CN111241554A - Digital image encryption and decryption system based on visual cipher - Google Patents

Abstract

The invention discloses an image encryption and decryption method and a system based on visual code (Visual Code) and adopting the Burch coding modified off-axis reference light computational hologram principle (CGH for short). Among them, the original image is encrypted by visual cryptography, and the original image is used to generate two encrypted shared images. During decryption, CGH is used to obtain the holograms corresponding to the two shared images. The light fields of the two holograms are reconstructed and superimposed to obtain the decrypted images. The invention adopts a new type of secret sharing technology, which enhances the security of encryption and the reliability of decryption for the situation that the secret information is an image; at the same time, different from the traditional visual encryption method, the hologram generated by using CGH cannot be directly obtained by superposition The original image further enhances the confidentiality; the experiment proves that the encryption and decryption of the present invention has excellent security performance.

Description

Digital image encryption and decryption system based on visual cipher

technical field

The invention relates to the technical field of digital image encryption, in particular to the technical field of airspace image encryption.

Background technique

Digital image is a widely used form of information carrier, which has a profound impact on national defense, industry, science and technology, economy and other fields. In some special fields, such as military, commercial and aviation, digital images also have higher security requirements. Facing the rapid development of decryption technology, traditional one-dimensional data encryption algorithms are facing severe challenges. The concept of image encryption technology is: a technology that uses the characteristics of digital images to design encryption algorithms to improve encryption security and operational efficiency. For the needs of practical application, digital image encryption technology needs to have the characteristics of being difficult to decipher and reliable in performance, so as to resist the attacks of various deciphering methods.

Image encryption technology can be divided into two categories, namely, spatial image encryption technology and compressed image encryption technology. Spatial image encryption technology encrypts an uncompressed image, which is characterized by operating the image as two-dimensional data. Visual Cryptography Scheme (VCS) for short is a new type of airspace image encryption technology, which was proposed by Naor and Shamir at the European Cryptography Conference in 1994. In the film, each share will not reveal any secret information. When decrypting, it is only necessary to superimpose the films that meet the conditions, and the secret can be directly recovered by the human visual system in the absence of a computer environment and the secret owner does not have any mathematical knowledge. Different from the traditional secret sharing method, visual cryptography is mainly aimed at the case where the secret information is an image. When the sharing structure is (k,n), where 2≤k≤n, the secret image is encrypted into n shared images ( shareimages), and then distribute the shared images to n different secret sharing participants. When recovering a secret image, at least k shared images need to be superimposed to recover the secret.

Generally speaking, the process of encrypting and decrypting digital images by visual cryptography is shown in Figure 1.

The existing visual cryptography technology can achieve concealment, because the pixels on the shared image are randomly distributed, the hidden secrets cannot be seen by ordinary people; secondly, the visual cryptography technology has security: it is impossible to analyze a single shared image. Get any useful information about the secret.

However, most of the existing visual cryptographic techniques do not require any mathematical calculation during decryption, and the decipherer does not need any mathematical knowledge. The secret image can be recovered by simply superimposing the shared image, which increases the preservation process of the shared image. The danger of stealing, thereby reducing the security of traditional visual password technology.

SUMMARY OF THE INVENTION

In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a digital image encryption and decryption system based on visual cipher and computer-made hologram, so as to improve the security of digital image encryption.

In one aspect, the present invention discloses a digital image encryption and decryption system based on visual cipher and computer-made hologram, comprising the following steps: a step of generating a shared image: processing an original image through a visual cipher algorithm, and generating two corresponding images of the original image Sharing image; hologram generation step: through the modified off-axis reference light computational hologram method encoded by Boqi, generate two computational holograms corresponding to the two shared images, that is, two encrypted images; image reconstruction step: through laser alignment The light field is reconstructed from two holograms, and the reconstructed image is obtained after overlapping on the screen;

In the above-mentioned digital image encryption and decryption system, the step of generating a shared image further includes: an image binarization step, a step of generating a shared image A and a step of generating a shared image B. Among them, in the image binarization step, the original RGB digital image is converted into a grayscale image, and then the grayscale image is converted into a binarized image according to the average value of the image. In the step of generating the shared image A, each pixel in the binarized image matrix of the original image is represented by a group of four pixels in the shared image A, and the pseudo-random number sequence is used to binarize each group of four pixels. Assignment is divided into six combination cases, and each case in each group has two pixels as 1 and two pixels as 0. Steps for generating shared picture B. Shared picture B and shared picture A have the same image size. According to the value of each pixel of the binary image matrix of the original image, the value of each group of 2 × 2 four pixels in the shared image B and the corresponding value of each group of 2 × 2 four pixels in the shared image A respectively the same or respectively and sum to 1.

，重新构成全息函数： In the above-mentioned digital image encryption and decryption system, the hologram generation step further includes: a random phase factor adding step, a Boqi coding correction off-axis reference light step, and a hologram normalization step. Among them, the random phase factor addition step is to assign a value to the complex matrix A1. The modulus of each element in A1 is equal to the value of the corresponding pixel point of the shared image A, and the phase is assigned by a pseudo-random number matrix to smooth the Fourier transform of the function. Transform spectrum; Boqi coding corrects the off-axis reference light step, performs two-dimensional fast Fourier transform on the complex matrix A1 and shifts the frequency to the center to obtain a two-dimensional frequency domain matrix A2, and compares each complex element in A2 with the off-axis reference light. Each complex element in the frequency domain matrix R is subjected to Boqi coding. The specific operation of the coding is: remove the DC offset term

, reconstruct the holographic function:

；

;

In the hologram normalization step, the holographic function is normalized to obtain the modified off-axis reference light computational hologram A3 of the Boqi encoding shared in Figure A, and the above operations are repeated to obtain the modified Boqi encoding of the shared Figure B. The off-axis reference light computational hologram B3, A3 and B3 are two encrypted images.

In the above digital image encryption and decryption system, the image reconstruction step further includes: a shared image hologram reconstruction step and a reconstructed image overlay step. Among them, in the step of sharing the hologram reconstruction, the argument and modulus of the Fourier transform spectrum of each element of the hologram A3 are calculated, and the modulus of each point is normalized, and the low-frequency components of the spectrum are moved to the center to avoid the reproduction of The image is scattered around the edges, resulting in a reconstructed image A4 of the shared image A. The above steps are repeated to obtain the reconstructed image B4 of the shared image B; the reconstructed image overlay step is to add the elements in the reconstructed images A4 and B4, and normalize the obtained matrix to obtain the reconstructed image of the original image.

Compared with the prior art, the present invention has the following advantages:

(1) Concealment: Since the pixels on the encrypted image are not spatially related to the original image, the hidden secret image cannot be seen or cracked by simple overlapping, which reduces the confidentiality requirements for shared images;

(2) Absolute security: no useful information about the secret can be obtained by analyzing a single encrypted graph by any method or any means;

(3) Reliability of secret recovery: Unlike any other traditional image encryption technology, the present invention can choose computer-aided or physical implementation in decryption. Computer-aided means that two encrypted images are Fourier transformed and superimposed Obtain the reconstructed image, the physical realization is to use the laser to irradiate the encrypted image to reconstruct the light field, and overlap and decrypt on the screen to obtain the reconstructed image;

(4) Universality: Users do not need cryptography knowledge, and anyone can use the technology. This is also an important aspect that is different from other cryptographic techniques;

(5) Fastness: Due to the use of the Boqi coding modified off-axis reference light hologram, which replaces the DC component of the calculated hologram, the autocorrelation component in the frequency domain no longer appears. The maximum frequency of the transmittance function in the two-dimensional direction becomes half of the original in the x and y directions, the sampling interval becomes twice the original in the x and y directions, and the total number of sampling points is reduced to no 25% when encoding, thereby increasing the rate at which holograms (encrypted images) are generated.

Description of drawings

FIG. 1 is a flow chart of encryption and decryption of a visual password in the prior art.

FIG. 2 is a flow chart of the encryption and decryption system based on the visual password in the present invention.

FIG. 3 is the original image that needs to be encrypted in the present invention.

FIG. 4 is two shared images obtained through a visual cryptographic algorithm in the present invention.

FIG. 5 shows two holograms (encrypted images) corresponding to the two shared images after the off-axis reference light CGH is corrected by Boqi coding in the present invention.

FIG. 6 is a reconstructed image of two shared images obtained after Fourier transform and frequency shifting of two holograms (encrypted images) in the present invention.

FIG. 7 is an original image reconstruction image (decryption image) obtained by superimposing two shared image reconstruction images in the present invention.

FIG. 8 is a structural block diagram of the encryption and decryption process of the present invention.

FIG. 9 and FIG. 10 are schematic diagrams of the principle of visual password.

Detailed ways

The objects, features and advantages of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

Based on the consideration of security performance, the present invention improves and innovates the traditional visual cryptography technology on the basis of the prior art, that is, adopts the Boqi coding modified off-axis reference light computational hologram technology, on the basis of visual cryptography encryption Improve security and anti-deciphering capabilities.

Referring to Fig. 2, Fig. 2 is a flow chart of the encryption and decryption system based on visual cipher of the present invention, comprising the following three steps: a step of generating a shared graph: processing the original image by a visual cipher algorithm, and generating two corresponding images of the original image. Share pictures. The hologram generation step: through the modified off-axis reference light computational hologram method encoded by Boqi, two computational holograms corresponding to the two shared images are generated, that is, two encrypted images. Image reconstruction steps: Reconstruct the light field of the two holograms by laser, and obtain the reconstructed image after overlapping on the screen; or perform two-dimensional fast inverse Fourier transform on the two holograms respectively, and overlap to obtain the reconstructed image, that is, the decryption map.

The steps of generating two shared images of the binarized original image by the visual cryptography technology will be described in detail below with reference to FIG. 4 , FIG. 9 and FIG. 10 .

，当且仅当第i个透明胶片上第j个子像素是 黑色，即

时。当把这些透明胶片以恰当地对齐子像素的方式重叠起来，我们就可以 看到一个结合的分享，这个结合分享中的黑色子像素是由所构成的m个列向量各自经过布 尔或运算得到的结果表示的。这个结合分享的灰度级与基于“或”运算的m维矢量的汉明权 重H(V)成比例。对满足固定阈值1≤d≤m的和满足相对差

的情况来说，如果H(V)≥d， 灰度级被人类视觉系统理解为黑色，如果

则被解读为白色。 The simplest model of the visual cryptographic problem is to assume that the secret information is a combination of a series of black and white pixels, each of which is processed individually. Each original pixel is divided into n shares (one share corresponds to a transparencies), where each share contains m sub-pixels, these black and white sub-pixels printed on the transparencies are very similar to each other, so that human vision The system averages out their characteristic black or white contributions. The structure of a raw pixel after the above processing can be described as an n×m Boolean matrix

, if and only if the jth subpixel on the ith transparency is black, i.e.

Time. When these transparencies are overlapped in such a way that the sub-pixels are properly aligned, we can see a combined share where the black sub-pixels in the combined share are formed by the boolean OR operation of each of the m column vectors. results indicated. The gray level shared by this combination is proportional to the Hamming weight H(V) of the OR-based m-dimensional vector. Satisfy the relative difference for the sum that satisfies the fixed threshold 1≤d≤m

In the case of , if H(V)≥d, the gray level is understood as black by the human visual system, if

is interpreted as white.

is the number of pixels in a share. It represents the loss of resolution from the original image to this shared image. We want the smaller the better. is the relative difference in weight between the combined share of a white pixel and a black pixel in the original image. It represents the loss of contrast. We hope the bigger the better. is the size of the set and (the two do not need to be the same size, but both are the same in all our scenarios). Represents the number of random bytes required to generate a combined share, it does not affect the quality of the image.

的相对差来区别颜色。 In particular, the visual effect produced by a black sub-pixel in a certain share cannot be deciphered by the color of that pixel in other shares that have been untangled. Unlike ordinary encryption techniques, this singularity adds random noise to the plaintext during encryption and removes this random noise from the ciphertext during decryption. This model also differs from the more natural model. Usually, a more natural model is that a white pixel is represented entirely by a set of white subpixels, and a black pixel is entirely represented by a set of black subpixels. Therefore, we must use a threshold d and

relative difference to distinguish colors.

和

，这两个集合都是由n×m布 尔矩阵组成的。要分享一个白色像素，我们就从集合

中随机选择一个矩阵；要分享一个黑 色像素，就从集合

中随机选择一个矩阵。选择的矩阵决定了n个透明胶片中所有子像素的 颜色。这个解只有满足以下三个条件时才是有效的。 The solution of the (k,n) visual secret sharing scheme contains two sets

and

, both sets consist of n×m Boolean matrices. To share a white pixel, we start with the collection

A matrix is randomly selected from ; to share a black pixel,

Choose a matrix at random. The chosen matrix determines the colors of all subpixels in the n transparencies. This solution is valid only if the following three conditions are met.

中的任意矩阵S，n行中的任意k行经过“或”运算得到的矢量均满足

。 for collection

Any matrix S in , the vector obtained by any k rows in n rows after the OR operation satisfies the

.

中的任意矩阵S，n行中的任意k行经过“或”运算得到的矢量均满足H (V)≥d。更具体普适的视觉密码算法记载在【M.Naor and A. Shamir, Visual cryptography [C], Advances in Cryptology ,Eurocrypt, Lecture Notes in Computer Science, 1995, Vol.950:1-12】的文献中。 for collection

For any matrix S in , the vector obtained by any k rows in n rows after the OR operation satisfies H (V)≥d. More specific and general visual cryptography algorithms are described in [M.Naor and A. Shamir, Visual cryptography [C], Advances in Cryptology ,Eurocrypt, Lecture Notes in Computer Science, 1995, Vol.950:1-12]. .

Referring to FIG. 5 , the principle of the Boqi-encoded modified off-axis reference light computational hologram will be described in detail. For the traditional optical off-axis corrected reference light hologram, the transmittance function is:

。 The first two terms in the formula are used as DC bias, and the third term contains all the information of the hologram. Therefore, the first two items are completely unnecessary, but their existence increases the bandwidth requirement of the hologram. Therefore, artificial DC bias is added to replace the first two items to reconstruct the holographic function:

.

。 where K is a constant such that h(x, y) is a non-negative real number for all x, y values, after normalization max(|A(x, y)|)=1 and R=1, the holographic function becomes:

.

After replacing the DC component of the calculated hologram, the autocorrelation component in the frequency domain no longer appears. In order to avoid the overlap between the components on the frequency plane, the highest frequency of the transmittance function in the two-dimensional direction is in the x and y directions. All of them become half of the original, the sampling interval in the x and y directions becomes twice the original, and the total number of sampling points is reduced to 25% of that without coding. A random phase factor needs to be multiplied first, which smoothes the Fourier transform spectrum but introduces speckle noise in the diffracted image at the output image plane.

In addition, if the random phase factor multiplied by the same random phase factor is the same when the two shared pictures are used for the Boqi coding correction type off-axis reference light CGH, then the shared picture hologram obtained can be overlapped first, and then the Fourier transform or laser irradiation can be performed. Get a reconstructed image of the original image.

Claims (4)

1. A digital image encryption and decryption system based on visual passwords is characterized by comprising the following steps:

a sharing graph generation step: processing the original image through a visual password algorithm to generate two sharing images corresponding to the original image;

a hologram generation step: generating two computed holograms corresponding to the two sharing images, namely two encrypted images, by a correction type off-axis reference light computed hologram method of Boqi coding;

an image reconstruction step: reconstructing a light field of the two holograms by laser, and overlapping the light field on a screen to obtain a reconstructed image; or two holograms are respectively subjected to two-dimensional fast inverse Fourier transform and overlapped to obtain a reconstructed image, namely a decryption image.

2. The digital image encryption and decryption system according to claim 1, wherein the sharing map generation step further comprises:

an image binarization step: the method comprises the steps of changing an original RGB digital image into a gray image, and changing the gray image into a binary image according to an image mean value;

a sharing graph A generation step: representing each pixel point in a binarization image matrix of an original image by using a group of four pixel points in a sharing graph A, and performing binarization assignment on each group of four pixel points by using a pseudo random number column, wherein the combination is divided into six combination conditions, two pixel points are 1 and two pixel points are 0 in each condition of each group;

a sharing graph B generation step: the image size of the sharing image B is the same as that of the sharing image A;

according to the value of each pixel point of the binary image matrix of the original image, the values of each group of 2 × 2 four pixel points in the sharing graph B are respectively the same as or respectively 1 with the values of each group of 2 × 2 four pixel points corresponding to the sharing graph A.

3. The digital image encryption and decryption system of claim 1 wherein the hologram generation step is further characterized by:

random phase factor adding step: assigning a complex matrix A1, wherein the modulus of each element in A1 is equal to the value of a corresponding pixel point of a sharing graph A, and the phase is assigned by a pseudo-random number matrix and is used for smoothing the Fourier transform spectrum of a function;

performing two-dimensional fast Fourier transform on a complex matrix A1 and shifting the frequency to the center to obtain a two-dimensional frequency domain matrix A2, and performing Bosch coding on each complex element in A2 and each complex element in a frequency domain matrix R corresponding to the off-axis reference light, wherein the specific operation of the coding is that a direct current bias item is removed and a holographic function is reconstructed by h1(x, y) = K +2RA1(x, y) cos [2 pi α x-phi (x, y) ];

and (3) hologram normalization: and normalizing the holographic function to obtain a modified off-axis reference light calculation hologram A3 of the Bosch code of the shared graph A, and repeating the operation to obtain a modified off-axis reference light calculation hologram B3 of the Bosch code of the shared graph B, wherein A3 and B3 are two ciphers.

4. The digital image encryption and decryption system of claim 1 wherein the image reconstruction step further comprises:

reconstruction of a shared graph hologram: calculating the argument and the modulus of the Fourier transform spectrum of each element of the hologram A3, normalizing the modulus of each point, and moving the low-frequency component of the spectrum to the center to avoid the dispersion of the image at the edge during reproduction, thereby obtaining a reconstructed image A4 of the shared image A;

repeating the steps to obtain a reconstructed image B4 of the sharing image B;

and a reconstructed image superposition step: adding the elements in the reconstructed image A4 and the B4, and normalizing the obtained matrix to obtain a reconstructed image of the original picture, namely a decryption graph.

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