CN110136045B - A Method of Concealment and Restoration Based on Mutual Scrambling of Two Images - Google Patents

Abstract

The invention discloses a method for scrambling, hiding and recovering two images based on the generalized Chinese remainder theorem. According to the method, two images with the same image size are subjected to modulus extraction respectively based on a set of preset two-by-two prime numbers to obtain two groups of sub-images, then partial sub-image pairs are randomly selected from the two groups of sub-images to perform pixel part interchange at corresponding positions, two groups of sub-images after scrambling and hiding are obtained, and simultaneous encryption of the original image pairs is achieved. When in recovery processing, firstly, all unordered pixel pairs are accurately recovered from two given sub-images based on a group of pairwise prime numbers set during scrambling and hiding processing, then the unordered pixel pairs in the obtained pixel pairs are accurately divided into two types according to the characteristics of the images, and the original two images are recovered without damage based on classification results, so that the encryption transmission interaction of the image pairs is realized. The invention can efficiently and accurately recover the encrypted image and has small operand. And greatly increases the deciphering difficulty of illegal users.

Description

A Method of Concealment and Restoration Based on Mutual Scrambling of Two Images

technical field

The invention belongs to the technical field of secure communication and image information processing, and in particular relates to an image information hiding and restoring method.

Background technique

With the development of Internet digital multimedia technology, information security issues are becoming more and more important because they involve personal privacy, commercial interests, and state secrets. Therefore, reliable encryption of transmitted information has become the most important research direction in the field of information security.

Due to the large amount of data of digital images and the easy confusion caused by vision, information encryption technology using images as carriers has become one of the research hotspots in information security transmission. One of the techniques for hiding images is to scramble them, that is, the sender uses mathematics or other techniques to transform the hidden digital image so that it becomes an image that cannot be recognized by the naked eye before being used for transmission; In the process, even if it is intercepted by an illegal identity person, the information of the original image cannot be obtained from the image, so as to achieve the purpose of image encryption. The receiving party can decrypt through a predetermined method, so as to restore the original image. The scrambling encryption process can be carried out in the position space and color space of the image, that is, in the space domain, and can also be carried out in its frequency domain, and can even be carried out in both the space domain and the frequency domain. Therefore, the encryption method is flexible and diverse, and legal users can freely control the selection of algorithms, parameter selection and use of random number technology, which greatly increases the difficulty of deciphering for illegal interceptors.

The existing image scrambling algorithms can be divided into scrambling based on image position space, image color space and image frequency domain space. Specifically, classical scrambling methods based on image position space, such as image scrambling methods based on Arnold transformation, Hilbert curve, magic square transformation, queue transformation, etc. Image scrambling methods based on color space, such as image scrambling based on chaotic sequence and Gray code, etc. The above methods are all based on a single image, and there are relatively few studies on scrambling based on multiple images. The present invention proposes a scrambling method based on two images, which has the advantages of high difficulty in deciphering and high image information transmission efficiency.

Contents of the invention

The object of the present invention is to provide a scheme for mutual scrambling, hiding and restoration of two images based on the generalized Chinese remainder theorem for the above-mentioned problems.

In the present invention, the pixels of the two pictures are firstly passed through several pairs of mutually prime modes, and then these pixels are formed into sub-images according to the original positions, wherein the two pictures of the same mode are called the same mode pair images. In the phase of image scrambling and encryption, the pixels of the partial identical model pairs of the two sets of images are exchanged. Then transfer them separately. At the receiving end, through the generalized Chinese remainder theorem, two disordered pixel pairs are recovered first. Then, according to the received images, the pixels corresponding to the two images are respectively determined.

The hiding method based on mutual scrambling of two images of the present invention is realized through a technical solution based on the generalized Chinese remainder theorem method, which specifically includes the following steps:

其中，n表示所选取的模的数量。Step 1: Select an appropriate pairwise coprime modulus m ₁ ,m ₂ ,...,m _n , so that any pixel pair in the image can be uniquely recovered under this modulus, based on the generalized Chinese remainder Theorem, in the present invention, the selected module should satisfy following relational expression:

Among them, n represents the number of modules selected.

Step 2: The two images to be processed with each other are represented by images A and B respectively, and the image sizes of images A and B are the same;

Perform modulo operations on all pixels of image A with respect to m ₁ , m ₂ ,...,m _n respectively, and obtain the pixel value a _i,j after modulus of each pixel: a _i,j ≡p _i mod m _j , i=1,2,...,S,j=1,2,...,n, wherein, p _i represents the pixel value of the i-th pixel of the image A, and S represents the number of pixels of the mutual image;

Thus obtain the image after the modulus operation of different modulus m _j (ie, the sub-image of image A): A ₁ , A ₂ ,...,A _n ;

Step 3: Perform modulo operations on all pixels of image B with respect to m ₁ , m ₂ ,...,m _n respectively, and obtain the pixel value b _i,j after modulo of each pixel: b _i,j ≡q _i modm _j ,i=1,2,...,S,j=1,2,...,n; where, q _i represents the pixel value of the i-th pixel of image B;

Thereby obtain the image after the modulus operation of different modulus m _j (ie the subgraph of image B): B ₁ , B ₂ ,..., B _n ;

作为部分像素互换的对象，即将待进行部分像素(随机选取子图中的部分像素点作为待互换像素点)互换的图像对中的同一像素点位置的像素进行互换，从而得到互换后的图像对

Step 4: Randomly select t pairs of image pairs from n pairs of image pairs (A ₁ ,B ₁ ),…,(A _n ,B _n )

As the object of partial pixel exchange, the pixels at the same pixel position in the image pair to be exchanged (randomly select some pixels in the sub-image as the pixels to be exchanged) are exchanged, so as to obtain the exchange Image pair after swapping

Step 5: After the exchange processing in step 4, the encrypted image after the exchange processing is obtained:

A sequence of n subimages belonging to A:

A sequence of n subimages belonging to B:

取上整后的值。In order to further ensure that the two images can be completely recovered from the scrambled sub-images, in the present invention, t can be set to be less than

Take the rounded value.

The technical effect brought by the above-mentioned image encryption method by exchanging processing methods of the present invention is:

(1) The purpose of information hiding is achieved by making full use of the information of the given two images and their sub-images. Since the entire system does not require additional images, the difficulty of system design is greatly reduced.

(2) The method of scrambling two images based on the generalized Chinese remainder theorem, because illegal users cannot determine which image pairs and which pixels in the image pairs have been exchanged, it is impossible to use the traditional Chinese remainder theorem method or search method Accurately recovering two images greatly increases the difficulty of deciphering for illegal users.

(3) The two-image scrambling method based on the generalized Chinese remainder theorem does not add redundant information during the whole process of image information hiding, so the transmission efficiency of image information is increased.

Corresponding to the concealment method based on mutual scrambling of two images of the present invention, the present invention also discloses a restoration method of two images based on the generalized Chinese remainder theorem, which includes the following steps:

其中，

分别表示两组子图像序列中序列相同的两副子图，且j＝1,2,...,n，n表示图像对数量；Step 1: For the received two sets of sub-image sequences processed based on the two-image mutual scrambling hiding method (each set of sub-image sequences corresponds to an image to be restored), the sub-images of the two sets of sub-image sequences are combined in sequence , to get multiple pairs of graphs relative to each other, denoted as

in,

represent two subimages with the same sequence in the two subimage sequences respectively, and j=1,2,...,n, n represents the number of image pairs;

其中，

表示子图像

在第i个像素点的像素值，

表示子图像

在第i个像素点的像素值，j＝1,2,...,n，m₁,m₂,...,m_n表示两图像互置乱隐藏方法处理中的n个两两互质的模，符号

表示x关于m_j取模后的余数。Taking the image pair as the unit, calculate the remainder c _i,j of the sum of the pixel values of the same pixel in each image pair with respect to m _j modulo according to the formula:

in,

Represents a sub-image

The pixel value of the i-th pixel point,

Represents a sub-image

The pixel value at the i-th pixel point, j=1, 2,..., n, m ₁ , m ₂ ,..., m _n represent the n pairwise mutual quality model, symbol

Indicates the remainder after taking the modulus of x with respect to m _j .

满足

并计算以下两个参数：Step 2: record M=m ₁ m ₂ ... m _n , M _i =M/m _i and

Satisfy

and calculate the following two parameters:

为上取整函数。in,

is the upper integer function.

Step 3: Solve the two roots of the equation (xs _i ) ² −(ξ _i,1 −2s _i )(xs _i )+ξ _i,2 =0: { _xi,1 , _xi,2 }.

Step 4: Determine the respective pixels of the image to be restored:

计算参数e_j；确定子图像

对应的待恢复图像A的每个像素p_i：

According to the formula

Compute parameter e _j ; determine subimage

Corresponding to each pixel p _i of image A to be restored:

对应的待恢复图像B的每个像素q_i：q_i＝{x_i,1,x_i,2}\{p_i}。Determine the sub-image

Corresponding to each pixel q _i of the image B to be restored: q _i ={ _xi,1 , _xi,2 }\{p _i }.

Step 5: Based on the respective pixels of each restored image determined in step 4, the restored images A and B are obtained, that is, the original images A and B respectively corresponding to the two sub-image sequences are restored.

In summary, owing to adopting above-mentioned technical scheme, the beneficial effect of the present invention is:

Compared with the existing image restoration method, the two image scrambling restoration method and system proposed by the present invention based on the generalized Chinese remainder theorem have the following advantages.

1. The present invention makes full use of the information of the given two images and their sub-images to achieve the purpose of information hiding. Since the entire system does not require additional images, the design difficulty of the system is greatly reduced.

2. The method for scrambling two images based on the generalized Chinese remainder theorem provided by the present invention cannot use the traditional Chinese remainder theorem method or search method because illegal users cannot determine which image pairs and which pixels in the image pairs have been exchanged. To accurately restore the two images by other methods, it greatly increases the difficulty of deciphering for illegal users.

3. The two-image scrambling method based on the generalized Chinese remainder theorem provided by the present invention does not add redundant information during the entire process of image information hiding, so the transmission efficiency of image information is increased.

4. The restoration method of the scrambling of two images based on the generalized Chinese remainder theorem provided by the present invention is highly efficient and requires a small amount of computation.

Description of drawings

Fig. 1 is a schematic diagram of the processing flow of mutual scrambling and hiding of two images in a specific embodiment;

Fig. 2 is a schematic diagram of the reply processing flow of two groups of sub-image sequences after mutual scrambling and concealment processing of two images in a specific embodiment;

Fig. 3 is the image after performing modulo operation on the image A (named Lena) in the specific embodiment: the sub-images shown in A1-A5 in the figure;

Fig. 4 is in the specific embodiment, the image (named as Zelda) after carrying out modulus operation to the image: the sub-image shown in B1～B5 among the figure;

Fig. 5 is in the specific embodiment, the sub-image after sub-image is replaced by the pixel of part corresponding position in sub-image pair A4 and B4, A5 and B5;

Fig. 6 is in the specific embodiment, adopts two images after the Chinese remainder theorem method restores;

Fig. 7 shows two images restored by using the generalized Chinese remainder theorem method of the present invention in the specific implementation manner.

detailed description

In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the implementation methods and accompanying drawings.

Referring to Fig. 1, Fig. 3 and Fig. 4, in order to realize the mutual scrambling and hiding of the two images of the image A and the image B to be transmitted, that is to realize the mutual encryption processing of the image pair (A, B), the specific implementation process is as follows:

其中j＝1,2,...,n；本具体实施方式中，设置了一组包括5个模的模组，其依次分别为：4，5， 7，11，13；该组模将共享于图像接收端，用于图像的恢复处理；Firstly, set a set of pairwise coprime modules (also called prime numbers) m ₁ ,m ₂ ,...,m _n , and

Wherein j=1,2,...,n; In this embodiment, a group of modules comprising 5 modules is set, which are respectively: 4,5,7,11,13; Shared at the image receiving end for image recovery processing;

Then take the modulus of images A and B with respect to the pairwise prime numbers m ₁ , m ₂ ,...,m ₅ respectively, and then obtain two groups of sub-images, which are respectively marked as A1～A5 and B1～B5, as shown in the figure 3 and 4; where images A and B have the same size, in this embodiment, they are both 512×512.

和

和

和

为了保证两图像能从置乱后的子图像中完整地恢复出来，要求t小于

取上整后的值。将这t对图像对应位置的像素部分互换，得到t对新的子图分别记为

和

和

和

进而得到关于模m₁,m₂,...,m_n的两组子图分别为：

和

Then take t pairs of subgraphs from these two sets of subimages:

with

with

with

In order to ensure that the two images can be completely recovered from the scrambled sub-image, it is required that t be less than

Take the rounded value. Swap the pixels of the corresponding positions of the t pairs of images to obtain t pairs of new subimages, respectively denoted as

with

with

with

Then two groups of subgraphs about modulus m ₁ , m ₂ ,...,m _n are obtained:

with

In this specific embodiment, the value of setting t is 2, and the sub-image pair of interchange is set to: A4 and B4, A5 and B5, thereby obtain two groups of sub-images after mutual scrambling and hiding as shown in Figure 5; And send the two groups of sub-image sequences to the receiving end.

和

本发明利用广义的中国余数定理恢复出两图像的像素对后再根据图像的特征找出对应的像素。See Figure 2, for the two received sub-image sequences:

with

The invention recovers the pixel pairs of the two images by using the generalized Chinese remainder theorem, and then finds the corresponding pixels according to the features of the images.

The specific process is as follows:

First, for the sub-image pairs formed in order, calculate the remainder of the sum of the pixel values at the same pixel position with respect to the modulus of the corresponding modulus, and match the corresponding modulus through the sequence index, for example, for the first pair of sub-image pairs, then match The modulus of is m ₁ , the second pair corresponds to m ₂ , and so on.

After the corresponding operation processing, all unordered pixel pairs {p _i ,q _i } are accurately restored from the two sub-images, that is, according to the solution equation (xs _i ) ² -(ξ _i,1 -2s _i )(xs _i )+ξ _i,2 =0 to get two roots { _xi,1 , _xi,2 }. Then according to the characteristics of the image, the unordered pixel pairs in the obtained pixel pairs are accurately classified, that is, the pixels belonging to A and B are respectively found out. After all the pixels are accurately classified, the original two images can be restored without loss. , and the recovery results are shown in Figure 7.

Compared with the existing two images restored by the Chinese remainder theorem method (as shown in FIG. 6 ), the invention can efficiently and accurately restore the encrypted image with a small amount of computation. And because the illegal user cannot determine which image pairs and which pixels in the image pair have been exchanged, it is impossible to use the traditional Chinese remainder theorem method or search method to accurately recover the two images, which greatly increases the illegal user's deciphering. difficulty.

The above is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless specifically stated, can be replaced by other equivalent or alternative features with similar purposes; all the disclosed features, or All method or process steps may be combined in any way, except for mutually exclusive features and/or steps.

Claims (2)

1. A method for hiding based on two images being scrambled mutually, is characterized in that, comprises the following steps: Step 1: Select a set of module sequences that are relatively prime in pairs: m ₁ ,m ₂ ,...,m _n , where n represents the number of modules selected; The selected modulus satisfies:

Step 2: The two images to be processed with each other are represented by images A and B respectively, and the image sizes of images A and B are the same; Perform modulo operations on all pixels of image A with respect to m ₁ , m ₂ ,...,m _n respectively to obtain the pixel value a _i,j after modulus of each pixel: a _i,j ≡p _i mod m _j , i=1,2,...,S,j=1,2,...,n, wherein, p _i represents the pixel value of the i-th pixel of the image A, and S represents the number of pixels of the mutual image; So as to obtain the subgraph sequence after the modulus operation of different modulus m _j : A ₁ , A ₂ ,...,A _n ; Step 3: Perform modulo operations on all pixels of image B with respect to m ₁ , m ₂ ,...,m _n respectively, and obtain the pixel value b _i,j after modulo of each pixel: b _i,j ≡q _i mod m _j ,i=1,2,...,S,j=1,2,...,n; where, q _i represents the pixel value of the i-th pixel of image B; So as to obtain the subgraph sequence after the modulus operation of different modulus m _j : B ₁ , B ₂ ,...,B _n ; Step 4: Randomly select t pairs of image pairs from n pairs of image pairs (A ₁ ,B ₁ ),...,(A _n ,B _n )

As the object of partial pixel swapping, the swapped image pair is obtained

where t is less than

Take the rounded value; Step 5: Obtain two sets of image sequences after mutual scrambling and hidden processing: A sequence of n subimages belonging to A:

A sequence of n subimages belonging to B:

2. a kind of two image recovery method based on generalized Chinese remainder theorem, it is characterized in that, comprises the following steps: Step 1: For the received two groups of sub-image sequences processed based on the two-image mutual scrambling concealment method described in claim 1, the sub-images of the two groups of sub-image sequences are combined in order to obtain multiple pairs of images relative to each other. , denoted as

in,

represent two subimages with the same sequence in the two subimage sequences respectively, and j=1,2,...,n; Taking the image pair as the unit, according to the modulus sequence used in the processing based on the mutual scrambling of two images: m ₁ ,m ₂ ,...,m _n , calculate the sum of the pixel values of the same pixel in each pair of image pairs Regarding the remainder c _i,j after taking the modulus of each modulus; in,

Represents a sub-image

The pixel value of the i-th pixel point,

Represents a sub-image

The pixel value of the i-th pixel, j=1,2,...,n, symbol

Indicates the remainder after taking the modulus of x with respect to m _j ; Step 2: record the parameter M=m ₁ m ₂ ... m _n , M _i =M/m _i and

Satisfy

and calculate the following two parameters:

in,

is the upper integer function; Step 3: Solve the equation (xs _i ) ² -(ξ _i,1 -2s _i )(xs _i )+ξ _i,2 = 0 to get two roots: { _xi,1 , _xi,2 }; Step 4: Determine the respective pixels of the image to be restored: According to the formula

Compute parameter e _j ; determine subimage

Corresponding to each pixel p _i of image A to be restored:

Determine the sub-image

Corresponding to each pixel q _i of image B to be restored: q _i ={ _xi,1 , _xi,2 }\{p _i }; Step 5: Obtain restored images A and B based on the respective pixels of each restored image determined in step 4.

Images