CN104240177A - Colored image encryption method based on chaotic system and fractional order Fourier transform - Google Patents

Abstract

The invention discloses a color image encryption method based on a chaotic system and fractional Fourier transform, and relates to the field of image encryption systems. The method adopted is as follows: First, use the Logistic chaotic system to generate a chaotic sequence, and perform global pixel scrambling on the reorganized color image matrix; then perform a fractional Fourier transform on the result of the previous step; finally use the Logistic chaotic system to generate a chaotic sequence again, and perform One-step extraction of modulus length and phase angle and recombined matrix for global pixel scrambling, so as to realize the encryption of the image. The present invention introduces one image to construct a complex matrix, which reduces the space occupied by the algorithm for constructing a complex matrix from two images; introduces global pixel scrambling and fractional Fourier transform to encrypt pixel values, reduces the correlation of pixel points between images, and improves The anti-interference and anti-attack performance of the algorithm is improved, the encryption effect is good, and the security is high.

Description

A Color Image Encryption Method Based on Chaotic System and Fractional Fourier Transform

technical field

The invention belongs to the field of image processing and information security, in particular to a color image encryption method based on a chaotic system and fractional Fourier transform using a single image encryption method.

Background technique

With the rapid development of computer network technology, information security has become a serious problem in information transmission and storage, image information transmission and image encryption technology have attracted widespread attention. Image information itself has the characteristics of large amount of data and high correlation between data. Traditional encryption methods for plain text information, such as Data Encryption Standard (DES), International Data Encryption Algorithm, RSA Asymmetric Encryption Algorithm, etc., are not completely suitable for image information. encryption. Because the chaotic system has the characteristics of large key space, initial value sensitivity, aperiodicity, nonlinearity and unpredictability, the image encryption method based on chaos has advantages in security and adaptability, and has been extensively studied in recent years.

At present, chaotic image encryption methods can be divided into two categories according to the method of encrypting images: image pixel value transformation and pixel coordinate transformation. Image pixel value transformation is to encrypt the image by changing the gray value of the image, and pixel coordinate transformation is to change the encrypted image by changing the image pixel coordinates. However, the encryption keys of these two traditional encryption methods have nothing to do with plaintext images, so it is difficult to resist known plaintext attacks.

In addition, currently commonly used encryption methods based on chaotic images use dual-image encryption. Although double-image encryption has the advantages of high encryption complexity when used in image encryption, it has disadvantages such as large storage space occupied by the algorithm and inconvenient practical application. Using single image encryption, the encryption algorithm occupies a small space and is convenient for practical application. Compared with double image encryption, it has certain advantages in terms of image encryption efficiency and security.

Contents of the invention

The purpose of the present invention is to provide a color image encryption method based on chaotic system and fractional Fourier transform with good encryption effect and high security.

The present invention is achieved through the following technical solutions:

A color image encryption method based on chaotic system and fractional Fourier transform, comprising the following steps:

Step 1: Input a plaintext color pixel image I _in with a size of M×N, extract the three-color channel matrix R, G, B of the plaintext color pixel image and sequentially connect them into a 3M×N matrix I _irgb ;

Step 2: Substitute the initial parameter λ ₁ and the initial iterative value x ₀ into the Logistic chaotic system to iterate m+3MN times, ignore the results of the first m iterations, and obtain the chaotic sequence x={x _m+1 ,x _m+2 ,... ,x _m+3MN }, sort all the values of the chaotic sequence x to get a new sequence and get the sequence The position of each element value in the original chaotic sequence x T ₁ ={t ₁ ,t ₂ ,...,t _3MN }, that is $x_i={\stackrel{\‾}{x}}_{t_i}(i=\mathrm{1,2},...,3\mathrm{MN});$

Step 3: Perform global pixel scrambling on the matrix I _irgb , transform the matrix I _irgb into a 3MN×1 matrix I _t , rearrange all the rows of I _t according to T ₁ , that is, move the t ₁ row of I _t to the first row, move the t ₂ row of I _t to the second row, and so on, until the t _3MN row of I _t is moved to the last row, and obtain the matrix I ₁ ;

Step 4: Divide matrix I ₁ into two matrices I ₁₁ and I ₁₂ , let matrix I ₁₁ be used as the modulus, and matrix I ₁₂ be used as the phase angle to form a complex matrix $I_e=I_{11}{e}^{\mathrm{j\π}{I}_{12}};$

Step 5: Perform the fractional Fourier transform of the complex matrix I _e with a rotation angle of α to obtain the complex matrix I ₂ ;

Step 6: Extract the modulus and phase angle of the complex matrix I ₂ to obtain the matrices I ₂₁ and I ₂₂ , and combine the matrices I ₂₁ and I ₂₂ into a 3MN×1 matrix I ₃ ;

Step 7: Substituting the initial parameter λ ₂ and the initial iteration value y ₀ , repeating steps 2 to 3 to obtain the matrix I _orgb ;

Step 8: Divide I _orgb into three MN×1 matrices of equal length and rearrange them to obtain M×N matrices I _or , I _og , I _ob , and combine the three matrices to finally obtain the ciphertext image I _out .

The beneficial effects of the present invention are:

1. A single image is used for encryption, the algorithm occupies a small space, and the encryption algorithm runs fast. That is, the encryption time of the double-image encryption algorithm is 2.367s, and the decryption time is 2.376s; the encryption time of the present invention is 0.674s, and the decryption time is 0.688s.

2. Utilizing the advantages of more complex dynamic characteristics and higher security of the double chaotic system, it overcomes the shortcomings of a single chaotic system for image encryption with small key space and low security. That is to say, a double chaotic system is adopted (the number of keys is 6), the precision is 10 ^-15 and the key space is 10 ⁹⁰ , which is much larger than 2 ¹²⁸ . The key space is enough to resist various known attacks.

3. Utilize global pixel scrambling and fractional Fourier transform to encrypt pixel gray value, which greatly reduces the correlation between ciphertext pixel values. That is, the correlation between the pixels of the original image is above 99%, and the correlation between the pixels of the encrypted image in the present invention is reduced to below 2%.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention;

Figure 2a is the original image of Lena;

Fig. 2b is the R channel image of Fig. 2a;

Fig. 2c is the G channel image of Fig. 2a;

Figure 2d is the B channel image of Figure 2a;

Fig. 3a is the encrypted image of Fig. 2a;

Fig. 3b is the R channel image of Fig. 3a;

Fig. 3c is the G channel image of Fig. 3a;

Figure 3d is the B channel image of Figure 3a;

Figure 4a is the correct decrypted image of Figure 3a;

Fig. 4b is the decrypted image of the wrong parameter x ₀ in Fig. 4a;

Fig. 4c is the decrypted image of the wrong parameter y ₀ in Fig. 4a;

Fig. 4d is the decrypted image of the wrong parameter λ ₁ of Fig. 4a;

Fig. 4e is the wrong parameter λ ₂ decrypted image of Fig. 4a;

Figure 5a covers 20% of the image in Figure 3a;

Figure 5b is the Gaussian noise image with a mean square error of 0.05 added to Figure 3a;

Fig. 5c is the decrypted image of Fig. 5a;

Figure 5d is the decrypted image of Figure 5b;

Fig. 6 a is the original image and encrypted image R, G, pixel correlation table of each channel of B;

Figure 6b is a correlation table of pixels at the same position among R, G, and B channels;

Fig. 6c is a correlation table of pixels at adjacent positions among R, G, and B channels.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings.

As shown in Figure 1, a color image encryption method based on chaotic system and fractional Fourier transform comprises the following steps:

S1: Known plaintext color pixel image I _in (.bmp format), the size of the image is M×N, the three-color channel matrix R, G, B of the extracted image is sequentially connected to form a 3M×N matrix I _irgb .

S2: Set the initial parameter λ ₁ and the initial iteration value x ₀ , and substitute it into the Logistic chaotic system for m+3MN iterations. Ignoring the results of the first m iterations to avoid harmful effects, the chaotic sequence x={x _m+1 ,x _m+2 ,...,x _m+3MN } is obtained.

S3: Sort all the values of the chaotic sequence x to get a new sequence and get the sequence The position of each element value in the original sequence x T ₁ ={t ₁ ,t ₂ ,...,t _3MN }, that is

S4: Perform global pixel scrambling on I _irgb , that is, transform I _irgb into a 3MN×1 matrix I _t , rearrange all rows of I _t according to T ₁ , that is, move row t ₁ of I _t to the first row , the t ₂ row of I _t will be moved to the second row, and so on until the t _3MN row of I _t is moved to the last row, at this time we get the matrix I ₁ .

S5: Divide I ₁ into two parts, I ₁₁ and I ₁₂ , let I ₁₁ be the modulus and I ₁₂ the phase angle to form a complex matrix, namely At this point we get the matrix I _e .

S6: Perform fractional Fourier transform (DFrFT ^α ) of I _e with a rotation angle of α, and at this time we obtain matrix I ₂ .

S7: Extract the modulus and phase angle of the complex matrix I ₂ to obtain the matrices I ₂₁ and I ₂₂ respectively, combine I ₂₁ and I ₂₂ into a 3MN×1 matrix, and then we obtain the matrix I ₃ .

S8: Set the initial parameter λ ₂ and the initial iteration value y ₀ , repeat steps S2-S4, and now we get the matrix I _orgb .

S9: Divide I _orgb into three MN×1 matrices of equal length and rearrange them to obtain M×N matrices I _or , I _og , I _ob , and compound them to finally obtain the ciphertext image I _out (.bmp format ).

Use MATLAB software to simulate the image encryption method proposed by the present invention, the plaintext image selects the standard test color image Lena, image size 256 * 256) as shown in Figure 2a, it is carried out based on the encryption of chaotic system and fractional Fourier transform, key The parameters are encryption of x ₀ =0.8927, y ₀ =0.7035, m=300, n=349, α=0.5000, λ ₁ =3.9735, λ ₂ =3.9824, and the performance is analyzed. Figure 2b is the R channel image of Figure 2a, Figure 2c is the G channel image of Figure 2a, and Figure 2d is the B channel image of Figure 2a.

First, follow the steps S1-S9 of the plaintext image to obtain an encrypted image as shown in Figure 3a, Figure 3b is the R-channel image in Figure 3a, Figure 3c is the G-channel image in Figure 3a, and Figure 3d is the B-channel image in Figure 3a.

Key sensitivity analysis test: use the correct key x ₀ =0.8927, y ₀ =0.7035, m=300, n=349, α=0.5000, λ ₁ =3.9735, λ ₂ =3.9824 to decrypt, and the decrypted image is shown in Figure 4a , respectively use the wrong key x ₀ =0.8927+10 ^-15 , y ₀ =0.7035+10 ^-15 , λ ₁ =3.9735+10 ^-15 , λ ₂ =3.9824+10 ^-15 to get the decrypted image as shown in Figure 4b, Fig. 4c, Figure 4d, Figure 4e. It can be seen from the decryption results that the key sensitivity is extremely high and the key space is large, which can resist key attacks.

Anti-attack analysis and test of the encryption method: cover the encrypted result image 3a by 20% as shown in 5a, and decrypt it to obtain the decrypted result as shown in 5c; add Gaussian noise with a mean square error of 0.05 to the encrypted result image 3a as shown in the figure 5b, decrypt it, and obtain the decryption result as shown in Figure 5d. From the decryption results, it can be seen that the encrypted image can still be effectively decrypted after receiving a certain attack, which shows that the encryption method has good robustness and high resistance to attack.

Pixel correlation analysis test: The correlation of adjacent pixels can reflect the degree of diffusion of image pixels, and the correlation between two adjacent pixels in the original plaintext image is usually very large, try to make the correlation coefficient of adjacent pixels in the encrypted image close to zero. Table 1 shows the pixel correlation of the R, G, and B channels of the original image and the encrypted image, Table 2 shows the pixel correlation of the same position between the R, G, and B channels, and Table 3 shows the pixel correlation of adjacent positions between the R, G, and B channels sex. It can be seen from the above table that the original image has a strong correlation, and the encrypted image has a weak correlation and high security.

Decryption process:

The image decryption process is the reverse process of the image encryption process.

In the present invention, the decryption process can use the keys x ₀ =0.8927, y ₀ =0.7035, m=300, n=349, α=0.5000, λ ₁ =3.9735, λ ₂ =3.9824, through the reverse process of the encryption process Complete decryption.

For example, the image to be encrypted is a standard test color Lena image, the image size is 256×256, and the key for performing chaotic system and fractional Fourier transform on it is x ₀ , y ₀ ,m,n,α,λ ₁ ,λ ₂ If the color image is encrypted, the key parameters x ₀ , y ₀ , m, n, α, λ ₁ , λ ₂ can also be used to decrypt the reverse process of the encryption process.

An encryption method based on a chaotic system and fractional Fourier transform provided by the present invention has high security and strong anti-deciphering ability, and provides a new solution for image encryption. In the occasion of using images for communication, the encryption method has Very high use value.

Claims (1)

1. A color image encryption method based on chaotic system and fractional order Fourier transform, is characterized in that, comprises the following steps: Step 1: Input a plaintext color pixel image I _in with a size of M×N, extract the three-color channel matrix R, G, B of the plaintext color pixel image and sequentially connect them into a 3M×N matrix I _irgb ; Step 2: Substitute the initial parameter λ ₁ and the initial iterative value x ₀ into the Logistic chaotic system to iterate m+3MN times, ignore the results of the first m iterations, and obtain the chaotic sequence x={x _m+1 ,x _m+2 ,... ,x _m+3MN }, sort all the values of the chaotic sequence x to get a new sequence and get the sequence The position of each element value in the original chaotic sequence x T ₁ ={t ₁ ,t ₂ ,...,t _3MN }, that is $x_i={\stackrel{\‾}{x}}_{t_i}(i=\mathrm{1,2},...,3\mathrm{MN});$ Step 3: Perform global pixel scrambling on the matrix I _irgb , transform the matrix I _irgb into a 3MN×1 matrix I _t , rearrange all the rows of I _t according to T ₁ , that is, move the t ₁ row of I _t to the first row, move the t ₂ row of I _t to the second row, and so on, until the t _3MN row of I _t is moved to the last row, and obtain the matrix I ₁ ; Step 4: Divide matrix I ₁ into two matrices I ₁₁ and I ₁₂ , let matrix I ₁₁ be used as the modulus, and matrix I ₁₂ be used as the phase angle to form a complex matrix $I_e=I_{11}{e}^{\mathrm{j\π}{I}_{12}};$ Step 5: Perform the fractional Fourier transform of the complex matrix I _e with a rotation angle of α to obtain the complex matrix I ₂ ; Step 6: Extract the modulus and phase angle of the complex matrix I ₂ to obtain the matrices I ₂₁ and I ₂₂ , and combine the matrices I ₂₁ and I ₂₂ into a 3MN×1 matrix I ₃ ; Step 7: Substituting the initial parameter λ ₂ and the initial iteration value y ₀ , repeating steps 2 to 3 to obtain the matrix I _orgb ; Step 8: Divide I _orgb into three MN×1 matrices of equal length and rearrange them to obtain M×N matrices I _or , I _og , I _ob , and combine the three matrices to finally obtain the ciphertext image I _out .