In order to effectively increase embedding capacity and completely extract the watermarking information in information hiding of encrypted images, a new reversible watermarking embedding algorithm based on rhombus prediction model and difference histogram shifting ideas is proposed. Firstly, the images are pretreated according to rhombus prediction model. Then, the watermarking information is embedded in encrypted images by effective combination of homomorphism encryption scheme and reversible watermarking techniques. Finally, the watermarking information is completely extracted and the images are recovered based on computed difference histogram from left to right and from top to bottom. So, the efficiency and reversibility are ensured when watermarking information is embedded in encrypted image. Experiment results show that the proposed algorithm is simple and easy to realize, the embedding capacity is effectively increased, watermarking information is completely reversible, and the image can be recovered with no distortion.

With the advent of the digital age, media content gradually changes from analog to digital. Digital technology makes the multimedia data (image, video, and text) storage, replication, and communication become very convenient. Therefore, how to implement effective copyright protection and information security measures in the network environment has become an urgent realistic problem.

At present, there are three types of reversible watermarking methods: (1) compression based reversible watermarking [

Encryption technology [

According to the problem above, we propose a new reversible watermarking embedding algorithm in encrypted image. Figure

Sketch of reversible data hiding in encrypted image.

Our reversible watermarking embedding algorithm is based on rhombus prediction model and difference histogram shifting ideas; it can effectively increase embedding capacity and completely extract the watermarking information in information hiding of encrypted images while the efficiency and reversibility can be ensured. In order to achieve this innovation, we first pretreat the images according to rhombus prediction model, and then we embed the watermarking information in encrypted images by effective combination of homomorphism encryption scheme and reversible watermarking techniques; the watermarking information can be completely extracted and the images are recovered based on computed difference histogram from left to right and from top to bottom.

The remainder of this paper is organized as follows. In Section

The characteristics of homomorphic encryption are for some operations in plaintext and then encryption effect is equivalent to some operation directly in the ciphertext [

But the encryption methods and the corresponding homomorphism (addition, subtraction, multiplication, and division) must satisfy the image encryption. In order to make the image encryption have a low complexity, we choose the RC4 encryption [

Record

The encryption method is shown as follows:

The decryption method is shown as follows:

So, this encryption method satisfies the additive homomorphism. Correspondingly, use

The information entropy is used to measure the amount of information lost in the signal transmission process before it is received. After the image is encrypted, if the chaos degree of its pixels reaches maximum, then the image information entropy tends to the maximum value. Reference [

Suppose that

That is to say, the information entropy of

Suppose that a general parser divides

According to the definition in [

So, (

So

According to (

Because

In the proposed algorithm, the sender will encrypt image and embed data, but the encryption section should be divided into two parts, which are pretreatment phase and encryption phase. When the receiver gets an encrypted image containing embedded data, he can decrypt image, extract the additional data, and recover the original image.

This section is divided into three parts: part (1) is image pretreatment; part (2) is image encryption; part (3) is embedding watermarking information.

Rhombus prediction scheme.

Then, the predicted value

The dividing scheme of rhombus for difference error value.

We compute all white pixel corresponding error

If

If

If

If

If

If

In this way, we can get the two parts of the different histogram corresponding to the two location maps. The temporary maps Lm1 and Lm2 are encrypted and compressed; then they are transferred to the user of legitimate embedding watermarking. Once finishing the embedding watermarking at the sender, two temporary maps are immediately destroyed.

Legitimate user of the embedding watermarking information gets location maps Lm1 and Lmp2; he can find the embedding watermarking location according to Lm1; then, Lm1 is read by scanning from left to right and from top to bottom of the sequence of operation; if Lm1 = 1, directly operate Case

Embedding watermarking information

Until all the watermarking information is embedded, Lm1 and Lm2 are destructed; end and the encrypted image with watermarking is formed.

This section is divided into two parts: part (1) is image decryption; part (2) is extraction watermarking and restoration image.

The sender divides the same pixel as one group and calculates each part of the different error value

To process the plaintext with watermarking, it is shown as follows.

If

If

If

If

If

So, we can get the decrypted image with watermarking information; therefore, we send Lm3 (Lm3 has been compressed and encrypted) to the legitimate user who can extract the watermarking information.

In the algorithm, due to difference histogram change, corresponding pixels will change and cause overflow or underflow phenomenon. This phenomenon is not much; it can be processed according to the following.

If

If

If

If

If

If

Applying to Lm3, the legitimate user extracts the watermarking information and divides image again at the same sender’s pixel group.

If

If

In other cases, we directly judge the next embedding watermarking information and go to Step

When all the watermarking information is extracted, the two-part watermark information is extracted according to the first diamond inner, and then the diamond-four angle is connected. We can get all the watermark information, and the image gets recovery; end.

If

If

The RC4 encryption is stream ciphering algorithm with alterable length of key stream

Supposing the length of key stream

We adopt the rotation angle (RA) of

The test of resisting rotation attack.

Items | Datum | |||||||
---|---|---|---|---|---|---|---|---|

RA | | | | | | | | |

TT | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 |

SET | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 |

In order to verify the effectiveness of our method, simulation experiments are conducted by using MATLAB7.0 platform. We use the peak signal-to-noise (PSNR) and the embedding rate (ER) to evaluate the quality of the encrypted image and embedding capacity. For the

Then, the ER is

We select a standard test image Lean

Comparing image Lena encryption before and after: (a) original image; (b) encrypted image; (c) the histogram of the original image; (d) the histogram of the encrypted image.

After 15000 bits watermarking information is embedded in the encrypted image, we can get PSNR = 62.36 (dB) when it is decrypted, as shown in Figure

The ER and PSNR of the four test images.

Images | PSNR/dB | |||||
---|---|---|---|---|---|---|

ER/bpp | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 |

| ||||||

Lena | 70.36 | 67.08 | 65.56 | 64.26 | 63.18 | 62.64 |

Plane | 70.46 | 67.12 | 65.61 | 64.21 | 63.22 | 62.68 |

Milkdrop | 70.38 | 67.10 | 65.48 | 64.18 | 63.12 | 62.67 |

Woman2 | 70.62 | 67.32 | 65.52 | 64.32 | 63.28 | 62.72 |

The decrypted image Lena with watermarking and the ultimate recovery image Lena: (a) the decrypted image Lena with watermarking; (b) the ultimate recovery image Lena.

Four test images: (a) Lena; (b) Plane; (c) Milkdrop; (d) Woman2.

We use PSNR value to measure direct decrypted image with hidden information. For the images Lena, Plane, Milkdrop, and Woman2, we compare our algorithm with Zhang et al. [

The chart of our algorithm compared with algorithm Zhang’s and Ma’s.

Test image Lena

Test image Plane

Test image Milkdrop

Test image Woman2

The cipher image embedding technique is combined with the advantage of encryption technology and information hiding technology. It can be satisfied with the need of important privacy protection and become a new field. This paper presents a novel reversible watermarking embedding algorithm in encrypted image; the algorithm adopts rhombus prediction thought and histogram modification scheme. It truly realizes reversible watermarking extraction and image lossless recovery. Experiments show that the proposed algorithm is better than other algorithms.

The authors declare that they have no competing interests.

This work was supported by the National Nature Science Foundation of China (no. 61562059 and no. 61461027).

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