Multi-image encryption method based on improved z curve and chaotic signal

Abstract

The invention discloses a multi-image encryption method based on an improved z curve and a chaotic signal, and the method comprises the steps: randomly selecting R, G and B color channels of input images, and fusing the four input images with different sizes into a fused image; processing the fused image by using an SHA256 algorithm to obtain a secret key, performing grouping calculation to obtain an initial value of the grid multi-scroll chaotic system, performing zero padding operation and blocking operation on the fused image in sequence, then substituting the initial value into the grid multi-scroll chaotic system to obtain three chaotic sequences, and performing division on the chaotic sequences; performing scrambling operation on each sub-block through two algorithms in combination with a chaos sequence, and storing the scrambled sub-blocks into an array; performing dynamic DNA encoding and decoding operation on elements in the array by combining a chaos sequence to obtain a sequence DNAjiema; and carrying out grouping diffusion on the sequence DNAjiema through an improved center diffusion algorithm, and finally obtaining an encrypted image.

Description

Technical Field

[0001] The invention relates to the technical field of image encryption, in particular to a multi-image encryption method based on an improved z-curve and a chaotic signal. Background Art

[0002] With the rapid development of information technology, information security issues have become increasingly urgent, especially as images are an important carrier of information transmission, and their security has attracted much attention. With the rapid development of computer technology, various cracking technologies have emerged, and it is urgent to seek more secure and effective encryption algorithms.

[0003] Most of the existing image encryption algorithms are single-image encryption. However, with the rapid development of information technology, single-image encryption algorithms are no longer suitable for the requirements of the big data era for fast and efficient processing of massive information. Multi-image encryption not only provides higher security when protecting multiple image data, but also can process multiple images in parallel, significantly improving the efficiency of data encryption, and becoming an ideal choice for meeting the challenges of the big data era. Chaos theory has been widely used in the field of image encryption due to its high initial value sensitivity and randomness. Compared with conventional chaotic systems, multi-scroll chaotic systems have more complex chaotic behaviors and nonlinear characteristics. They can be used for image encryption to increase the randomness of signals and enhance resistance to various interferences. The application of space-filling curve scrambling in the field of image encryption can effectively increase the security of image encryption. However, the traditional space-filling curve route is relatively single, with weak randomness and easy to be cracked.

[0004] In view of this, the present invention provides a multi-image encryption algorithm based on an improved z-curve, a grid multi-scroll chaotic system and DNA dynamic coding. Summary of the invention

[0005] The present invention provides a multi-image encryption method based on an improved z-curve and a chaotic signal. Simulation results and security analysis show that the multi-image encryption algorithm can resist differential attacks, cropping attacks, noise attacks, etc., and has good security performance.

[0006] The present invention can be achieved through the following technical solutions:

[0007] A multi-image encryption method based on improved z-curve and chaotic signal comprises the following steps:

[0008] Step 1: By randomly selecting the R, G, and B color channels of the input images, four input images of different sizes are fused into a fused image O;

[0009] Step 2: Use the SHA256 algorithm to process the fused image O to obtain the key, and obtain the initial values ​​X0, Y0, and Z0 of the grid multi-scroll chaotic system through group calculation. At the same time, the fused image O is sequentially filled with zeros and divided into blocks. Then, the initial values ​​X0, Y0, and Z0 are substituted into the grid multi-scroll chaotic system to obtain three chaotic sequences of X, Y, and Z, and the chaotic sequences are divided into parts.

[0010] Step 3: Combine the divided chaotic sequence, and then use the improved z-curve and Knuth-DurstenfeldShuffle algorithm to scramble each sub-block, and store the scrambled sub-blocks into the cell array;

[0011] Step 4: By combining the divided chaotic sequences, the elements in the cell array are dynamically encoded, calculated and decoded to obtain the sequence DNAjiema;

[0012] Step 5: Diffusion of the sequence DNAjiema is performed in groups through the improved center diffusion algorithm, and finally the encrypted image is obtained.

[0013] Furthermore, in the step one, a channel is randomly selected from the three channels R, G, and B of each input image, and the image pixels of the selected channel are filled into a matrix of M*M size one by one to form the R channel of the fused image O. Then, a channel is randomly selected from the remaining two channels of each input image, and the image pixels of the selected channel are filled into a matrix of M*M size one by one to form the G channel of the fused image O. Finally, the image pixels in the remaining channel of each input image are filled into a matrix of M*M size one by one to form the B channel of the fused image O, thereby forming a fused image O of M*M size.

[0014] Furthermore, in the step 2, a channel is randomly selected from the fused image O, the image pixel average value of the channel is calculated, and it is used as the input of the SHA256 algorithm to obtain a 256-bit hash value K, i.e., the key K. The key K is divided into 32 groups and the initial values ​​X0, Y0, and Z0 of the grid multi-vortex chaotic system are calculated.

[0015] Furthermore, the initial values ​​X0, Y0, and Z0 of the grid multi-scroll chaotic system are calculated using the following equations.

[0016]

[0017] X0=(x0+y0) / 2

[0018] Y0=(z0+w0) / 2

[0019] Z0=(x0+y0+z0+w0) / 2

[0020] Furthermore, the fused image O is firstly padded with zeros to obtain a matrix of size M2*M2*3, and then divided into blocks. The size of the matrix corresponding to each sub-block is t*t. Then, the initial values ​​X0, Y0, and Z0 are brought into the grid multi-scroll chaotic system to calculate the chaotic sequences X, Y, and Z.

[0021] Then the 1st to 3rd*(M2) of the chaotic sequence X 2 / t 2 The chaotic sequence X1 is recorded as the chaotic sequence X1, and the 1+3*(M2) 2 / t 2 To 1+3*(M2) 2 / t 2 +M2*M2*24 is recorded as chaotic sequence X2, and the 1st + 3*(M2) of chaotic sequence X is recorded as 2 / t 2 +M2*M2*24 to 1st+3*(M2) 2 / t 2 +M2*M2*24+M2*M2*12 bits are recorded as chaotic sequence X3, the 1st to 24*M2*M2 bits of chaotic sequence Y are recorded as chaotic sequence Y1, the 1st+24*M2*M2 to 1+24*M2*M2+12*M2*M2 bits of chaotic sequence Y are recorded as chaotic sequence Y2, and the chaotic sequence Z remains unchanged.

[0022] Furthermore, in the step 2, the fused image O is divided into three two-dimensional matrices, and zero padding is performed on each of the two-dimensional matrices one by one. The size of each two-dimensional matrix after zero padding is M2*M2, and then each two-dimensional matrix after zero padding is divided into M2*M2 / t 2 Sub-blocks,

[0023] For each sub-block, the improved z-curve is first used in combination with the chaotic sequence X1 to scramble the sub-block, and then the Knuth-Durstenfeld Shuffle algorithm is used to further scramble the sub-block. The scrambled sub-blocks are then saved in the cell array in row order.

[0024] Further, the improved z-curve is set as a closed-loop curve, which is obtained by rotating the z-shaped curves 90 degrees in sequence, four times in total, and then connecting them end to end, including the first z-shaped curve to the fourth z-shaped curve in a clockwise direction, and four traversal modes are designed according to the starting position and the moving direction.

[0025] Traversal mode 1 is: traverse from the lower left corner along the first z-shaped curve; traversal mode 2 is: traverse from the upper left corner along the second z-shaped curve; traversal mode 3 is: traverse from the upper right corner along the third z-shaped curve; traversal mode 4 is: traverse from the lower right corner along the fourth z-shaped curve;

[0026] Use the following equation to convert each element in the chaotic sequence X1 into a number between 1 and 64.

[0027] X1=mod(ceil(abs(X1)*10 15 ),64)+1

[0028] Take t=8, use different values ​​in the converted chaotic sequence X1 as the starting points of different sub-blocks, and scramble the sub-blocks of size 8*8 according to the traversal mode.

[0029] Further, the method for obtaining the sequence DNA sequence in step 4 comprises the following steps:

[0030] Step I: first convert each element in the cell array into an eight-bit binary string to form a sequence hechengtu, then use the following equation to convert each element in the chaotic sequence X2 into a number between 0 and 7, and then use the converted chaotic sequence X2 to perform DNA encoding on the sequence hechengtu according to the DNA encoding rules in Table 1 to obtain the first sequence DNAbianma;

[0031] X2=mod(ceil(abs(X2)*10 15 ),8)

[0032] Table 1 DNA coding rules

[0033]

[0034] Step II, repeat step I, according to the DNA coding rules, use the chaotic sequence X3 to perform DNA coding on the chaotic sequence Z to obtain the second sequence DNAbianma, and then according to the DNA operation rules in Table 2, use the chaotic sequence Y1 to perform DNA operation on the first sequence DNAbianma and the second sequence DNAbianma to obtain the sequence DNAyunsuan,

[0035] Here, using the equation X3 = mod(ceil(abs(X3)*10 15 ),8), each element in the chaotic sequence X3 is processed as a number between 0 and 7;

[0036] Table 2 DNA algorithm

[0037]

[0038] Step III: According to the inverse operation of the DNA coding rule, the chaotic sequence Y2 is used to perform DNA decoding on the sequence DNAyunsuan to obtain the sequence DNAjiema.

[0039] Furthermore, in step II, each element in the chaotic sequence Y1 is processed into a number between 0 and 4 using the following equation;

[0040] Y1=mod(ceil(abs(Y1)*10 15 ),5)

[0041] Then the bases at the same position of the first sequence DNA code and the second sequence DNA code are traversed, and according to the DNA operation rules in Table 2, when Y1 is 0, the addition operation of the first sequence DNA code and the second sequence DNA code is performed, when Y1 is 1, the subtraction operation of the first sequence DNA code and the second sequence DNA code is performed, when Y1 is 2, the XOR operation of the first sequence DNA code and the second sequence DNA code is performed, when Y1 is 3, the XOR operation of the first sequence DNA code and the second sequence DNA code is performed, and when Y1 is 4, the inversion operation of the first sequence DNA code is performed.

[0042] Further, according to the improved central diffusion algorithm, the sequence DNAjiema is divided into a plurality of subsequences with a length of 8 in each group, the fourth and fifth bits of each subsequence are selected as the starting point, the values ​​of the fourth and fifth bits are compared, if the values ​​are different, all bits are inverted, if the values ​​are the same, the values ​​of the third and sixth bits are compared, if the values ​​of the third and sixth bits are different, the first to third bits and the sixth to eighth bits are inverted, if the values ​​are the same, the values ​​of the second and seventh bits are compared, if the values ​​of the second and seventh bits are different, the first, second, seventh and eighth bits are inverted, if the values ​​are the same, the values ​​of the first and eighth bits are compared, if the values ​​of the first and eighth bits are different, the first and eighth bits are inverted, if the values ​​are the same, the subsequence remains unchanged, thereby realizing the diffusion of image pixels, and then converting the diffused binary number into a decimal number, and converting the matrix into M2*M2*3 to obtain an encrypted image.

[0043] The beneficial technical effects of the present invention are:

[0044] 1. Compared with the existing image encryption technology, the multi-image encryption algorithm of the present invention first randomly fuses color images of different sizes to obtain a fused image, and randomly selects the image pixel average value of a channel from the fused image as the input of the SHA256 algorithm to generate a key, which is used as the initial value of the grid multi-vortex chaotic system. Then, the improved z-curve and Knuth-Durstenfeld Shuffle algorithm are used to scramble the pixels of the fused image to reduce the correlation between image pixels, thereby realizing image pixel-level encryption. Finally, the grid multi-vortex chaotic sequence, DNA dynamic coding, and improved center diffusion algorithm are used to diffuse image pixels to complete image encryption. In this way, four color images of different sizes are randomly combined through R, G, and B channels and fused into a color image for parallel encryption, thereby improving encryption efficiency. In addition, the chaotic key is associated with the pixel value of the fused image to enhance the randomness of the key, thereby realizing "one Figure 1 dense".

[0045] 2. In view of the limitations of traditional space-filling curve scrambling, the present invention designs an improved Z curve, which is a closed-loop curve. The Z curve is obtained by rotating the Z curve 90 degrees in sequence for four times and then connecting them end to end. All positions in a sub-block of 8*8 size can be used as starting points. The initial positions of the scrambled image pixels in the improved Z curve are determined by the chaotic sequence of the grid multi-vortex chaotic system. The original sub-blocks are scrambled, and the initial positions of the Z curve scrambling selected for different sub-blocks are different, making it difficult for attackers to infer the content of the original image by analyzing features such as histograms and frequency distributions, and it is not easy to be cracked.

[0046] 3. The present invention adopts dynamic DNA coding, grid multi-scroll chaotic sequence and improved center diffusion algorithm to perform diffusion operation on image pixels. First, DNA in biology is applied to image encryption, which adds extra complexity and randomness. Dynamic DNA coding changes the image pixel value into the base in DNA, and through the dynamic switching of different coding rules, the representation of image data is more complex, thereby enhancing the encryption strength; DNA operation includes calculation methods such as DNA addition, subtraction, XOR, XOR and negation. The operation rules are combined with the dynamic generation of multi-scroll chaotic sequence, so that the calculation method of each base is different, further improving the anti-attack ability; DNA decoding transforms the base into the image pixel value, thereby realizing the first diffusion of the image pixel; secondly, the improved center diffusion algorithm is applied to the diffusion processing of the image pixel, and its center point is selected as the starting point, and it is compared and diffused bit by bit, so as to realize the secondary diffusion of the image pixel, better resist statistical attack and differential attack, and further enhance the security of the encryption algorithm.

[0047] Simulation results and security analysis show that the multi-image encryption algorithm of the present invention has good security and resistance to various attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0049] Figure 2 A schematic diagram of the Lyapunov exponents of the grid multi-scroll chaotic system of the present invention;

[0050] Figure 3 Schematic diagrams of four modes of the improved z-curve of the present invention;

[0051] Figure 4 A schematic diagram of an improved z-curve scrambling process of the present invention;

[0052] Figure 5 It is the simulation result of the present invention, where (a) original images of Peppers, Baboon, House, and Plane (b) encrypted images (c) decrypted images of Peppers, Baboon, House, and Plane;

[0053] Figure 6 are histograms of the original image and the encrypted image of the present invention, wherein: (a) Peppers histogram (b) Baboon histogram (c) House histogram (d) Plane histogram (e) encrypted image histogram;

[0054] Figure 7 Schematic diagram of the key sensitivity test of the present invention, wherein: (a) x offset 10-14 Peppers decrypted image (b) x offset 10-14 Baboon decrypted image (c) x offset 10-14 House decrypted image (d) x offset 10-14 Plane decrypted image;

[0055] Figure 8 Schematic diagram of the correlation test of adjacent pixels of the present invention, wherein: (a) horizontal correlation distribution of Plane adjacent pixels (b) horizontal correlation distribution of encrypted image adjacent pixels (c) vertical correlation distribution of House adjacent pixels (d) vertical correlation distribution of encrypted image adjacent pixels (e) diagonal correlation distribution of Peppers adjacent pixels (f) diagonal correlation distribution of encrypted image adjacent pixels;

[0056] Fig. 9 Schematic diagram of the cropping attack experiment of the present invention, wherein (a) cropping 25% of the encrypted image and decrypted image in the upper left corner (b) cropping 25% of the encrypted image and decrypted image in the center (c) cropping 25% of the encrypted image and decrypted image above (d) cropping 25% of the encrypted image and decrypted image in the four corners;

[0057] Fig.10 Schematic diagram of the noise attack test of the present invention, wherein: (a) encrypted image after noise attack; (b) Peppers decrypted image after noise attack; (c) Baboon decrypted image after noise attack; (d) House decrypted image after noise attack; (e) Plane decrypted image after noise attack. DETAILED DESCRIPTION

[0058] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] See attached Figure 1 The invention provides a multi-image encryption algorithm based on an improved z-curve and a chaotic signal, including multi-image fusion, image pixel scrambling, dynamic DNA encoding and decoding, and image pixel diffusion. The multi-image fusion randomly selects R, G, and B color channels of the input image to fuse four input images of different sizes into a colored fused image, and then uses the pixel average value of the fused image as the input of the SHA-256 algorithm to obtain a key, obtains initial values ​​X0, Y0, and Z0 of a grid multi-scroll chaotic system through group calculation, and then substitutes the initial values ​​X0, Y0, and Z0 into the grid multi-scroll chaotic system to obtain three chaotic sequences of X, Y, and Z; the image pixel scrambling scrambles the image pixels through an improved z-curve and a Knuth-Durstenfeld Shuffle algorithm; the dynamic DNA encoding and decoding performs DNA encoding, DNA operation, and DNA decoding on the scrambled image sequence by combining the chaotic sequence; the image pixel diffusion performs pixel diffusion on the decoded sequence through an improved center diffusion algorithm to finally obtain an encrypted image.

[0060] Aiming at the limitation of traditional space filling curve scrambling, the present invention designs an improved Z curve, in which the initial position of the scrambled image pixels is determined by the chaotic sequence of the grid multi-scroll chaotic system, making it difficult to be cracked. At the same time, the image pixels are diffused by combining dynamic DNA coding, grid multi-scroll chaotic sequence and improved center diffusion algorithm, which further enhances the security of the encryption algorithm. Simulation results and security analysis show that the multi-image encryption algorithm of the present invention has good security and resistance to various attacks.

[0061] The details are as follows:

[0062] Step 1: Multi-image fusion

[0063] Input four color images of any size and read the size of each color image. The number of elements in a single channel is recorded as s, and the size of the fused image O is recorded as M*M*3. Randomly select one channel from the three channels R, G, and B of each color image, and fill the image pixels of the selected channel into a matrix of size M*M one by one to form the R, G, and B channels of the fused image O.

[0064] The sizes of the four input color images of any size are recorded as f*g*3, h*i*3, j*k*3, l*m*3, the number of elements in a single channel is recorded as s, and the size of the fused image O is M*M*3.

[0065] One channel is randomly selected from the three channels R, G, and B of each color image, and the image pixels of the selected channel are filled into the matrix of M*M size one by one to form the R channel of the fused image O. Then, one channel is randomly selected from the remaining two channels of each color image, and the image pixels of the selected channel are filled into the matrix of M*M size one by one to form the G channel of the fused image O. Finally, the image pixels in the remaining channel of each color image are filled into the matrix of M*M size one by one to form the B channel of the fused image O.

[0066] S and M are calculated as follows:

[0067] s=f*g+h*i+j*k+l*m

[0068] M = ceil(sqrt(s))

[0069] Among them, ceil is the round-up function, and sqrt is the square root function.

[0070] Step 2: Image pixel scrambling

[0071] S2.1. Use the SHA256 algorithm to process the fused image O to obtain the key, and obtain the initial values ​​X0, Y0, and Z0 of the grid multi-scroll chaotic system through group calculation. Then substitute the initial values ​​X0, Y0, and Z0 into the grid multi-scroll chaotic system to obtain the three chaotic sequences X, Y, and Z.

[0072] The grid multi-scroll chaotic system is a special type of multi-scroll chaotic system, which generates multiple scroll structures through system parameters to form more complex trajectories in the phase space, making the behavior of the system unpredictable and having better chaotic characteristics.

[0073] The mathematical model of the grid multi-scroll chaotic system is shown in formula (1):

[0074]

[0075] Among them, x, y, z represent system state variables, and a, b∈R are system parameters. f(x), g(y) are the summation parts of the symbolic function. The formulas of f(x) and g(y) are shown in formula (2):

[0076]

[0077] Among them, r, e, A, C∈R are positive constants, and n1, n2∈Z are positive integers used to control the number of rolling axes generated by the system.

[0078] When a=10, b=18, r=0.2857, e=2, A=2, d=1, C=1, (x0, y0, z0)=(0.2, 0, 0), n1=1, n2=0, the grid multi-scroll chaotic system has 5*3 scrolls.

[0079] like Figure 2 As shown, from the values ​​of the three Lyapounov exponents corresponding to the grid multi-scroll chaotic system at any time, it can be seen that at least one Lyapounov exponent has a value greater than zero, which indicates that the system is in a chaotic state.

[0080] The method of using the SHA256 algorithm to obtain the initial values ​​X0, Y0, and Z0 of the grid multi-scroll chaotic system is as follows: randomly select a channel from the fused image O, calculate the image pixel average of the channel, and use it as the input of the SHA256 algorithm to obtain a 256-bit hash value K, i.e., the key K. The key K is divided into 32 groups, which are recorded as K1, K2, …, K 32 , using groups K1, K2, ..., K 32 The initial values ​​X0, Y0, and Z0 of the grid multi-scroll chaotic system are calculated. The specific calculation formula is as follows:

[0081]

[0082] X0=(x0+y0) / 2

[0083] Y0=(z0+w0) / 2

[0084] Z0=(x0+y0+z0+w0) / 2

[0085] S2.2, zero padding operation

[0086] Calculate in the following way: divide the fused image O into three two-dimensional matrices, denoted as R, G, and B respectively; perform zero-padding operation on the three two-dimensional matrices R, G, and B, and denoted the size of the two-dimensional matrix after zero-padding as M2*M2.

[0087] R=O(:,:,1)

[0088] G=O(:,:,2)

[0089] B=O(:,:,3)

[0090] Then fill the three two-dimensional matrices of R, G, and B with zeros and calculate them as follows:

[0091] mod(M,t)=M1

[0092] R(M+1:M+t-M1,M+1:M+t-M1,1)=0

[0093] G(M+1:M+t-M1,M+1:M+t-M1,1)=0

[0094] B(M+1:M+t-M1,M+1:M+t-M1,1)=0

[0095] Here, t is the size of the block matrix, preferably t=8.

[0096] Through this step, the number of rows and columns of the image is padded to a number that is divisible by t, and the size of the two-dimensional matrix after zero padding is recorded as M2*M2.

[0097] S2.3. Bring the initial values ​​X0, Y0, and Z0 into the grid multi-scroll chaotic system to obtain three chaotic sequences X, Y, and Z. Then divide the chaotic sequence X into three parts: X1, X2, and X3, and divide the chaotic sequence Y into two parts: Y1 and Y2.

[0098] In order to avoid transient effects, the first 3001 items of each sequence are discarded to obtain three chaotic sequences X, Y, and Z. Then the chaotic sequence X is divided into three parts: X1, X2, and X3. The chaotic sequence X1 is used to select the initial position of the z curve, the chaotic sequence X2 is used to select the DNA encoding rule, and the chaotic sequence X3 is used to perform DNA encoding on the sequence Z. The chaotic sequence Y is divided into two parts: Y1 and Y2. The chaotic sequence Y1 is used to select the DNA operation rule, and the chaotic sequence Y2 is used to select the DNA decoding rule. The chaotic sequence Z is used for DNA diffusion.

[0099] Specifically, the 1st to 3rd*(M2) of the chaotic sequence X 2 / t 2 The chaotic sequence X1 is recorded as the chaotic sequence X1, and the 1+3*(M2) 2 / t 2 To 1+3*(M2) 2 / t 2 +M2*M2*24 is recorded as chaotic sequence X2, and the 1st + 3*(M2) of chaotic sequence X is recorded as 2 / t 2 +M2*M2*24 to 1st+3*(M2) 2 / t 2+M2*M2*24+M2*M2*12 bits are recorded as chaotic sequence X3, the 1st to 24*M2*M2 bits of chaotic sequence Y are recorded as chaotic sequence Y1, the 1st+24*M2*M2 to 1+24*M2*M2+12*M2*M2 bits of chaotic sequence Y are recorded as chaotic sequence Y2, and the chaotic sequence Z remains unchanged.

[0100] S2.4. Scrambling Operation

[0101] Divide each two-dimensional matrix into M2*M2 / t 2 sub-blocks, pre-process the chaotic sequence X1, scramble each sub-block using the improved z-curve, further scramble each sub-block after the z-curve scrambling using the Knuth-Durstenfeld Shuffle algorithm, and finally save each sub-block in the cell array in row order.

[0102] like Figure 3 As shown, the z-curve is an important space-filling curve. By scrambling the z-curve, it is difficult for attackers to infer the content of the original image by analyzing features such as histograms and frequency distribution. The traditional z-curve scanning route is relatively simple and easy to be cracked. Therefore, the present invention improves the traditional z-curve, and the improved z-curve has different scanning routes for image pixels located at different positions. The traditional z-curve can be described as: dividing a square into 4 small squares, starting from the center of the square in the upper left corner to the right to the center of the square in the upper right corner, then to the lower left to the center of the square in the lower left corner, and finally to the right to the center of the square in the lower right corner.

[0103] like Figure 4 As shown, the improved z-curve is set as a closed loop curve, which is obtained by rotating the z-shaped curves 90 degrees in sequence, four times in total, and then connecting them end to end. It includes the first z-shaped curve to the fourth z-shaped curve in a clockwise direction. According to the starting position and the moving direction, four traversal modes are designed. Figure 3 It can be seen that traversal mode 1 is: starting from the lower left corner and traversing according to the first z-shaped curve; traversal mode 2 is: starting from the upper left corner and traversing according to the second z-shaped curve; traversal mode 3 is: starting from the upper right corner and traversing according to the third z-shaped curve; traversal mode 4 is: starting from the lower right corner and traversing according to the fourth z-shaped curve.

[0104] In the 8*8 size sub-block, the improved z-curve has different scanning routes for image pixels at different positions. Since the improved z-curve is a closed-loop curve, any position can be selected as the initial position for scrambling in combination with the chaotic sequence, which has a certain randomness.

[0105] Specifically, each two-dimensional matrix is ​​divided into M2*M2 / t 2The chaotic sequence X1 is calculated as follows: each element is converted into a number between 1 and 64, and then each sub-block is scrambled according to the traversal mode. When 43 is selected as the initial position, the distribution of image pixels before and after scrambling is as follows: Figure 5 shown.

[0106] X1=mod(ceil(abs(X1)*10 15 ),64)+1

[0107] Among them, mod is the remainder function, ceil is the round-up function, and abs is the absolute value function.

[0108] Each sub-block is scrambled using the improved z-curve. After scrambling, the size of each sub-block is 1*t. 2 , and then use the Knuth-Durstenfeld Shuffle algorithm to further scramble each sub-block after the z-curve scrambling, and the result blocks are saved in the cell array.

[0109] Step 3: Dynamic DNA encoding and decoding

[0110] S3.1 DNA encoding

[0111] All elements in the cell array are connected in series into a row, and each element is converted into an 8-bit binary string to obtain the sequence hechengtu. The chaotic sequence X2 is preprocessed using the following equation, and each element is converted into a number between 1 and 8. According to the encoding rules in Table 1, the sequence hechengtu is dynamically DNA encoded using the processed chaotic sequence X2 to obtain the first DNAbianma of the sequence.

[0112] The chaotic sequence X2 is calculated as follows:

[0113] X2=mod(ceil(abs(X2)*10 15 ),8)

[0114] Table 1 DNA coding

[0115]

[0116] S3.2 DNA decoding

[0117] The chaotic sequences Y1, X3, Z and Y2 are preprocessed according to the following calculation method.

[0118] Y1=mod(ceil(abs(Y1)*10 15 ),5)

[0119] X3=mod(ceil(abs(X3)*1015 ),8)

[0120] Z=mod(ceil(abs(Z)*10 15 ),256)

[0121] Y2=mod(ceil(abs(Y2)*10 15 ),8)

[0122] Then, according to step S3.1, the chaotic sequence X3 is used to perform dynamic DNA encoding on the chaotic sequence Z to obtain the second sequence DNAbianma, and then according to the DNA operation rules in Table 2, the preprocessed chaotic sequence Y1 is used. DNA operation is performed on the first sequence DNAbianma and the second sequence DNAbianma. The bases in the first sequence DNAbianma correspond to the bases in the first row in Table 2, and the bases in the second sequence DNAbianma correspond to the bases in the first column in Table 2. The bases in the same position of the first sequence DNA encoding and the second sequence DNA encoding are traversed. When Y1 is 0, the addition operation of the first sequence DNA encoding and the second sequence DNA encoding is performed. When Y1 is 1, the subtraction operation of the first sequence DNA encoding and the second sequence DNA encoding is performed. When Y1 is 2, the XOR operation of the first sequence DNA encoding and the second sequence DNA encoding is performed. When Y1 is 3, the XOR operation of the first sequence DNA encoding and the second sequence DNA encoding is performed. When Y1 is 4, the inversion operation of the first sequence DNA encoding is performed. After the DNA operation, the sequence DNAyunsuan is obtained.

[0123] Table 2 DNA algorithm

[0124]

[0125] After the DNA operation is completed, the chaotic sequence Y2 after preprocessing is used to decode the sequence DNAyunsuan according to the inverse operation of the DNA coding rule in Table 1 to obtain the sequence DNAjiema.

[0126] Step 4: Image pixel diffusion

[0127] The sequence DNAjiema is grouped, and the pixels are diffused according to the improved center diffusion algorithm. The diffused binary numbers are converted into decimal numbers, and the matrix is ​​converted into M2*M2*3 to obtain the encrypted image.

[0128] The DNA sequence can be divided into multiple subsequences, and the center point of each subsequence is selected as the starting point, and the pixels of the image are diffused bit by bit. The binary numbers after diffusion are converted into decimal numbers, and the matrix is ​​converted into M2*M2*3 to obtain the encrypted image.

[0129] Specifically, the sequence DNAjiema is divided into a plurality of subsequences, each with a length of 8, and the fourth and fifth bits of each subsequence are selected as starting points, and the values ​​of the fourth and fifth bits are compared. If the values ​​are different, all bits are inverted. If the values ​​are the same, the values ​​of the third and sixth bits are compared. If the values ​​of the third and sixth bits are different, the first to third bits and the sixth to eighth bits are inverted. If the values ​​are the same, the values ​​of the second and seventh bits are compared. If the values ​​of the second and seventh bits are different, the first, second, seventh and eighth bits are inverted. If the values ​​are the same, the values ​​of the first and eighth bits are compared. If the values ​​of the first and eighth bits are different, the first and eighth bits are inverted. If the values ​​are the same, the subsequence remains unchanged, thereby realizing the diffusion of image pixels, and then converting the diffused binary number into a decimal number, and converting the matrix into M2*M2*3 to obtain an encrypted image.

[0130] In order to verify the feasibility of the multi-image encryption method of the present invention, we conduct the following experiments:

[0131] like Figure 5 As shown in the figure, the simulation experiment uses MATLAB 2019a as the simulation platform to read the original image. The test images with sizes of 192×192×3Pepper, 256×256×3Baboon, 384×384×3House and 512×512×3Plane are shown in Figure 6 The diagram corresponding to (a) is shown in the figure. When the B channel of the House image, the B channel of the Baboon image, the R channel of the Plane image, and the R channel of the Peppers image are selected to form the R channel of the fused image, the R channel of the House image, the G channel of the Baboon image, the G channel of the Plane image, and the G channel of the Peppers image are selected to form the G channel of the fused image, the G channel of the House image, the R channel of the Baboon image, the B channel of the Plane image, and the B channel of the Peppers image are selected to form the B channel of the fused image, and the R channel of the fused image O is selected to generate a key, the encrypted image of the fused image 720×720×3 is as follows Figure 6 The diagram corresponding to (b) is shown in the figure, and the decryption result is as follows Figure 6 The corresponding diagram of (c) is shown in Fig. 2. The decrypted image is the same as the image before encryption, which verifies that the designed algorithm can effectively encrypt and decrypt multiple images.

[0132] Key space is one of the important indicators to measure the security of encryption algorithms. It represents the total number of all possible keys in the encryption system. In this algorithm, the key space consists of two parts: the chaotic system parameters and the initial value. When the calculation accuracy is 10 -15 When , the total key space is 2 498 , much higher than the required 2 128, so the proposed algorithm can resist brute force decryption. Table 3 gives the comparison between the proposed algorithm and other algorithms in the key space. Among them, Chen algorithm comes from the literature [Chen Xiaoyang, Mou Jun, Cao Yinghong. Chaotic multiple-image encryption algorithmbased on block scrambling and dynamic DNA coding. International Journal of Bifurcation and Chaos, 2023, 33(16): 2350190.], Zuo algorithm comes from the literature [Zuo JiangGang, Wang Meng, Zhang Jie. Design of multi scroll chaotic attractor based on a novel multi-segmented memristor and its application in medical image encryption. Microelectronic Engineering, 2024, 287: 112156.], Song algorithm comes from the literature [Song Wei, Fu Chong, Zheng Yu, et al. Batch image encryption using cross image permutation and diffusion. Journal of Information Security and Applications, 2024, 80(C): 103686.], Gokyildirim algorithm comes from the literature [Gokyildirim Abdullah, CicekSerdar, Calgan Haris, et al.Fractional-order Sprott K chaotic system and its application to biometric iris image encryption.Computers in Biology and Medicine,2024,179:108864.]. The results show that the algorithm proposed in the present invention has a larger key space.

[0133] Table 3 Comparison of key spaces

[0134]

[0135] The histogram shows the distribution of pixel values ​​in an image. The ideal encrypted image histogram should show a nearly uniform distribution, which can effectively hide the information of the original image pixel distribution. The histograms of the four test images and the encrypted image are shown in Figure 1. Figure 6 shown.

[0136] In the analysis of encrypted images, the chi-square test can be used to detect whether the distribution of image pixel values ​​in each channel of the image conforms to the expected random distribution. The chi-square test formula is shown in formula (3):

[0137]

[0138] where hi and e represent the observed and proposed image pixel frequencies, respectively. When the significance level is α = 0.05, the χ 2 Lower than When , it can be proved that the histogram flatness is high. Table 2 shows the calculation results. Figure 6 From Table 4, we can see that the histogram of the encrypted image is evenly distributed, and the pixel values ​​of each channel image are distributed randomly. The proposed multi-image encryption algorithm meets the requirements.

[0139] Table 4 Results of chi-square test

[0140]

[0141]

[0142] Differential attack is to introduce slight changes in the plaintext image, resulting in significant changes in the encrypted image. When performing differential attack analysis, the pixel change percentage (NPCR) and average pixel change intensity (UACI) are usually used to measure the ability to resist differential attacks. The formula is shown in formula (4):

[0143]

[0144] Among them, P E1 (i,j) and P E2 (i,j) represents the image pixel value. If the image pixel changes, otherwise

[0145] Table 5 gives the comparison results of the multi-image encryption algorithm with other algorithms. Among them, the Yin algorithm comes from the literature [Yin Hai, Xu YuLiang, Zhang YongKang. Image compression encryption algorithm combining two-dimensional modular hyperchaotic map and compressed sensing. Physica Scripta, 2024, 99 (10): 105288.], and the Xu algorithm comes from the literature [Xu WeiJie, LiuLingFeng. An image autonomous selection encryption algorithm based on the delay exponential logistic chaotic model. Nonlinear Dynamics, 2024, 112 (13): 11501-11522.]. The results show that the algorithm proposed in the present invention has a strong ability to resist differential attacks, and the NPCR value and UACI value are closer to the ideal value.

[0146] Table 5 Comparison of differential attacks

[0147]

[0148] Key sensitivity means that when the key changes slightly, the encrypted image will show obvious changes. Figure 7 As shown in the figure, when the offset of the key x is set to 10-14, the correct image cannot be obtained during the decryption process. The analysis of key sensitivity is shown in Table 6. Among them, the Fang algorithm comes from the literature [Fang Jie, Zhao KaiHui, Liang WanYong. Anovel color image encryption scheme using elliptic curvecryptography and hyperchaotic system. Physica Scripta, 2023, 98(11): 115257.], and the Zhu algorithm comes from the literature [Zhu ShenLi, Deng XiaoHeng, Zhang WenDong, et al. Secure image encryption scheme based on a new robust chaotic map and strong S-box.

[0149] Mathematics and Computers in Simulation, 2023, 207: 322-346.]. The results show that the algorithm proposed in this invention has strong key sensitivity.

[0150] Table 6 Key sensitivity analysis

[0151]

[0152] Usually, there is a high correlation between adjacent pixels in the original image, and an effective encryption algorithm makes the adjacent pixels in the encrypted image in the horizontal, vertical and diagonal directions independent and random. The correlation between adjacent pixels is shown in formula (5):

[0153]

[0154] Among them, E(x), D(x), cov(x, y) represent the mean, variance and covariance respectively, x i ,y i Represent the image pixel values ​​respectively.

[0155] The present invention randomly selects 10,000 pairs of image pixels from the image and calculates the correlation between adjacent pixels of the original image and the encrypted image. Table 7 gives the specific numerical comparison of the correlation before and after encryption. The correlation of adjacent pixels is as follows: Figure 8 As shown, it can be seen that the correlation between the three directions of the image before encryption is very strong, while the correlation between the encrypted images is greatly reduced.

[0156] Table 7 Correlation between adjacent pixels of original image and encrypted image

[0157]

[0158] The two-dimensional correlation coefficient (CC) between the original image and the encrypted image and decrypted image is also an important metric for evaluating encryption algorithms. The calculation formula of CC is shown in formula (6):

[0159]

[0160] Among them, A and B represent two images, Represents the image pixel average of two images.

[0161] The correlation between the original image and the encrypted image and the decrypted image is shown in Table 8. From Table 8, it can be seen that the correlation between the encrypted image and the original image is low, while the decrypted image is consistent with the original image.

[0162] Table 8 Correlation coefficient analysis

[0163]

[0164] The mean square error (MSE) is used to measure the difference between the original image and the encrypted image. The larger the MSE value, the better the encryption effect. The calculation formula of MSE is shown in formula (7):

[0165]

[0166] Among them, f(i,j) and f0(i,j) represent the image pixel intensity functions at the corresponding positions of the image.

[0167] The mean square error of the multi-image encryption algorithm is shown in Table 9. As can be seen from Table 9, the difference between the encrypted image and the original image is large, while the difference between the decrypted image and the original image is zero.

[0168] Table 9 MSE, PSNR and SSIM between original and decrypted images

[0169]

[0170] Peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) are used to evaluate the quality and similarity of the encrypted image relative to the original image. The calculation formula of PSNR is shown in formula (8). The PSNR and SSIM values ​​of the multi-image encryption algorithm are shown in Table 9.

[0171]

[0172] Shannon entropy reflects the randomness of the pixel value distribution of the encrypted image. The calculation formula of Shannon entropy is shown in formula (9):

[0173]

[0174] Where H(s) represents the Shannon entropy of the encrypted image, s i ,P(s i ) represent the pixel intensity and occurrence frequency of the image pixels respectively.

[0175] The Shannon entropy values ​​of the encrypted images are shown in Table 10. Among them, the Laiphrakpam algorithm comes from the literature [Laiphrakpam Dolendro Singh, Akash Lahoty, Chanubala Devi, et al. Image encryption using dynamic S-boxes generated using elliptic curve points and chaotic system. Journal of Information Security and Applications, 2024, 83: 103793.], the Demirtas algorithm comes from the literature [Demirtas Mehmet. Multiple-image encryption using sine quadratic polynomial mapping and u-shaped scanning techniques. Traitement Du Signal, 2024, 41 (1): 99-113.], and the Li algorithm comes from the literature [Li Li Zong. A novel chaotic map application in image encryption algorithm. Expert Systems with Applications, 2024, 252 (Part B): 124316.], compared with other algorithms, the image encrypted by the algorithm designed by the present invention has strong randomness and unpredictability.

[0176] Table 10 Shannon entropy

[0177]

[0178]

[0179] During data transmission, due to signal instability and other reasons, image data may be partially lost or cropped, resulting in leakage. Therefore, the encryption algorithm needs to ensure that the image can still be decrypted to a certain extent after some parts of the image are lost or cropped due to transmission, reflecting the robustness of the encryption algorithm.

[0180] Cropping at 4 different locations of the encrypted image, using the correct key to decrypt the cropped encrypted image, the test results are as follows Fig. 9 As shown. Fig. 9 As shown in the figure, the original image can still be seen after decryption, which shows that the multi-image encryption algorithm has good anti-cropping attack capability.

[0181] Similarly, noise attack is also a common threat. During the image transmission or storage process, random noise is introduced to disrupt the data structure of the encrypted image, thereby destroying the quality of the decrypted image. Therefore, the multi-image encryption algorithm must have sufficient noise resistance.

[0182] In the noise attack, a noise with a strength of 0.05 is applied to the encrypted image, and then the noisy image is decrypted with the correct key. The decrypted image is as follows: Fig.10 The PSNR values ​​of the decrypted images are shown in Table 11. Fig.10 As shown, the plaintext information can still be observed after decryption, indicating that the multi-image encryption algorithm has good noise resistance.

[0183] Table 11 PSNR values ​​of salt and pepper noise attack tests

[0184]

[0185] Although specific embodiments of the present invention are described above, those skilled in the art should understand that these are merely examples and that various changes or modifications may be made to these embodiments without departing from the principles and essence of the present invention. Therefore, the scope of protection of the present invention is limited by the appended claims.

Claims

1. A multi-image encryption method based on improved z-curve and chaotic signal, characterized in that The following steps are involved: Step 1: By randomly selecting the R, G, and B color channels of the input images, four input images of different sizes are fused into a fused image O; Step 2: Use the SHA256 algorithm to process the fused image O to obtain the key, and obtain the initial values ​​X0, Y0, and Z0 of the grid multi-scroll chaotic system through group calculation. At the same time, the fused image O is sequentially filled with zeros and divided into blocks. Then, the initial values ​​X0, Y0, and Z0 are substituted into the grid multi-scroll chaotic system to obtain three chaotic sequences of X, Y, and Z, and the chaotic sequences are divided into parts. Step 3: Combine the divided chaotic sequence, and then use the improved z-curve and Knuth-DurstenfeldShuffle algorithm to scramble each sub-block, and store the scrambled sub-blocks into the cell array; Step 4: Through the combined chaotic sequence after division, the elements in the cell array are dynamically encoded, calculated and decoded to obtain the sequence DNAjiema; Step 5: Diffusion of the sequence DNAjiema is performed in groups through the improved center diffusion algorithm, and finally the encrypted image is obtained.

2. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 1, characterized in that: In the step 1, a channel is randomly selected from the three channels R, G, and B of each input image, and the image pixels of the selected channel are filled into a matrix of M*M size one by one to form the R channel of the fused image O. Then, a channel is randomly selected from the remaining two channels of each input image, and the image pixels of the selected channel are filled into a matrix of M*M size one by one to form the G channel of the fused image O. Finally, the image pixels in the remaining channel of each input image are filled into a matrix of M*M size one by one to form the B channel of the fused image O, thereby forming a fused image O of M*M size.

3. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 2, characterized in that: In the step 2, a channel is randomly selected from the fused image O, the image pixel average value of the channel is calculated, and it is used as the input of the SHA256 algorithm to obtain a 256-bit hash value K, i.e., the key K. The key K is divided into 32 groups and the initial values ​​X0, Y0, and Z0 of the grid multi-vortex chaotic system are calculated.

4. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 3 is characterized in that: Using the following equation, the initial values ​​X0, Y0, and Z0 of the grid multi-scroll chaotic system are calculated. X0=(x0+y0) / 2 Y0=(z0+w0) / 2 Z0=(x0+y0+z0+w0) / 2 。 5. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 1, characterized in that: First, the fused image O is padded with zeros to obtain a matrix of size M2*M2*3, and then a block operation is performed. The size of the matrix corresponding to each sub-block is t*t. Then, the initial values ​​X0, Y0, and Z0 are brought into the grid multi-scroll chaotic system to calculate the chaotic sequences X, Y, and Z. Then the 1st to 3rd*(M2) of the chaotic sequence X 2 / t 2 The chaotic sequence X1 is recorded as the chaotic sequence X1, and the 1+3*(M2) 2 / t 2 To 1+3*(M2) 2 / t 2 +M2*M2*24 is recorded as chaotic sequence X2, and the 1st + 3*(M2) of chaotic sequence X is recorded as 2 / t 2 +M2*M2*24 to 1st+3*(M2) 2 / t 2 +M2*M2*24+M2*M2*12 bits are recorded as chaotic sequence X3, the 1st to 24*M2*M2 bits of chaotic sequence Y are recorded as chaotic sequence Y1, the 1st+24*M2*M2 to 1+24*M2*M2+12*M2*M2 bits of chaotic sequence Y are recorded as chaotic sequence Y2, and the chaotic sequence Z remains unchanged.

6. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 5, characterized in that: In the step 2, the fused image O is divided into three two-dimensional matrices, and zero padding is performed on each of the two-dimensional matrices one by one. The size of each two-dimensional matrix after zero padding is M2*M2, and then each two-dimensional matrix after zero padding is divided into M2*M2 / t 2 Sub-blocks, For each sub-block, the improved z-curve is first used in combination with the chaotic sequence X1 to scramble the sub-block, and then the Knuth-Durstenfeld Shuffle algorithm is used to further scramble the sub-block. The scrambled sub-blocks are then saved in the cell array in row order.

7. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 6, characterized in that: The improved z-curve is set as a closed-loop curve, which is obtained by rotating the z-shaped curves 90 degrees in sequence, four times in total, and then connecting them end to end, and includes the first z-shaped curve to the fourth z-shaped curve in sequence in a clockwise direction. Four traversal modes are designed according to the starting position and the moving direction. Traversal mode 1 is: traversal starts from the lower left corner and follows the first z-shaped curve; traversal mode 2 is: traversal starts from the upper left corner and follows the second z-shaped curve; traversal mode 3 is: traversal starts from the upper right corner and follows the third z-shaped curve; traversal mode 4 is: traversal starts from the lower right corner and follows the fourth z-shaped curve; Use the following equation to convert each element in the chaotic sequence X1 into a number between 1 and 64. X1=mod(ceil(abs(X1)*10 15 ),64)+1 Take t=8, use different values ​​in the converted chaotic sequence X1 as the starting points of different sub-blocks, and scramble the sub-blocks of size 8*8 according to the traversal mode.

8. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 5, characterized in that: The method for obtaining the sequence DNA sequence in step 4 comprises the following steps: Step I: first convert each element in the cell array into an eight-bit binary string to form a sequence hechengtu, then use the following equation to convert each element in the chaotic sequence X2 into a number between 0 and 7, and then use the converted chaotic sequence X2 to perform DNA encoding on the sequence hechengtu according to the DNA encoding rules in Table 1 to obtain the first sequence DNAbianma; X2=mod(ceil(abs(X2)*10 15 ),8) Table 1 DNA coding rules Step II, repeat step I, according to the DNA coding rules, use the chaotic sequence X3 to perform DNA coding on the chaotic sequence Z to obtain the second sequence DNAbianma, and then according to the DNA operation rules in Table 2, use the chaotic sequence Y1 to perform DNA operation on the first sequence DNAbianma and the second sequence DNAbianma to obtain the sequence DNAyunsuan, Here, using the equation X3 = mod(ceil(abs(X3)*10 15 ),8), each element in the chaotic sequence X3 is processed as a number between 0 and 7; Table 2 DNA algorithm Step III: According to the inverse operation of the DNA coding rule, the chaotic sequence Y2 is used to perform DNA decoding on the sequence DNAyunsuan to obtain the sequence DNAjiema.

9. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 8, characterized in that: In step II, each element in the chaotic sequence Y1 is first processed into a number between 0 and 4 using the following equation; Y1=mod(ceil(abs(Y1)*10 15 ),5) Then the bases at the same position of the first sequence DNA code and the second sequence DNA code are traversed, and according to the DNA operation rules in Table 2, when Y1 is 0, the addition operation of the first sequence DNA code and the second sequence DNA code is performed, when Y1 is 1, the subtraction operation of the first sequence DNA code and the second sequence DNA code is performed, when Y1 is 2, the XOR operation of the first sequence DNA code and the second sequence DNA code is performed, when Y1 is 3, the XOR operation of the first sequence DNA code and the second sequence DNA code is performed, and when Y1 is 4, the inversion operation of the first sequence DNA code is performed.

10. The multi-image encryption method based on improved z-curve and chaotic signal according to claim 1, characterized in that: According to the improved central diffusion algorithm, the sequence DNAjiema is divided into a plurality of subsequences with a length of 8 in each group, the fourth and fifth bits of each subsequence are selected as the starting point, the values ​​of the fourth and fifth bits are compared, if the values ​​are different, all bits are inverted, if the values ​​are the same, the values ​​of the third and sixth bits are compared, if the values ​​of the third and sixth bits are different, the first to third bits and the sixth to eighth bits are inverted, if the values ​​are the same, the values ​​of the second and seventh bits are compared, if the values ​​of the second and seventh bits are different, the first, second, seventh and eighth bits are inverted, if the values ​​are the same, the values ​​of the first and eighth bits are compared, if the values ​​of the first and eighth bits are different, the first and eighth bits are inverted, if the values ​​are the same, the subsequence remains unchanged, so as to realize the diffusion of image pixels, and then the diffused binary number is converted into a decimal number, and the matrix is ​​converted into M2*M2*3 to obtain an encrypted image.

Images