A chaotic image encryption method based on logistic large key space bit scrambling

Abstract

The invention discloses a logistic-based large key space bit scrambling chaotic image encryption method, which improves the existing logistic chaotic mapping formula, solves the problem of limited control parameter range, increases the key space, and effectively resists exhaustive attacks, and can also retain more original information. Moreover, because the chaotic system is extremely sensitive to initial values, as well as nonlinearity, pseudo-randomness and other properties, this encryption method effectively improves the ability of the image to resist attacks; the image encrypted by the logistic chaotic system of the invention has great progress in security and other aspects, and promotes the research progress of chaotic system on image encryption.

Description

Technical Field

[0001] The invention relates to image encryption technology, and in particular to a logistic-based large key space bit scrambling chaotic image encryption method. Background Art

[0002] In the era of big data, the most valuable thing is information, and the convenience and powerful functions of information are obvious to all. Cryptography is a core discipline in the field of information security research. It mainly studies information security and solves information security problems in the process of transmission and storage. Images are an important carrier of information, and the information hidden in some images is crucial. Therefore, it is necessary to ensure that the transmission, storage, and access of digital images are safe and reliable; image encryption is one of the most effective ways to protect image security. Image encryption technology that ensures the privacy and confidentiality of multimedia data plays an important role in many applications, such as military image databases, pay TV, confidential video conferencing, health management systems, online private photo albums, etc.

[0003] The current popular method for image encryption is to use chaotic system encryption. There are two types of existing chaotic system encryption methods: one focuses on the generation of random sequences in the encryption system; the other focuses on the structural design of the encryption algorithm. Many existing chaotic systems have the disadvantages of limited control parameter range, uneven distribution of generation points, and short periodicity.

[0004] The parameter range of the existing logistic chaotic system is between 0 and 4, which results in a small key space and is vulnerable to exhaustive attacks. In addition, the sequences generated by the chaotic mapping for all parameters cannot traverse the entire state space and do not have uniform distribution. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to solve the deficiencies in the prior art and to provide a logistic-based large key space bit scrambling chaotic image encryption method.

[0006] Technical solution: The present invention is a logistic-based large key space bit scrambling chaotic image encryption method, which improves the one-dimensional logistic chaotic system to generate a new chaotic system, and then encrypts the image. The specific steps are as follows:

[0007] Step (1), improving the logistic chaotic mapping formula, that is, the chaotic mapping formula (1) is modified into formula (2);

[0008] X n+1 =u×X n ×(1-X n ) (1)

[0009] Xn+1 = RS(u × X n × (1 - X n )) (2)

[0010] In formula (2), u is a control parameter and u ≠ 0. The function RS(x) is a right shift function. First, the function RS(x) obtains the number of digits n of the integer part of the parameter x, and then performs the operation x × 10 -n , and returns the operation result, so that 0 ≤ RS(u × X n × (1 - X n )) < 1, that is, 0 ≤ X n+1 < 1, so that the control parameter u is no longer restricted between 0 and 4, and the generated sequence is in a chaotic state. In this way, the chaotic region of the system can be expanded, and the number of selectable encryption keys is also increased; the sequence generated by formula (2) is in a chaotic state (and the sequence distribution is uniform and the parameters are not restricted);

[0011] Step (2), determine the encryption key

[0012] Set 7 keys: X1, r1, X2, r2, N, Z, S; where the first four keys (X1, r1, X2, r2) are two pairs of control parameters and initial values (X1, r1)(X2, r2) of the improved Logistic chaotic system, N is the number of digits taken after the decimal point when the sequence value is converted into a binary form, and Z is the plaintext-related quantity obtained from the encryption formula (3);

[0013]

[0014] f(x, y) represents the input plaintext image, with a size of M × L; Z is the plaintext-related quantity obtained after calculation by formula (3), and S is the number of bits of sequence variation when obtaining X n data each time (that is, the number of bits reversed each time in step (2.2));

[0015] Step (3), perform a one-step random selection and reversal on the generated sequence to make the generated sequence have better chaotic characteristics; the specific steps are as follows:

[0016] Step 1: First, set the control parameter u and the loop variable i, and set the initial value i = 0; set the initial value X i sequence X0 (0 < X0 < 1); then substitute X i into formula (2) to obtain X i+1 , and then shift X i+1 so that X i+1 < 1, and then convert X i+1 into a binary form (X i+1 ) B ;

[0017] Select a positive integer N, (for example, N can be 9) for (X i ) B The first N digits are randomly selected The bit is inverted. The operation is to round down, and the inversion operation is to change the binary 0 to 1 and 1 to 0; assuming X i =0.625, then 0.625→0.101000000. Assuming the number of bits selected is 2, 4, and 6, then 0.101000000→0.111101000.

[0018] Step 3: Transform the (X i+1 ) B Convert to decimal again, 0.111101000→0.953125, and then substitute the obtained decimal into iterative formula (2) for the next iteration to get the next value;

[0019] Repeat steps 1-3, and the number of bits inverted in each round is different, until i = M × L. After the iteration, a chaotic sequence {X1,…,X n}, n = M × L; use S, which records the number of inverted bits, as the key for image restoration; after reading the size of the encrypted image, create N blank images of the same size, each pixel of each image represents the 1 to N bits of the corresponding pixel after the generated chaotic sequence is converted into a matrix, if the xth bit is inverted, the corresponding pixel value of the xth image is 1, otherwise it is 0, and finally splice the N images together as the key S;

[0020] Step (4), applying the improved logistic chaotic system to encrypt the image;

[0021] First, use the keys X1, r1, N and Z to iterate the improved Logistics encryption algorithm Z times to pass the transition state, and then iterate M×L times to generate a chaotic sequence K1 with a length of M×L; the size of the plaintext image f is M×L; the chaotic sequence K1 is converted into a preliminary encryption matrix F1 of the same size as the plaintext image as the encryption matrix; the preliminary encryption matrix F1 is encrypted with the plaintext image f by bitwise XOR operation to obtain a new image Then, a block operation is performed to divide f into four equal parts, each of which is M / 2×L / 2 in size. Then, a scrambling-diffusion operation is performed on each block. The scrambled-diffused image is reassembled into one block, rotated 90° counterclockwise, and the above scrambling-diffusion operation is repeated to obtain the final encrypted image fH.

[0022] In order to reduce the correlation between the plaintext image and the ciphertext image, the pixels are diffused so that the information of any pixel is hidden in as many ciphertext pixels as possible. The scrambling-diffusion operation is further performed on the divided image. The specific method is as follows:

[0023] Step I: Generate two positions D1 and D2 to be replaced; position D1 is the sequential position m, m is taken sequentially from the first position); position D2 is obtained by the chaotic system obtained in step (1) and formula (4):

[0024] First, the key X2, r2, N, and Z are used to iterate Z times in the improved Logistic system to obtain d, where d is the middle value of the positions D1 and D2 obtained by using the chaotic system. The position D2 is calculated as follows;

[0025] D = mod (floor (d × 10 N ),M / 2×L / 2)+1;

[0026] D1=m; (4)

[0027] D2=mod(D⊕D1,M / 2×L / 2)+1;

[0028] Step II, determine whether positions D1 and D2 are repeatedly selected; if D1 has been selected, select the next position in sequence as m, and similarly when position D2 has been selected, select the next position in sequence as D2;

[0029] Step III, using bit parity rearrangement and dynamic XOR operation to diffuse the pixel values ​​PCD1 and PCD2 at positions D1 and D2, and then obtain new pixels NCD1 and NCD2 respectively: bit parity rearrangement and dynamic XOR;

[0030] Step IV, swap the pixel values ​​at positions D1 and D2;

[0031] Generate a new initial value X2 using the following formula, bring it into the improved Logistic chaotic system to generate a new d value, and then substitute it into formula (4) to generate a new D2 position. The D1 position is sequentially increased by 1 to become D1 = m + 1;

[0032] X2=mod(d×D2,1).

[0033] Furthermore, the bit parity rearrangement refers to averaging the pixel values ​​PCD1 and PCD2 corresponding to the position D1 and the position D2 into 8-bit binary numbers, and then sequentially placing the odd-numbered bit values ​​in the first half and the even-numbered bit values ​​in the second half to generate a new pixel value;

[0034] Dynamic XOR operation means generating Y by using the following formula at the two positions D1 and D2;

[0035] Y = mod ((D1 × D2) + Zd, 256);

[0036] Finally, the grayscale values ​​PCD1 and PCD2 are dynamically XORed with Y to generate new pixels NCD1 and NCD2.

[0037] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0038] (1) The present invention solves the problem of limited control parameter range, increases the key space, and thus effectively resists exhaustive attacks. It can also retain more original information. In addition, because it utilizes the chaotic system's extreme sensitivity to initial values, as well as its nonlinearity, pseudo-randomness and other properties, this encryption method effectively improves the image's ability to resist attacks.

[0039] (2) The present invention is based on the existing logistic chaotic system and makes improvements on the existing logistic chaotic system to address the problems of uneven distribution of chaotic sequences and limited number of keys. As a result, the image encrypted by the logistic chaotic system of the present invention has made great progress in terms of security and other aspects, thus promoting the research progress of chaotic system in image encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is the overall flow chart of the present invention;

[0041] Figure 2 is an overall flow chart of the scrambling-diffusion operation in the present invention;

[0042] Figure 3 It is a schematic diagram for comparing the binary diagrams in the embodiments;

[0043] Figure 4 This is a schematic diagram of the comparison of Lyapunov exponent analysis in the embodiment;

[0044] Figure 5 This is a comparison chart of the experimental results of the Lena image and the Plane image in the embodiment. DETAILED DESCRIPTION

[0045] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0046] like Figure 1 As shown, the present invention is a logistic-based large key space bit scrambling chaotic image encryption method, which improves the one-dimensional logistic chaotic system to generate a new chaotic system, and then encrypts the image. The specific steps are as follows:

[0047] Step (1), improving the logistic chaotic mapping formula, that is, the chaotic mapping formula (1) is modified into formula (2);

[0048] X n+1 =u×X n ×(1-X n ) (1)

[0049] X n+1 =RS(u×X n ×(1-X n )) (2)

[0050] In this formula, u is the control parameter, and u≠0. The function RS(x) is a right shift function. First, the RS(x) function obtains the number of digits n of the integer part of the parameter x, and then operates x×10 on the parameter x. -n , and return the result of the operation. n ×(1-X n ))<1, that is, 0≤X n+1 <1, so that the control parameter u is no longer limited to between 0 and 4, and the sequence generated by the control is in a chaotic state, so that the chaotic region of the system can be expanded, and the number of selectable keys is also increased; the sequence generated by formula (2) is in a chaotic state (and the sequence distribution uniformity parameter is not limited);

[0051] Step (2): Determine the encryption key

[0052] Set 7 keys: X1, r1, X2, r2, N, Z, S. The first four keys: X1, r1, X2, r2 are the control parameters and initial values ​​of two pairs of improved Logistic chaotic systems (X1, r1) (X2, r2). N is the number of digits after the decimal point when the sequence value is converted into binary form. Z is the plaintext correlation value obtained by formula (3). S is the number of digits reversed each time in step (2.2).

[0053] The encryption method is as follows:

[0054] f(x,y) represents the input plaintext image, which is of size M×L; Z is the plaintext correlation obtained after calculation by formula (3), and S is the n The number of bits of sequence variation when the data is

[0055] Next, this paper performs a random selection reversal on the generated sequence to make the generated sequence have better chaotic characteristics.

[0056] Step (3), randomly selecting and reversing the generated sequence, so that the generated sequence has better chaotic characteristics; the specific steps are as follows:

[0057] Step 1: First, set the control parameter u and the loop variable i, and set the initial value i = 0; set the initial value of the X i sequence X0 (0 < X0 < 1); then substitute X i into Equation (2) to obtain X i+1 , and then shift X i+1 so that X i+1 < 1, and then convert X i+1 to binary form (X i+1 ) B ;

[0058] Step 2: Select a positive integer N (for example, N can take the value of 9), and randomly select i the first N bits of (X B ) for the bitwise negation operation, the operation is to round down, and the bitwise negation operation changes binary 0 to 1 and 1 to 0; assume X i = 0.625, then 0.625 → 0.101000000, assume the selected bits are 2, 4, 6, then 0.101000000 → 0.111101000.

[0059] Step 3: Convert the transformed (X i+1 ) B back to decimal again, 0.111101000 → 0.953125, and then substitute the obtained decimal fraction into the iterative formula (2) for the next iteration to obtain the next value; repeat Steps 1 - 3, and the number of bits reversed in each round is different, until i = M × L, after the iteration ends, a chaotic sequence {X1,..., X n} of length n is obtained, n = M × L;

[0060] And the S recording the number of reversed bits will be used as a kind of image key to participate in the restoration of the image. After reading the size of the encrypted image, create N blank images of the same size. Each pixel of each image represents the 1 to N bits of the corresponding pixel after the generated chaotic sequence is converted into a matrix. If the x - th bit is reversed, the corresponding pixel value of the x - th image is 1, otherwise it is 0. Finally, splice the N images together as the key S.

[0061] Step (4), encrypt the image using the improved logistics chaotic system;

[0062] First, use the keys X1, r1, N and Z to iterate the improved Logistics encryption algorithm Z times to pass the transition state, and then iterate M×L times to generate a chaotic sequence K1 with a length of M×L; the size of the plaintext image f is M×L; the chaotic sequence K1 is converted into a preliminary encryption matrix F1 of the same size as the plaintext image as the encryption matrix; the preliminary encryption matrix F1 and the plaintext image f are subjected to a bitwise XOR operation for the first encryption to obtain a new image f: f=f⊕F1; then a block operation is performed to divide f into four equal-sized parts, each of which is M / 2×L / 2 in size, and then each block is subjected to a scrambling-diffusion operation; the scrambled-diffused image is reassembled into one piece, rotated 90° counterclockwise, and then the above scrambling-diffusion operation is repeated to obtain the final encrypted image fH.

[0063] like Figure 2 As shown, the specific method of the scrambling-diffusion operation in this embodiment is:

[0064] Step I: Generate two positions D1 and D2 to be replaced; position D1 is the sequential position m, m is taken sequentially from the first position); position D2 is obtained by the chaotic system obtained in step (1) and formula (4):

[0065] First, the key X2, r2, N, Z is used to iterate Z times in the improved Logistic system to obtain d, where d is the middle value of the positions D1 and D2 obtained by using the chaotic system. The position D2 is calculated as follows;

[0066] D = mod (floor (d × 10 N ),M / 2×L / 2)+1;

[0067] D1=m; (4)

[0068] D2=mod(D⊕D1,M / 2×L / 2)+1;

[0069] Step II, determine whether positions D1 and D2 are repeatedly selected; if D1 has been selected, select the next position in sequence as m, and similarly when position D2 has been selected, select the next position in sequence as D2;

[0070] Step III, using bit parity rearrangement and dynamic XOR operation to diffuse the pixel values ​​PCD1 and PCD2 at positions D1 and D2, and then obtain new pixels NCD1 and NCD2 respectively: bit parity rearrangement and dynamic XOR;

[0071] Step IV, swap the pixel values ​​at positions D1 and D2;

[0072] Generate a new initial value X2 using the following formula, bring it into the improved Logistic chaotic system to generate a new d value, and then substitute it into formula (4) to generate a new D2 position. The D1 position is sequentially increased by 1 to become D1 = m + 1;

[0073] X2=mod(d×D2,1).

[0074] In this embodiment, the bit parity rearrangement refers to equalizing the pixel values ​​PCD1 and PCD2 corresponding to the position D1 and the position D2 into 8-bit binary numbers, and then sequentially placing the odd-numbered bit values ​​in the first half and the even-numbered bit values ​​in the second half to generate a new pixel value;

[0075] Dynamic XOR operation means generating Y by using the following formula at the two positions D1 and D2;

[0076] Y = mod ((D1 × D2) + Zd, 256);

[0077] Finally, the grayscale values ​​PCD1 and PCD2 are dynamically XORed with Y to generate new pixels NCD1 and NCD2.

[0078] Through the above-mentioned embodiment process, it can be seen that the present invention adds a shift operation to the existing logistic mapping, and introduces a random number factor to perform bit operation; uses the generated grayscale matrix and the plaintext image to perform XOR pre-encryption; then uses bit rearrangement and scrambling diffusion to further encrypt the preprocessed image to obtain the final encrypted image.

[0079] The effect of the present invention is analyzed below by using two indicators: bifurcation diagram and Lyapunov index.

[0080] (a) Bifurcation diagram analysis.

[0081] For binary X n Random selection and reversal have the advantage of improving the chaotic performance of the sequence. When the initial value of the system and the control parameter method change slightly, the difference between the points of the two orbits in the initial chaotic transition state is very small, and the sequence value in the transition state does not change much, and the same integer will be generated with a high probability. Random selection and reversal of sequences with small differences can increase the difference, so that the generated chaotic sequence has better chaotic characteristics. Figure 3 (a) and Figure 3 (b) are the bifurcation diagrams of the Logistic mapping and the improved Logistic mapping. After comparison, we found that the improved large key space bit scrambled chaotic Logistic mapping has a larger chaotic parameter range, and the new encryption system has better chaotic characteristics in the range of (0,4].

[0082] (b) Lyapunov exponent analysis.

[0083] The Lyapunov index is used to determine whether a nonlinear time series is a chaotic system and to display its chaotic properties. The larger the value of the Lyapunov index of a chaotic system, the better its chaotic properties. Figure 4 (a) and Figure 4 b) are the Lyapunov index graph of the Logistic mapping and the Lyapunov index graph of the improved Logistic mapping. It can be seen from the comparative analysis of this embodiment that Figure 4 The Lyapunov exponent of (b) is increasing, and most of the values ​​are positive, which proves that it has chaotic characteristics and the chaotic characteristics are constantly increasing.

[0084] Embodiment 1:

[0085] In order to verify the security of the encryption method of the present invention, this embodiment uses 256×256 Lena image and Plane image to conduct experiments, and the key settings of the encryption system are as follows: X1=0.76, r1=17.92, X2=0.21, r2=0.35, N=9.

[0086] The encryption result of Lena image is as follows Figure 5 (a) and Figure 5 (b) shows the Lena plaintext and ciphertext images and their pixel histograms.

[0087] Figure 5 (c) and Figure 5 (d) shows the Plane plaintext and ciphertext images and their pixel histograms.

[0088] Figure 5 (e) and Figure 5 (f) shows the village plaintext and ciphertext images and their pixel histograms.

[0089] Figure 5 (g) and Figure 5 (h) shows the Arab girls plaintext and ciphertext images and their pixel histograms.

[0090] A. Key space size analysis

[0091] The keys of this embodiment include X1, X2, r1, r2, N, Z and S.

[0092] The value range of X1 and X2 is set to be between 0 and 1, and u1 and u2 are any non-negative integers. Here, the step size of the keys X1, X2, r1 and r2 is set to be 10. -12 , the key space of this embodiment exceeds 10 48 , greatly expanding the key space.

[0093] B. Analysis of Statistical Characteristics of Ciphertext

[0094] Through the above histogram analysis, after the pixel histogram of the image is drawn, the distribution characteristics of the pixel values ​​of the image can be clearly seen. By observing the ciphertext histogram obtained by the experiment, it can be found that the pixel values ​​of the ciphertext image are approximately evenly distributed, which shows that the encryption method of the present invention has a good effect on encrypting picture information and hides the statistical characteristics of the original image well, and can effectively resist statistical attacks based on image pixel values, thereby achieving the effect of image encryption.

[0095] C. Correlation analysis of adjacent pixels

[0096] In this embodiment, in order to test the correlation of adjacent pixels of the ciphertext image, 2000 adjacent pixel values ​​are randomly selected in each direction of the ciphertext image, and the adjacent pixel correlation coefficient is calculated by formulas (7)-(10). The calculation results are shown in Table 1. From the correlation coefficient calculation results, it can be seen that the correlation of adjacent pixels of the plaintext image in each direction is very strong, while the correlation of the ciphertext image in each direction is very weak.

[0097] The results of the present invention are compared with those of the related prior art, and the results show that the encryption algorithm of the present invention can better reduce the correlation between adjacent pixels.

[0098]

[0099]

[0100]

[0101]

[0102] Table 1

[0103]

[0104] D. Information entropy analysis

[0105] Information entropy is a criterion used to reflect the randomness or uncertainty of an image. The more random an image is, the closer its information entropy is to the mathematical theoretical value

[10] .

[0106] The calculation formula of information entropy is formula (11).

[0107]

[0108] Where T is the number of gray levels, and p(i) represents the probability of gray value i appearing. For a gray random image with T=256, the theoretical value of H is 8. The information entropy results of each plaintext image and ciphertext image are shown in Table 2. The information entropy of the ciphertext image is close to the ideal value. Compared with the prior art, the present invention has better information entropy results and can better resist information entropy attacks.

[0109] Table 2

[0110]

[0111] In summary, the present invention improves the existing Logistic chaotic mapping algorithm, uses binary shift and bit flip operations, and solves the problems of uneven distribution and limited parameters of the traditional Logistic mapping chaotic sequence. After the improved algorithm is used for initial encryption, the scrambling-diffusion operation is used to use bit parity rearrangement and dynamic XOR to hide as much information of the plaintext pixel points as possible in the ciphertext pixel points, thereby enhancing the security and robustness of the ciphertext image.

[0112] After security testing, it can be known that the image encryption algorithm used in this article has good security and can resist brute force attacks, information entropy attacks, statistical attacks, etc.

Claims

1. A large key space bit scrambling chaotic image encryption method based on logistic, characterized by: The one-dimensional logistic chaotic system is improved to generate a new chaotic system, and then the image is encrypted. The specific steps are as follows: Step (1), improving the logistic chaotic mapping formula, that is, the chaotic mapping formula (1) is modified into formula (2); X n+1 =u×X n ×(1-X n )(1) X n+1 =RS(u×X n ×(1-X n ))(2) In formula (2), u is the control parameter and u≠0; Formula (2) uses the right shift function RS(x) to convert u×X in formula (1) n ×(1-X n ) to shift all integer digits to the decimal point, so that 0≤X n+1 ≤1, which makes the sequence generated by formula (2) in a chaotic state; Step (2): Determine the encryption key Set 7 keys: X1, r1, X2, r2, N, Z, S; Among them, (X1, r1) is a pair of control parameters and initial values ​​of the improved logistic chaotic system. (X2, r2) are another pair of control parameters and initial values ​​of the improved logistic chaotic system, N is the number of digits after the decimal point when the sequence value is converted into binary form, which is a positive integer; f(x,y) represents the input plaintext image, with a size of M×L; Z is the plaintext correlation obtained after calculation by formula (3); Step (3), perform a random selection and reversal on the generated sequence. The specific steps are as follows: Step (3.1), set the control parameter u, u≠0 and the loop variable i, set the initial value i=0; set X i Sequence initial value X0, 0 <X0<1; Step (3.2), X i Substituting into formula (2) we get X i+1 Then, X i+1 Shift so that X i+1 <1, then X i+1 Convert to binary form (X i+1 ) B ; Step (3.3), select a positive integer N, and i ) B The first N digits are randomly selected The bit is inverted. The operation is to round down, and the inversion operation is to change the binary 0 to 1 and 1 to 0; Step (3.4), transform the transformed (X i+1 ) B Convert to decimal again, and then convert the resulting decimal number X i+1 The next iteration is performed until i = M × L, and the number of bits reversed in each round is different; After the iteration, a chaotic sequence {X1,…,X n }, n = M × L; S, which records the number of reversed bits, is used as a key to restore the image; Step (4), encrypting the image based on the chaotic system obtained in step (1) and the encryption key obtained in step (2); first using the keys X1, r1, N and Z to iterate the improved logistics chaotic system Z times and then iterate M×L times to generate a chaotic sequence K1={X1,…,X n }; The chaotic sequence K1 is converted into a preliminary encryption matrix F1 of the same size as the plaintext image as the encryption matrix; the preliminary encryption matrix F1 is subjected to a row-bit XOR operation with the pixel blocks of the plaintext image f(x, y) to achieve the initial encryption, and the new image is obtained. Then, a block operation is performed to divide f into four equal parts, each of which is M / 2×L / 2 in size. Then, a scrambling-diffusion operation is performed on each block. The scrambled-diffused image is reassembled into one block, rotated 90° counterclockwise, and the above scrambling-diffusion operation is repeated to obtain the final encrypted image fH.

2. The large key space bit scrambling chaotic image encryption method based on logistic according to claim 1 is characterized in that: The specific method of scrambling-diffusion is: Step I: Generate two positions D1 and D2 to be replaced; position D1 is the sequential position m, m is taken sequentially from the first position; position D2 is the chaotic system obtained in step (1) and calculated by formula (4): First, the keys X2, r2, N, and Z are used to iterate Z times in the improved logistic system to obtain d, where d is the intermediate value of the positions D1 and D2 obtained by using the chaotic system. The positions D1 and D2 are calculated as follows; Step II, determine whether positions D1 and D2 are repeatedly selected; if D1 has been selected, select the next position in sequence as m, that is, m=m+1, D1=m, and similarly when position D2 has been selected, select the next position in sequence as D2; Step III, using bit parity rearrangement and dynamic XOR operation to diffuse the pixel values ​​PCD1 and PCD2 at positions D1 and D2, and then obtain new pixel values ​​NCD1 and NCD2 respectively; Step IV, swap the pixel values ​​at positions D1 and D2; Generate a new initial value X2 using the following formula, bring it into the improved logistic chaotic system to generate a new d value, and then substitute it into formula (4) to generate a new D2 position. The D1 position is sequentially increased by 1 to become D1 = m + 1; X2=mod(d×D2,1).

3. The large key space bit scrambling chaotic image encryption method based on logistic according to claim 2 is characterized in that: The bit parity rearrangement refers to averaging the pixel values ​​PCD1 and PCD2 corresponding to the position D1 and the position D2 into 8-bit binary values, and then sequentially placing the odd bit values ​​in the first half and the even bit values ​​in the second half to generate a new pixel value; Dynamic XOR operation means generating Y by using the following formula at the two positions D1 and D2; Y = mod ((D1 × D2) + Zd, 256); Finally, the pixel values ​​PCD1 and PCD2 are dynamically XORed with Y to generate new pixel values ​​NCD1 and NCD2.

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