Remote sensing image encryption method

Abstract

The invention discloses a remote sensing image encryption method, belongs to the technical field of information security, and particularly relates to a novel image encryption algorithm based on a chaotic system. The objective of the invention is to solve the problems of low security and low anti-attack ability of an existing image encryption method based on a chaotic system. The remote sensing image encryption method specifically comprises the following steps: step 1, constructing a six-dimensional chaotic system; step 2, obtaining the size of a to-be-encrypted image, m being the length of the to-be-encrypted image, and n being the width of the to-be-encrypted image; 3, setting a secret key, taking the secret key as a six-dimensional chaotic system variable initial value and a six-dimensional chaotic system parameter, and generating a sequence of six-dimensional chaotic system variables x, y, z, w, u and v based on the six-dimensional chaotic system variable initial value and the six-dimensional chaotic system parameter; and step 4, performing image encryption on the to-be-encrypted image by using the sequence of the variables x, y, z, w, u and v of the six-dimensional chaotic system obtained in the step 3.

Description

Technical Field

[0001] The present invention belongs to the technical field of information security, and particularly relates to a new image encryption algorithm based on a chaotic system. Background Art

[0002] With the rapid development of information technology, digital images have become an important medium for information exchange. However, digital images are vulnerable to tampering, theft, and attacks during storage and transmission. Therefore, designing efficient and secure image encryption algorithms has become a research hotspot in the field of information security.

[0003] Currently, although traditional encryption algorithms such as AES and DES perform excellently in text encryption, they have problems such as high computational complexity and low efficiency when directly applied to image encryption. To overcome these deficiencies, in recent years, encryption methods based on chaotic systems have become the focus of research in the field of image encryption due to their initial value sensitivity, randomness, and complex dynamic characteristics. However, the existing chaotic systems have a low dimension and relatively simple chaotic behavior, resulting in limited security and anti-attack capabilities. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems of low security and low anti-attack capabilities existing in the existing image encryption methods based on chaotic systems, and to propose a remote sensing image encryption method.

[0005] The specific process of a remote sensing image encryption method is as follows:

[0006] Step 1: Construct a six-dimensional chaotic system;

[0007] Step 2: Obtain the size of the image to be encrypted, where m is the length of the image to be encrypted and n is the width of the image to be encrypted;

[0008] Step 3: Set the key, use the key as the initial value of the six-dimensional chaotic system variables and the parameters of the six-dimensional chaotic system, and generate sequences of six-dimensional chaotic system variables x, y, z, w, u, and v based on the initial value of the six-dimensional chaotic system variables and the parameters of the six-dimensional chaotic system;

[0009] Step 4: Use the sequences of the six-dimensional chaotic system variables x, y, z, w, u, and v obtained in Step 3 to encrypt the image to be encrypted.

[0010] The beneficial effects of the present invention are as follows:

[0011] The present invention realizes the efficient encryption and security protection of image data by constructing a six-dimensional chaotic system and combining technical means such as DNA coding and Fisher-Yates scrambling algorithm, and has important application value.

[0012] In view of the above problems, the present invention designs a novel image encryption algorithm based on a six-dimensional chaotic system, which utilizes the complex dynamic behavior of a high-dimensional chaotic system to improve the security and anti-attack ability of the encryption algorithm. The algorithm also introduces various technical means such as DNA sequence encoding, circular shifting, and block scrambling, further enhancing the reliability and confidentiality of image encryption while ensuring high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is the flow chart of the present invention;

[0014] Figure 2 is the schematic diagram of matrix block division and recombination restoration. a) is the schematic diagram of matrix block division when F = 2, b) is the schematic diagram of matrix block division when F = 4, and c) is the schematic diagram of matrix recombination restoration when F = 2;

[0015] Figure 3 is the encryption flow chart;

[0016] Figure 4 is the comparison diagram of encryption and decryption effect pictures; a1) Picture 1, a2) Encrypted picture of Picture 1, a3) Decrypted picture of Picture 1;

[0017] b1) Picture 2, b2) Encrypted picture of Picture 2, b3) Decrypted picture of Picture 2; c1) Picture 3, c2) Encrypted picture of Picture 3, c3)

[0018] Decrypted picture of Picture 3; d1) Picture 4, d2) Encrypted picture of Picture 4, d3) Decrypted picture of Picture 4; e1) Picture 5, e2) Encrypted picture of Picture 5, e3) Decrypted picture of Picture 5;

[0019] Figure 5 is the scatter plot of the correlation before and after encryption of different images. a1) Correlation of the R channel before encryption of Picture 1, b1) Correlation of the G channel before encryption of Picture 1, c1) Correlation of the B channel before encryption of Picture 1, d1) Correlation of the R channel after encryption of Picture 1, e1) Correlation of the G channel after encryption of Picture 1, f1) Correlation of the B channel after encryption of Picture 1;

[0020] a2) Correlation of the R channel before encryption of Picture 2, b2) Correlation of the G channel before encryption of Picture 2, c2) Correlation of the B channel before encryption of Picture 2, d2) Correlation of the R channel after encryption of Picture 2, e2) Correlation of the G channel after encryption of Picture 2, f2) Correlation of the B channel after encryption of Picture 2;

[0021] a3) Correlation of the R channel before encryption of Picture 3, b3) Correlation of the G channel before encryption of Picture 3, c3) Correlation of the B channel before encryption of Picture 3, d3) Correlation of the R channel after encryption of Picture 3, e3) Correlation of the G channel after encryption of Picture 3, f3) Correlation of the B channel after encryption of Picture 3;

[0022] a4) Correlation of the R channel of Picture 4 before encryption, b4) Correlation of the G channel of Picture 4 before encryption, c4) Correlation of the B channel of Picture 4 before encryption, d4) Correlation of the R channel of Picture 4 after encryption, e4) Correlation of the G channel of Picture 4 after encryption, f4) Correlation of the B channel of Picture 4 after encryption;

[0023] a5) Correlation of the R channel of Picture 5 before encryption, b5) Correlation of the G channel of Picture 5 before encryption, c5) Correlation of the B channel of Picture 5 before encryption, d5) Correlation of the R channel of Picture 5 after encryption, e5) Correlation of the G channel of Picture 5 after encryption, f5) Correlation of the B channel of Picture 5 after encryption;

[0024] Figure 6 For the comparison chart of histograms of different images before and after encryption, a1) Histogram of the R channel of Picture 1 before encryption, b1) Histogram of the G channel of Picture 1 before encryption, c1) Histogram of the B channel of Picture 1 before encryption, d1) Histogram of the R channel of Picture 1 after encryption, e1) Histogram of the G channel of Picture 1 after encryption, f1) Histogram of the B channel of Picture 1 after encryption;

[0025] a2) Histogram of the R channel of Picture 2 before encryption, b2) Histogram of the G channel of Picture 2 before encryption, c2) Histogram of the B channel of Picture 2 before encryption, d2) Histogram of the R channel of Picture 2 after encryption, e2) Histogram of the G channel of Picture 2 after encryption, f2) Histogram of the B channel of Picture 2 after encryption;

[0026] a3) Histogram of the R channel of Picture 3 before encryption, b3) Histogram of the G channel of Picture 3 before encryption, c3) Histogram of the B channel of Picture 3 before encryption, d3) Histogram of the R channel of Picture 3 after encryption, e3) Histogram of the G channel of Picture 3 after encryption, f3) Histogram of the B channel of Picture 3 after encryption;

[0027] a4) Histogram of the R channel of Picture 4 before encryption, b4) Histogram of the G channel of Picture 4 before encryption, c4) Histogram of the B channel of Picture 4 before encryption, d4) Histogram of the R channel of Picture 4 after encryption, e4) Histogram of the G channel of Picture 4 after encryption, f4) Histogram of the B channel of Picture 4 after encryption;

[0028] a5) Histogram of the R channel of Picture 5 before encryption, b5) Histogram of the G channel of Picture 5 before encryption, c5) Histogram of the B channel of Picture 5 before encryption, d5) Histogram of the R channel of Picture 5 after encryption, e5) Histogram of the G channel of Picture 5 after encryption, f5) Histogram of the B channel of Picture 5 after encryption;

[0029] Figure 7Test images for noise attacks under different degrees of shearing. a1) Encrypted image at 1 / 32, a2) Result after decrypting the 1 / 32 encrypted image, b1) Encrypted image at 1 / 16, b2) Result after decrypting the 1 / 16 encrypted image, c1) Encrypted image at 1 / 8, c2) Result after decrypting the 1 / 8 encrypted image, d1) Encrypted image at 1 / 4, d2) Result after decrypting the 1 / 4 encrypted image;

[0030] Figure 8 Test images for noise attacks under different noise intensities. a) Decrypted images after adding salt-and-pepper noise with an intensity of 0.01 to the ciphertext images respectively, b) Decrypted images after adding salt-and-pepper noise with an intensity of 0.02 to the ciphertext images respectively, c) Decrypted images after adding salt-and-pepper noise with an intensity of 0.03 to the ciphertext images respectively, d) Decrypted images after adding salt-and-pepper noise with an intensity of 0.04 to the ciphertext images respectively. Detailed implementation

[0031] Detailed implementation one: The specific process of a remote sensing image encryption method in this implementation is as follows:

[0032] Step 1: Construct a six-dimensional chaotic system;

[0033] Step 2: Obtain the size of the image to be encrypted. m is the length of the image to be encrypted, and n is the width of the image to be encrypted;

[0034] Step 3: Set the secret key (the secret key includes the initial values of the system variables (x, y, z, w, u, v) of the six-dimensional chaotic system and the system parameters (a, b, c, d, e, f, g, h, k, l)). Use the secret key as the initial values of the six-dimensional chaotic system variables (x, y, z, w, u, v) and the six-dimensional chaotic system parameters (a, b, c, d, e, f, g, h, k, l). Generate sequences of the six-dimensional chaotic system variables x, y, z, w, u, v based on the initial values of the six-dimensional chaotic system variables (x, y, z, w, u, v) and the six-dimensional chaotic system parameters (a, b, c, d, e, f, g, h, k, l);

[0035] Step 4: Use the sequences of the six-dimensional chaotic system variables x, y, z, w, u, v obtained in Step 3 to encrypt the image to be encrypted.

[0036] Detailed implementation two: The difference between this implementation and detailed implementation one is that in Step 1, the six-dimensional chaotic system is constructed; the specific process is as follows:

[0037] The six-dimensional chaotic system is shown in formula (1):

[0038]

[0039] Among them, x, y, z, w, u, v respectively represent the six-dimensional chaotic system variables;

[0040] respectively represent the derivatives of x, y, z, w, u, v with respect to time;

[0041] a, b, c, d, e, f, g, h, k, l represent the parameters of the six-dimensional chaotic system;

[0042] Other steps and parameters are the same as those in the first specific implementation manner.

[0043] Specific implementation manner three: The difference between this implementation manner and the first or second specific implementation manner is that in step 3, a secret key is set (the secret key includes the initial values of the system variables (x, y, z, w, u, v) of the six-dimensional chaotic system and the system parameters (a, b, c, d, e, f, g, h, k, l)), and the secret key is used as the initial values of the six-dimensional chaotic system variables (x, y, z, w, u, v) and the six-dimensional chaotic system parameters (a, b, c, d, e, f, g, h, k, l). Based on the initial values of the six-dimensional chaotic system variables (x, y, z, w, u, v) and the six-dimensional chaotic system parameters (a, b, c, d, e, f, g, h, k, l), a sequence of the six-dimensional chaotic system variables x, y, z, w, u, v is generated; the specific process is as follows:

[0044] Step 31: Based on the initial values of the six-dimensional chaotic system variables x, y, z, w, u, v, obtain formula (2), which is expressed as:

[0045]

[0046] where, H 01 represents the first-dimensional parameter corresponding to the first recursion, H 02 represents the second-dimensional parameter corresponding to the first recursion, H 03 represents the third-dimensional parameter corresponding to the first recursion, H 04 represents the fourth-dimensional parameter corresponding to the first recursion, H 05 represents the fifth-dimensional parameter corresponding to the first recursion, H 06 represents the sixth-dimensional parameter corresponding to the first recursion, all of which are intermediate variables; t represents the number of recursions;

[0047] Step 32: Based on formula (2) and the six-dimensional chaotic system parameters (a, b, c, d, e, f, g, h, k, l), obtain formula (3), which is expressed as:

[0048]

[0049] where, H 11 represents the first-dimensional parameter corresponding to the second recursion, H 12 represents the second-dimensional parameter corresponding to the second recursion, H 13Represents the third - dimensional parameter corresponding to the second recursion, H 14 Represents the fourth - dimensional parameter corresponding to the second recursion, H 15 Represents the fifth - dimensional parameter corresponding to the second recursion, H 16 Represents the sixth - dimensional parameter corresponding to the second recursion, all of which are intermediate variables;

[0050] Step 33: Based on Formula (2) and Formula (3), obtain Formula (4), which is expressed as:

[0051]

[0052] where, H 21 Represents the first - dimensional parameter corresponding to the third recursion, H 22 Represents the second - dimensional parameter corresponding to the third recursion, H 23 Represents the third - dimensional parameter corresponding to the third recursion, H 24 Represents the fourth - dimensional parameter corresponding to the third recursion, H 25 Represents the fifth - dimensional parameter corresponding to the third recursion, H 26 Represents the sixth - dimensional parameter corresponding to the third recursion, all of which are intermediate variables; h represents the discrete step size;

[0053] Step 34: Substitute H 21 、H 22 、H 23 、H 24 、H 25 、H 26 into Formula (1), and respectively replace H 01 、H 02 、H 03 、H 04 、H 05 、H 06 , and repeat the execution of Formula (2) - Formula (4) N times, where N > m×n;

[0054] Take all the H obtained after N times 21 、H 22 、H 23 、H 24 、H 25 、H 26 respectively as the sequences of the six - dimensional chaotic system variables x, y, z, w, u, v (Take all the H obtained after N times 21 as the sequence of the six - dimensional chaotic system variable x, take all the H obtained after N times 22 as the sequence of the six - dimensional chaotic system variable y, take all the H obtained after N times 23 as the sequence of the six - dimensional chaotic system variable z, take all the H obtained after N times 24As the sequence of the variable w of the six-dimensional chaotic system, all the H obtained N times 25 As the sequence of the variable u of the six-dimensional chaotic system, all the H obtained N times 26 As the sequence of the variable v of the six-dimensional chaotic system).

[0055] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0056] Specific implementation manner four: The difference between this implementation manner and one of the first to third specific implementation manners is that in step 4, the sequences of the six-dimensional chaotic system variables x, y, z, w, u, and v obtained in step 3 are used to perform image encryption on the image to be encrypted; the specific process is as follows:

[0057] Step 41: Read the RGB three channels of the original image P.

[0058] Step 42: Perform block processing on the original image P of the R channel to obtain L blocks of the image P of the R channel.

[0059] Step 43: Use a scrambling algorithm to scramble the image in each block area.

[0060] Step 44: Recombine and restore the scrambled block areas according to the block process to obtain the scrambled image P1; as Figure 2 in 3);

[0061] Step 45: Calculate the sum of all pixel values in the image P1 to obtain the variable Pr E ;

[0062] Step 46: Further process the variable Pr E to obtain the variable rx.

[0063] Step 47: Further process the variable rx and P1 to obtain the variable Pr.

[0064] Step 48: Convert the variable Pr into a binary variable matrix Pr_Bit.

[0065] Step 49: Perform DNA coding operation on the binary variable matrix Pr_Bit to obtain the DNA sequence Pr_DNA; for example, the binary variable matrix Pr_Bit is:

[0066]

[0067] Perform DNA coding operation on the binary variable matrix Pr_Bit according to the first coding rule to obtain the DNA sequence Pr_DNA as:

[0068]

[0069] The specific encoding process is as shown in 1:

[0070] Table 1 DNA encoding and decoding rules

[0071]

[0072] The table shows 8 encoding rules. The selection of the specific rules is determined by the variable rx. Through the encoding rules shown in Table 1, binary data can be processed into a DNA sequence Pr_DNA arranged, for example, as CGTA;

[0073] Step 410: Perform a row and column cyclic shift operation on the DNA sequence Pr_DNA to obtain a new sequence Cr_DNA;

[0074] Step 411: After performing DNA decoding on the new sequence Cr_DNA, obtain a binary sequence Cr_bit (by reverse deduction according to Step 49);

[0075] Step 412: Convert the binary sequence Cr_bit to a decimal sequence Cr_bit. The decimal sequence Cr_bit is the encrypted R-component image;

[0076] Step 413: Repeat Step 42 - Step 412 to obtain the encrypted G-component image and the encrypted B-component image;

[0077] Step 414: Superimpose the encrypted R-component image, the encrypted G-component image, and the encrypted B-component image to obtain the encrypted image.

[0078] Figure 3 Shows the overall schematic diagram of the encryption algorithm of this patent; decrypt the encrypted image to obtain the decrypted image; this encryption algorithm is a symmetric encryption algorithm, and decryption is the reverse process of encryption.

[0079] Other steps and parameters are the same as those in any one of the specific embodiments 1 to 3.

[0080] Specific embodiment 5: The difference between this embodiment and any one of the specific embodiments 1 to 4 is that in Step 42, the original image P of the R channel is block-processed to obtain L blocks of the image P of the R channel; the specific process is as follows:

[0081] The block process is as Figure 2 shown, where a parameter F is introduced to control the block size; the parameter F will be transmitted as a key for the decryption operation of the image;

[0082] Introduce the parameter F, and the parameter F performs block processing on the R-channel image P matrix m×n to obtain L blocks;

[0083] The image matrix size of each block area is F×n.

[0084] The other steps and parameters are the same as those in any one of the first to fourth specific embodiments.

[0085] Specific Embodiment Six: The difference between this embodiment and any one of the first to fifth specific embodiments is that in step 43, a scrambling algorithm is used to scramble the images of each sub-block area; the specific scrambling process is as follows:

[0086] Step 431: Expand the image of each sub-block area into a one-dimensional vector by rows or columns, denoted as A;

[0087] Step 432: Use formula (5) to generate a pseudo-random sequence B with a sequence length of m×n, B = B(1), B(2), …, B(m×n); the expression is:

[0088]

[0089] In the formula, SUM is the number of elements in A;

[0090] x(i) represents the i-th value in the six-dimensional chaotic system variable x (sequence) obtained in step 3;

[0091] y(i) represents the i-th value in the six-dimensional chaotic system variable y (sequence) obtained in step 3;

[0092] mod represents the modulo function, represents rounding down;

[0093] Step 433: Only keep the first occurrence of B(i) for the repeatedly occurring B(i) in the pseudo-random sequence B;

[0094] Add the numerical values in the set {1, 2, …, m×n} that do not appear in the pseudo-random sequence B to the end of the pseudo-random sequence B in ascending order;

[0095] Step 434: Exchange the image numerical values at positions B(i) and B(m×n - i + 1) in the chaotic sequences A(B(i)) and A(B(m×n - i + 1));

[0096] A(B(i)) represents the image numerical value at position B(i) in A;

[0097] A(B(m×n - i + 1)) represents the image numerical value at position B(m×n - i + 1) in A;

[0098] For example: B(1) = 3, B(2) = 2, B(3) = 1, B(4) = 4;

[0099] B = (B(1), B(2), B(3), B(4)) = (3, 2, 1, 4)

[0100]

[0101] It represents the exchange of the image values at positions 3 and 4 in the chaotic sequence A;

[0102]

[0103] It represents the exchange of the image values at positions 2 and 1 in the chaotic sequence A.

[0104] Other steps and parameters are the same as those in any one of the first to fifth specific embodiments.

[0105] Specific embodiment seven: The difference between this embodiment and any one of the first to sixth specific embodiments is that in step 46, the variable Pr E is further processed to obtain the variable rx; the expression is:

[0106]

[0107] In the formula,

[0108] z(N) represents the Nth value in the six-dimensional chaotic system variable z (sequence) obtained in step 3.

[0109] Other steps and parameters are the same as those in any one of the first to sixth specific embodiments.

[0110] Specific embodiment eight: The difference between this embodiment and any one of the first to seventh specific embodiments is that in step 47, the variables rx and P1 are further processed to obtain the variable Pr; the expression is:

[0111]

[0112] In the formula,

[0113] w(i) represents the ith value in the six-dimensional chaotic system variable w (sequence) obtained in step 3;

[0114] S′(rx) represents the summation operation on the variable rx.

[0115] represents rounding up.

[0116] Other steps and parameters are the same as those in any one of the first to seventh specific embodiments.

[0117] Specific embodiment nine: The difference between this embodiment and any one of the first to eighth specific embodiments is that in step 410, the DNA sequence Pr_DNA is subjected to row and column cyclic shift operations to obtain a new sequence Cr_DNA; the specific process is:

[0118] 1), Determine the cyclic shift step size of each row in the DNA sequence Pr_DNA based on formula (8);

[0119]

[0120] Shift the β-th row of the DNA sequence Pr_DNA to the right according to the shift step size of the β-th row, and supplement the shifted-out elements to the positions of the missing elements on the left side of the β-th row; Repeat the execution of 1) until all rows of the DNA sequence Pr_DNA are shifted and supplemented to obtain a new DNA sequence Pr_DNA;

[0121] Among them,

[0122] u(β) represents the β-th value in the six-dimensional chaotic system variable u (sequence) obtained in step 3, β < N;

[0123] Key left (β) represents the left shift step size of the β-th row;

[0124] Pg represents the variable obtained by performing steps 42 to 47 on the original image P of the G channel;

[0125] Pb represents the variable obtained by performing steps 42 to 47 on the original image P of the B channel;

[0126] 2), Determine the cyclic shift step size of each column in the DNA sequence Pr_DNA based on formula (9);

[0127]

[0128] Shift the γ-th column of the new DNA sequence Pr_DNA obtained in 1) downward according to the shift step size of the γ-th column, and supplement the shifted-out elements to the positions of the missing elements above the γ-th column; Repeat the execution of 2) until all columns of the new DNA sequence Pr_DNA are shifted and supplemented to obtain a new sequence Cr_DNA;

[0129] Among them,

[0130] v(γ) represents the γ-th value in the six-dimensional chaotic system variable v (sequence) obtained in step 3, γ < N;

[0131] Key right (γ) represents the right shift step size of the γ-th column.

[0132] Other steps and parameters are the same as one of the specific embodiments one to eight.

[0133] Example:

[0134] 3. Security analysis

[0135] 3.1 Encryption and decryption effects

[0136] Figure 4 The rendered results of encrypting and decrypting various types of images are shown. It can be seen that the encryption algorithm proposed in this chapter can effectively protect the picture information visually and can restore the image, with encryption and decryption functions.

[0137] 3.2 Information Entropy

[0138] The method for calculating the information entropy of the images used in this test is shown in Equation (10):

[0139]

[0140] In the formula, P(S i ) is the probability of the pixel S i appearing; v is the gray level of the pixel;

[0141] The closer the information entropy of the encrypted image is to 8, the higher the security of the encryption algorithm;

[0142] Table 2 gives the information entropy of different test images after encryption;

[0143] Table 2 Information Entropy Test

[0144]

[0145] 3.3 Adjacent Pixel Correlation

[0146] The correlation coefficients between adjacent pixel points are shown in Formulas (11) to (13). The closer the correlation coefficient of the ciphertext is to 0, the higher the security;

[0147]

[0148] In the formula, x and y are the pixel values at the positions of two adjacent pixels; N represents the value of the total number of pixels selected in the image;

[0149] D(x) and D(y) are the variances of x and y respectively;

[0150] In this test, the above formula is used to calculate the correlation coefficients between adjacent pixel points of the encrypted image. By comparing the correlation scatter plots of the Lena image before and after encryption (as Figure 5 shown), it can be more directly observed that the correlation in each direction after encryption is significantly reduced. Table 3 shows the comparison of the correlation coefficients of different encrypted images with other encryption algorithms, indicating the security of the algorithm proposed in the present invention.

[0151] Table 3 Comparison of Correlation Coefficients of Different Encrypted Images with Other Algorithms

[0152]

[0153] 3.4 Histogram and Chi-Square Test

[0154] Since the histogram can reflect the distribution characteristics of pixel values in an image, it is a commonly used tool for analyzing the encryption effect of images in security tests. Figure 6 The histograms before and after encrypting different images are depicted. It can be seen that the histogram before encryption reflects the distribution characteristics of different pixel values in the image. After encryption, the image histogram tends to be evenly distributed, hiding the distribution characteristics of the original image pixel values, indicating that the encryption algorithm designed in this chapter has good security.

[0155] In addition, the chi-square test can also be used to examine the histogram distribution. When the calculation result is less than 293.2483 according to formula (14) for calculating the image, it is considered that the encrypted image is relatively evenly distributed in the histogram.

[0156]

[0157] In the formula, K i is the number of times the i-th pixel appears in the image; S i is the expected frequency value.

[0158] The results of the chi-square test on the encrypted image are shown in Table 4, further indicating that the encryption algorithm hides the distribution characteristics of the original image pixel values.

[0159] Table 4 Chi-square test results

[0160]

[0161] 3. Resistance to shearing attack

[0162] Since the encrypted image may be maliciously sheared during transmission. Therefore, it is necessary to simulate the malicious shearing during transmission by shearing the ciphertext image to different degrees, and decrypt the sheared image to verify the anti-shearing ability of the algorithm. Figure 7 Shows the decryption results of images sheared to different degrees.

[0163] 3. Resistance to noise attack

[0164] To simulate the possible noise influence on the encrypted image during channel transmission, the ciphertext image is respectively added with salt-and-pepper noise with intensities of 0.01, 0.02, 0.03, and 0.04 and then decrypted to verify the anti-noise ability of the encryption algorithm in this chapter. The decrypted image effects are as Figure 8 shown. It can be seen that even if the encrypted image is affected by a certain degree of noise during channel transmission, after being decrypted by the encryption algorithm proposed in this chapter, the decrypted image can still restore the visual information of the original image to a certain extent, proving that the encryption scheme proposed in this chapter has a certain anti-noise ability.

[0165] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention. However, these corresponding changes and modifications should all fall within the protection scope of the appended claims of the present invention.

Claims

1. A remote sensing image encryption method, characterized in that: The specific process of the method is: Step 1: Construct a six-dimensional chaotic system; Step 2: Get the size of the image to be encrypted, where m is the length of the image to be encrypted and n is the width of the image to be encrypted; Step 3, setting a key, using the key as the initial value of the six-dimensional chaotic system variable and the six-dimensional chaotic system parameter, and generating a sequence of six-dimensional chaotic system variables x, y, z, w, u, v based on the initial value of the six-dimensional chaotic system variable and the six-dimensional chaotic system parameter; Step 4: Use the sequence of six-dimensional chaotic system variables x, y, z, w, u, and v obtained in step 3 to encrypt the image to be encrypted.

2. A remote sensing image encryption method according to claim 1, characterized in that: In step 1, a six-dimensional chaotic system is constructed; the specific process is as follows: The six-dimensional chaotic system is shown in formula (1): Among them, x, y, z, w, u, and v represent the variables of the six-dimensional chaotic system respectively; Respectively represent the time derivatives of x, y, z, w, u, and v; a, b, c, d, e, f, g, h, k, and l represent the parameters of the six-dimensional chaotic system.

3. A remote sensing image encryption method according to claim 2, characterized in that: In the step 3, a key is set, and the key is used as an initial value of a six-dimensional chaotic system variable and a six-dimensional chaotic system parameter, and a sequence of six-dimensional chaotic system variables x, y, z, w, u, and v is generated based on the initial value of the six-dimensional chaotic system variable and the six-dimensional chaotic system parameter; The specific process is: Step 31, based on the initial values ​​of the six-dimensional chaotic system variables x, y, z, w, u, v, obtain formula (2), expressed as: Among them, H 01 Indicates the first dimension parameter corresponding to the first recursion, H 02 Indicates the second dimension parameter corresponding to the first recursion, H 03 Indicates the third dimension parameter corresponding to the first recursion, H 04 Indicates the fourth dimension parameter corresponding to the first recursion, H 05 Indicates the fifth dimension parameter corresponding to the first recursion, H 06 Indicates the sixth dimension parameter corresponding to the first recursion, all of which are intermediate variables; t indicates the number of recursions; Step 32: Based on formula (2) and the six-dimensional chaotic system parameters, formula (3) is obtained, which is expressed as: Among them, H 11 Indicates the first dimension parameter corresponding to the second recursion, H 12 Indicates the second dimension parameter corresponding to the second recursion, H 13 Indicates the third dimension parameter corresponding to the second recursion, H 14 Indicates the fourth dimension parameter corresponding to the second recursion, H 15 Indicates the fifth dimension parameter corresponding to the second recursion, H 16 Indicates the sixth dimension parameters corresponding to the second recursion, all of which are intermediate variables; Step 33: Based on formula (2) and formula (3), obtain formula (4), which is expressed as: Among them, H 21 Indicates the first dimension parameter corresponding to the third recursion, H 22 Indicates the second dimension parameter corresponding to the third recursion, H 23 Indicates the third dimension parameter corresponding to the third recursion, H 24 Indicates the fourth dimension parameter corresponding to the third recursion, H 25 Indicates the fifth dimension parameter corresponding to the third recursion, H 26 represents the sixth dimension parameter corresponding to the third recursion, which are all intermediate variables; h represents the discrete step length; Step 34: Replace H in formula (4) 21 , H 22 , H 23 , H 24 , H 25 , H 26 Substitute into formula (1) and replace H 01 , H 02 , H 03 , H 04 , H 05 , H 06 , repeat formula (2)-formula (4) N times, N>m×n; All H obtained N times 21 , H 22 , H 23 , H 24 , H 25 , H 26 They are respectively regarded as sequences of six-dimensional chaotic system variables x, y, z, w, u, and v.

4. A remote sensing image encryption method according to claim 3, characterized in that: In the step 4, the sequence of six-dimensional chaotic system variables x, y, z, w, u, and v obtained in step 3 is used to encrypt the image to be encrypted; The specific process is: Step 41: Read the three RGB channels of the original image P; Step 42: performing block processing on the original image P of the R channel to obtain L blocks of the image P of the R channel; Step 43: Use a scrambling algorithm to scramble the image of each block area; Step 44: Reassemble and restore the scrambled block regions according to the block process to obtain the scrambled image P1; Step 45: Calculate the sum of all pixel values ​​in image P1 to obtain variable Pr E ; Step 46: Set the variable Pr E Further processing is performed to obtain the variable rx; Step 47: further process the variables rx and P1 to obtain the variable Pr; Step 48: Perform binary conversion on the variable Pr to obtain a binary variable matrix Pr_Bit; Step 49: Perform DNA encoding operation on the binary variable matrix Pr_Bit to obtain a DNA sequence Pr_DNA; Step 410: Perform row-column cyclic shift operation on the DNA sequence Pr_DNA to obtain a new sequence Cr_DNA; Step 411: Perform DNA decoding on the new sequence Cr_DNA to obtain a binary sequence Cr_bit; Step 412: convert the binary sequence Cr_bit into a decimal sequence Cr_bit, where the decimal sequence Cr_bit is the encrypted R component image; Step 413: repeating steps 42 to 412 to obtain an encrypted G component image and an encrypted B component image; Step 414: superimpose the encrypted R component image, the encrypted G component image, and the encrypted B component image to obtain an encrypted image.

5. A remote sensing image encryption method according to claim 4, characterized in that: In step 42, the original image P of the R channel is processed into blocks to obtain L blocks of the image P of the R channel; The specific process is: Introduce parameter F, which divides the R channel image P matrix m×n into blocks to obtain L blocks; The image matrix size of each block area is F×n.

6. A remote sensing image encryption method according to claim 5, characterized in that: In step 43, a scrambling algorithm is used to scramble the image of each block area; the specific scrambling process is as follows: Step 431: Expand the image of each block area into a one-dimensional vector by row or column, denoted as A; Step 432: Generate a pseudo-random sequence B with a sequence length of m×n using formula (5), where B=B(1), B(2), …, B(m×n); the expression is: In the formula, SUM is the number of elements in A; x(i) represents the i-th value of the six-dimensional chaotic system variable x (sequence) obtained in step 3; y(i) represents the i-th value of the six-dimensional chaotic system variable y (sequence) obtained in step 3; mod represents the modulo function, Indicates rounding down; Step 433: For B(i) that appears repeatedly in the pseudo-random sequence B, only the first occurrence of B(i) is retained; Add the values ​​in the set {1,2,…,m×n} that do not appear in the pseudo-random sequence B to the end of the pseudo-random sequence B in ascending order; Step 434: exchange the image values ​​at positions B(i) and B(m×n-i+1) in the chaotic sequence A(B(i)) and A(B(m×n-i+1)); A(B(i)) represents the image value at position B(i) in A; A(B(m×n-i+1)) represents the image value at position B(m×n-i+1) in A.

7. A remote sensing image encryption method according to claim 6, characterized in that: In step 46, the variable Pr E Further processing is performed to obtain the variable rx; the expression is: In the formula, z(N) represents the Nth value of the six-dimensional chaotic system variable z (sequence) obtained in step 3.

8. A remote sensing image encryption method according to claim 7, characterized in that: In step 47, the variables rx and P1 are further processed to obtain the variable Pr; the expression is: In the formula, w(i) represents the i-th value of the six-dimensional chaotic system variable w (sequence) obtained in step 3; S′(rx) represents a sum operation on the variable rx. Indicates rounding up.

9. A remote sensing image encryption method according to claim 8, characterized in that: In step 410, a row-column cyclic shift operation is performed on the DNA sequence Pr_DNA to obtain a new sequence Cr_DNA; The specific process is: 1) Determine the cyclic shift step length of each row in the DNA sequence Pr_DNA based on formula (8); Shift the βth row of the DNA sequence Pr_DNA to the right according to the shift step of the βth row, and fill the shifted elements to the position of the missing elements on the left side of the βth row; repeat 1) until all rows of the DNA sequence Pr_DNA are shifted and filled, and a new DNA sequence Pr_DNA is obtained; in, u(β) represents the βth value of the six-dimensional chaotic system variable u (sequence) obtained in step 3, β<N; Key left (β) represents the left shift step size of the βth row; Pg represents the variable obtained by executing steps 42 to 47 on the original image P of the G channel; Pb represents the variable obtained by executing steps 42 to 47 for the original image P of the B channel; 2) Determine the shift step length of each column cycle in the DNA sequence Pr_DNA based on formula (9); The γth column of the new DNA sequence Pr_DNA obtained in 1) is shifted downward according to the shift step of the γth column, and the shifted elements are added to the position of the missing elements on the γth column; 2) is repeated until all columns of the new DNA sequence Pr_DNA are shifted and added, and a new sequence Cr_DNA is obtained; in, v(γ) represents the γth value of the six-dimensional chaotic system variable v (sequence) obtained in step 3, γ<N; Key right (γ) represents the right shift step size of the γth column.

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