded space before encryption without any embedded information. The reserved space is often a relatively concentrated contiguous areas, which may cause copyright protection loopholes. However, due to its real conveniency, high efficiency, and good embedding performance, RRBE is suitable for some applications that have not strict security requirements.

Mo et al. [

The VRAE scheme is completely carried out on the encrypted domain, so it is not easy to leak plaintext information. It has a higher practical value and attracts more attention. Zhang [

RDH technique based on homomorphic encryption has the advantages of higher embedding rate as well as better visual performance. Wu et al. [

Specifically, Lai et al. [

In the carrier encryption phase, the content owner converts the secret image and the target image in terms of sub-blocks to obtain the transformed camouflage encrypted image with an encryption key

In the information embedding phase, the camouflage encrypted image is a meaningful image compared to traditional RDHEI methods. Therefore, the information hider can select a classical RDH method according to embedding capacity and image quality. This paper uses a RDH based bit plane compression to embed the secret information with

In the information extraction and secret image recovery phase, the receiver extracts the secret information and recovers the secret image based on the owned key.

The camouflage encryption mainly performs the conversion of the plaintext image by performing coarse-grained sub-block matching and fine-grained data reversible conversion on the image carrier. The effect of camouflage encryption is mainly determined by the rationality of sub-block matching and the accuracy of conversion. At present, the camouflage encryption algorithm based on cluster matching achieves the high success rate of similar sub-block matching under low auxiliary information as much as possible and reduces the distortion by using translation and conversion. However, the algorithm has two problems. One is that it does not consider the edge distortion problem between sub-blocks, which may affect image quality. The other one is that it performs translation and truncation operations on sub-blocks with out-of-bounds pixels, which increases the pixel difference between sub-blocks, and results in image distortion. Moreover, the operations increase the volume of auxiliary information, which must be embedded into the camouflage image. In this paper, a new out-of-bounds pixel processing strategy is designed. This strategy can recover the pixel information only by recording whether the pixel is out of bounds, which optimizes the image edge distortion without adding auxiliary information.

Given the secret image

Image segmentation. The secret image

Sub-block classification. Sub-blocks

Sub-block matching. The secret image

Sub-block conversion. The sub-block of the image

Cross-border processing. For out-of-bounds pixels, we design a new processing strategy in combination with the modulo operation as shown in

where _{i}

In this paper, we set the corresponding position map _{i}_{i}

Sub-block rotation. Each sub-block is rotated in four directions of 0

Edge optimization. In order to improve the smoothness of the sub-block edge, the prediction algorithm and neighborhood data of edge pixels are used for edge optimization. The following edge pixel

Taking into account the pixel correlation within the sub-block, the prediction value

From the above, we finally get the encrypted image

Since the encrypted image

(1) Bit plane separation. Each plane can be separated and obtained by:

where _{SC}_{SC}

In the natural binary code, there are big differences in the codewords of some adjacent data, so the natural binary code can be converted to the Gray code by:

Among them, the natural binary code is defined as

(2) Sub-block tag and sub-block compression. The matrix is divided into a series of non-overlapping blocks of size _{0} represents the number of 0 elements in the sub-block, and _{1} represents the number of 1 elements in the sub-block, _{t}

For the sub-blocks whose

For the sub-blocks of type 1 and type 2, the original information can be completely recovered according to the marked block type information, and no additional auxiliary information is needed, that is, corresponding available embedded space

Block type | Type description | Type tag |
---|---|---|

1 | _{1} = 0 |
00 |

2 | _{0} = 0 |
01 |

3 | 10 | |

4 | 11 | |

5 | _{t} |
– |

The sub-blocks of type 3 and type 4 are binary sparse matrices. In order to completely recover the relevant information in the extraction phase. In addition to the block type information, information of the sparse elements also need to be recorded. Since the sub-block values are only 0 and 1, and the sparse element values can be determined from the type information, only the number of sparse elements and the relative positions in the sub-blocks need to be recorded. Set the minimum remaining space

(3) Information embedding. First, each sub-block information is read in the raster scanning order to obtain its embedded space _{i}_{mi}

Secondly, the type of information tag and the secret information is operated in the first four types of sub-blocks in order, and the sub-blocks are obtained after being encrypted, and the type 5 sub-block is not operated. For the lowest bit plane, if the embedded space satisfies _{1} secret information and _{1} are transmitted to the adjacent bit plane;

Finally, if the bit plane embedded space satisfies _{i −1}, and the information of the remaining length _{i}_{em}

In this process, the length of embedded information _{i}_{i}_{m0} = 0 ; when the secret information cannot be completely hidden by the ordered integer sub-blocks, the remaining space of the last sub-block can be filled with random bit data.

When the receiver obtains the encrypted carrier _{em}

According to the embedded key _{i}_{m(i −1)}. of each bit plane and the _{i}

Bit plane separation. After Gray coding and separation, each bit plane data

Mark identification. According to the _{i}

Information extraction. For different types of sub-blocks, according to the compression embedding method used, the corresponding data extraction and sub-block recovery methods are as follows:

For the sub-blocks of type 1 and type 2, except for the first two marked bits, the other bits are encrypted information. Relevant information can be extracted by reading them in order of embedding sequence. And the sub-blocks are restored to all 0 or all 1 according to the sub-block type;

For the sub-blocks of type 3 and type 4, the number of sparse elements and the encoded position information are obtained according to the agreed embedding position, the rare element positions are obtained by de-encoding the position information, and the encrypted information is obtained by reading the rest of the positions based on the embedding order. The atomic blocks are recovered with the type information;

The first _{i}_{m(i −1)} are _{i −1} data of the adjacent low plane. Data

Bit plane recovery. The bit plane recovered from above is obtained by Gray coding, and the corresponding decoding can be used to recover the original bit plane without loss. Finally, the secret information and the encrypted image are obtained.

Secret image recovery. According to the

Edge recovery. For the edge modification operation in the encryption step,

Among them, because the neighborhood data remains unchanged, the mean value

Rotation recovery. Based on the related information of sub-block rotation direction obtained from the auxiliary information, each sub-block is rotated in the opposite direction to realize rotation recovery.

Out-of-bounds data recovery. According to the recovered location map

Conversion recovery. The reversible transformation of a sub-block is independent of its class, and the sub-block’s shift transformation in the auxiliary information can be directly used to restore.

We use the image in

Block size | RMSE | SSIM | Auxiliary information(bpp) |
---|---|---|---|

5.74 | 0.9905 | 2.1992 | |

7.77 | 0.9826 | 1.0119 | |

10.39 | 0.9690 | 0.5715 | |

11.88 | 0.9598 | 0.3628 | |

13.56 | 0.9464 | 0.2573 | |

16.68 | 0.9227 | 0.1426 |

In order to further analyze the influence of the choice of the target object on the encryption algorithm, we take

It can be seen from

Target -camouflage image | RMSE | SSIM | Auxiliary information (bpp) |
---|---|---|---|

10.81 | 0.9707 | 0.5713 | |

9.35 | 0.9866 | 0.5949 | |

10.95 | 0.9778 | 0.5840 | |

21.27 | 0.8575 | 0.5751 | |

16.86 | 0.9507 | 0.5925 |

We compare the encryption algorithm with current similar algorithms [

The experimental results are shown in

Algorithm | RMSE | SSIM |
---|---|---|

Reference [ |
22.38 | 0.3562 |

Reference [ |
13.85 | 0.6535 |

This paper |
11.07 | 0.7792 |

In the experiment, the compression embedding of data is carried out from the low-bit plane to the high-bit plane to reduce the effect of embedding on the whole image. In order to make full use of the redundant space of camouflage image, we also block the carrier in the data hiding stage according to the size of _{t}

We use

In order to better explain the performance of the steganographic algorithm, this section starts from the embedding capacity and imperceptibility of steganography and conducts performance testing and comparative experiments on encrypted carrier images. The experimental carrier is the corresponding image of

First, we use the generated camouflage encrypted images in

Camouflage encrypted image | Lowest plane | Second low plane | ||
---|---|---|---|---|

This paper | Ordinary binary | This paper | Ordinary binary | |

Airplane | 2365 | 766 | 16437 | 2220 |

Peppers | 2300 | 697 | 16342 | 2496 |

Baboon | 2297 | 796 | 12743 | 2181 |

Boat | 2484 | 772 | 17575 | 2333 |

Barbara | 2176 | 793 | 15138 | 2330 |

Camouflage encrypted image | Third low plane | forth low plane | ||

This paper | Ordinary binary | This paper | Ordinary binary | |

Airplane | 54769 | 17012 | 100219 | 56437 |

Peppers | 52942 | 15804 | 98917 | 55640 |

Baboon | 41079 | 12587 | 82415 | 42270 |

Boat | 53678 | 16910 | 102095 | 55634 |

Barbara | 49969 | 14453 | 96055 | 50360 |

In order to better evaluate the performance of the algorithm, we compare the proposed scheme with other similar schemes. Considering the particularity of the algorithm in this paper, we choose the existing classical reversible steganography algorithm [

Camouflage encrypted image | Capacity (bit) | This paper PSNR (dB) | Reference [ |
Reference [ |
---|---|---|---|---|

Airplane | 20000 | 58.87 | 58.03 | 58.69 |

Peppers | 20000 | 58.94 | 57.99 | 57.86 |

Baboon | 20000 | 56.64 | 57.92 | 56.53 |

Boat | 20000 | 59.35 | 58.14 | 58.02 |

Barbara | 20000 | 58.53 | 58.05 | 57.91 |

Average | 20000 | 58.47 | 58.03 | 57.80 |

In this paper, a reversible steganography algorithm based on image camouflage encryption and bit plane compression is proposed, and an edge optimization method based on the prediction algorithm is designed. The experimental results show that the method can achieve a good balance between embedding capacity and image quality, effectively improve the encryption quality, and have good performance.