Image encryption method based on two-dimensional Sine-Polynomial chaotic mapping and DNA operation

Abstract

The invention relates to an image encryption method based on two-dimensional Sine-Polynomial chaotic mapping and DNA (Deoxyribose Nucleic Acid) operation. The method mainly comprises the following steps: (1) providing a new two-dimensional Sine-Polynomil (2D-SPN) chaotic system; (2) proposing a cyclic scrambling method based on a random sequence; (3) proposing a DNA operation rule; and (4) providing an image encryption method based on 2D-SPN and DNA operation.

Description

Technical Field

[0001] The present invention relates to the field of information security and privacy protection, and in particular to an image encryption method based on two-dimensional Sine-Polynomial chaotic mapping and DNA operation. Background Art

[0002] The increasing development of information and communication technology has led to rapid changes in data transmission and storage methods. Especially through the Internet, the exchange and storage of large amounts of data has also brought new security challenges. Therefore, protecting sensitive information from unauthorized access has become a major concern in finance, healthcare, government, and personal data management. As images are commonly used information carriers, how to effectively encrypt them is particularly important.

[0003] Over time, encryption technology has become the main solution that can protect data from intrusion or cyberattacks. Cryptography provides various techniques for encoding data to prevent unauthorized access to data and protect its confidentiality, integrity and authenticity. Compared with traditional text data, images are different from text in several aspects: they have large data capacity and high correlation and sensitivity between adjacent pixels. Traditional encryption algorithms, such as RSA, DES and AES, have many shortcomings in image encryption and are not suitable for high-security image applications. Encryption based on chaotic systems is one of the innovative methods in cryptography. Chaotic encryption is based on the principles of chaos theory and has important characteristics such as high sensitivity to initial conditions, unpredictable behavior and dynamic complexity. Without the correct key, it is almost impossible for unauthorized entities to decrypt the encrypted content. Therefore, chaotic encryption shows good application prospects in image encryption.

[0004] The principle of image encryption using chaotic mapping is to use chaotic mapping with randomness and sensitivity, and encrypt through certain scrambling and diffusion methods for pixels. Some chaotic systems, such as logical mapping, Lorentz system, Heron map, etc. have been used for image encryption.

[0005] The invention first constructs a new two-dimensional Sine-Polynomial chaotic map, which has good chaotic performance. Based on this, an image encryption method based on the two-dimensional Sine-Polynomial chaotic map and DNA operation is constructed, which can take into account both security and efficiency. Summary of the invention

[0006] The invention constructs a two-dimensional Sine-Polynomial (2D-SPN) chaotic system. On this basis, an image encryption method based on DNA operation is constructed.

[0007] The specific contents are as follows:

[0008] 1. Construct a two-dimensional Sine-Polynomial (2D-SPN) chaotic system, defined as follows:

[0009]

[0010] Where a, b∈R are system parameters. The chaotic system is obtained by coupling Sine mapping with polynomials. The chaotic characteristics of the system are analyzed by trajectory diagram, Lyapunov index, phase diagram and information entropy. The results show that 2D-SPN has good chaotic performance, and when a=100, b∈[20,100), the 2D-SPN mapping is in a chaotic state.

[0011] 2. Construct a cyclic scrambling method based on random sequence. The specific scrambling process is as follows:

[0012] Assume a 4×4 matrix M,

[0013]

[0014] (1) The matrix M1 is obtained by changing the order of each row in the matrix M. Specifically, the i-th row of the matrix M1 is the ni-th row of the matrix M, where i=1, 2, ..., n, and n represents the number of rows of the matrix M.

[0015]

[0016] (2) If the matrix M is a square matrix, then transpose the matrix M1 to obtain the matrix M2. Specifically, the element G2(i,j) in the matrix M2 is equal to the element G1(j,i) in the matrix M1. Where i = 1, 2, ..., n, j = 1, 2, ..., n. If the matrix M is not a square matrix, then skip this step and directly execute the operation in (3).

[0017]

[0018] (3) Circularly move the jth column in the matrix M2 vertically (-1) j V(j) positions are used to get the matrix M3. V is a random sequence, and v(j) represents the jth element in the sequence. For ease of demonstration, assume a sequence of length 4:

[0019] V=1,2,3,4

[0020] get:

[0021] (-1) j V=-1,2,-3,4

[0022] Among them, positive and negative represent the direction of the circular movement. If it is positive, it moves upward, and if it is negative, it moves downward. Correspondingly, -1 represents moving down one position, and 2 represents moving up two positions, and M3 is obtained as follows.

[0023]

[0024] (4) Circularly move the i-th row in matrix M3 horizontally (-1) i+1 W(i) positions are used to get the matrix M4. Where W is a random sequence and W(i) represents the i-th element in the sequence. Assume that:

[0025] (-1) i+1 W=1,-2,3,-4

[0026] The positive and negative represent the direction of the circular movement. If it is positive, it moves to the right, and if it is negative, it moves to the left. Correspondingly, 1 represents moving one position to the right, and -2 represents moving two positions to the left, and M4 is obtained as follows.

[0027]

[0028] 3. Construct a DNA operation rule as follows:

[0029] Common DNA operation rules include addition, subtraction, XOR and XOR, as follows:

[0030] addition A G C T Subtraction A G C T A A G C T A A T C G G G C T A G G A T C C C T A G C C G A T T T A G C T T C G A XOR A G C T Same or A G C T A A C G T A T C G A G G T A C G C T A G C C A T G C G A T C T T G C A T A G C T

[0031] Construct a special DNA operation, denoted as ·, and the specific operation rules are as follows:

[0032] · A G C T A T G C A G C A G T C A C T G T G T A C

[0033] 4. Construct an image encryption method based on 2D-SPN and DNA operation.

[0034] The image encryption method is mainly divided into two parts. The first part is that the 2D-SPN chaotic system generates the random sequence required in the encryption process. The initial value of the system is related to the plaintext image. Therefore, for different plaintext images, the random sequence generated by 2D-SPN is different. The second part is the image encryption process, which mainly includes the cyclic scrambling process and DNA operation. See the detailed workflow for details. Figure 1 , the specific steps are as follows:

[0035] (1) Calculate the initial plaintext image P through SHA-256 m×( The 256-bit hash value K is then divided into 8 groups, each with 32 bits, recorded as: K = k1k2,…,k i , where i = 1, 2, ..., 8, k i∈[0,255=。

[0036] (2) Set the key key = {a, b, x1, y1, x2, y2, z1, z2} and update the initial value of the 2D-SPN chaotic map according to the following formula:

[0037]

[0038] (3) Iterate the 2D-SPN system mn+z1 times using the initial values ​​x′1, y′1, and discard the first z1 values ​​of each sequence. Get two sequences X and Y of length mn, and take the first m and n values ​​of sequences X and Y to form new sequences S1 and S2 respectively. Finally, perform modulo operation on S1 and S2 respectively: S1 = mod(S1×10 8 , m); S2 = mod(S2 × 10 8 , n).

[0039] (4) Use the initial values ​​x′2, y′2 to iterate the 2D-SPN system 2mn+z2 times, and discard the first z2 values ​​of each sequence. Get two sequences K and Z of length 2mn, and concatenate the two sequences to get a sequence S3 of length 4mn. Perform a modulus operation on S3: S3 = mod(S3×10 8 , 4). Finally, S3 is converted into a matrix A of size m×4n.

[0040] (5) Change the order of the rows in the initial plaintext image P to obtain the matrix P1. The i-th row of the matrix P1 is the mi-th row of P, where i = 1, 2, ..., m.

[0041] (6) If m=n, transpose the matrix P1 to obtain P2. Otherwise, let P2=P1.

[0042] (7) Perform column cyclic shift on matrix P2, and move the jth column by (-1) j S2(j) positions, where j = 1, 2, ..., n. If j is an even number, the column is cyclically shifted upwards, and if j is an odd number, the column is cyclically shifted downwards, to obtain the matrix P3.

[0043] (8) Perform row cyclic shift on matrix P3, and shift the i-th column by (-1) i+1 S1(i) positions, where i = 1, 2, ..., m. If i is an odd number, the row is cyclically shifted to the right, and if i is an even number, the row is cyclically shifted to the left, to obtain the matrix P4.

[0044] (9) Convert the matrix P4 to binary, and you get a binary matrix B of size m×8n. Each value in the matrix P4 corresponds to an 8-bit binary value in B. From right to left, take the 1st, 7th, and 8th binary values ​​to form a new 3-bit binary value, which can represent a range of 0 to 7, and get a corresponding matrix G of size m×n.

[0045] (10) There are eight rules for DNA coding:

[0046] Coding Rules 0 1 2 3 4 5 6 7 00 A A C G C G T T 01 C G A A T T C G 10 G C T T A A G C 11 T T G C G C A A

[0047] Then each value in the matrix G corresponds to the DNA encoding rule of the 8-bit binary value in B. According to the corresponding rule, DNA encoding is performed on the matrix B to obtain a DNA matrix R of size m×4n.

[0048] (11) The matrix A obtained in step (4) is operated on the matrix R obtained in step (10), and the operation rules are in accordance with the special DNA operation constructed above, namely A·R, to obtain the matrix O.

[0049] (12) Decode the matrix O according to A–00, C–01, G–10, T–11 to obtain the ciphertext image C. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The figure is a flow chart of the algorithm of the present invention. DETAILED DESCRIPTION

[0051] The present invention is an image encryption method based on two-dimensional Sine-Polynomial chaotic mapping and DNA operation, which mainly includes the following four steps:

[0052] Step 1: Generate a random sequence;

[0053] Step 2: Circular scrambling operation;

[0054] Step 3: DNA manipulation;

[0055] The implementation platform is MATLAB and the operating system is macOS15. The details are as follows:

[0056] Step 1: Generate a random sequence

[0057] (1) Calculate the initial plaintext image P m×( The 256-bit hash value K is divided into 8 groups, each with 32 bits, denoted as: K = k1k2,…,k i , where i = 1, 2, ..., 8, k i ∈[0,255=。

[0058] (2) Set the key key = {a, b, x1, y1, x2, y2, z1, z2} and update the initial value of 2D-SPN:

[0059]

[0060] (3) Iterate the 2D-SPN system mn+z1 times using the initial values ​​x′1, y′1, and discard the first z1 values ​​of each sequence. Get two sequences X and Y of length mn, and take the first m and n values ​​of sequences X and Y to form new sequences S1 and S2 respectively. Finally, perform modulo operation on S1 and S2 respectively: S1 = mod(S1×10 8 , m); S2 = mod(S2 × 10 8 , n).

[0061] (4) Use the initial values ​​x′2, y′2 to iterate the 2D-SPN system 2mn+z2 times, and discard the first z2 values ​​of each sequence. Get two sequences K and Z of length 2mn, and concatenate the two sequences to get a sequence S3 of length 4mn. Perform a modulus operation on S3: S3 = mod(S3×10 8 , 4). Finally, S3 is converted into a matrix A of size m×4n.

[0062] Step 2: Loop scrambling operation

[0063] (1) Change the order of the rows in the initial plaintext image P to obtain the matrix P1. The i-th row of the matrix P1 is the mi-th row of P, where i = 1, 2, ..., m.

[0064] (2) If m=n, then transpose the matrix P1 to obtain P2. Otherwise, let P2=P1.

[0065] (3) Perform column cyclic shift on matrix P2, and move the jth column by (-1) j S2(j) positions, where j = 1, 2, ..., n. If j is an even number, the column is cyclically shifted upwards, and if j is an odd number, the column is cyclically shifted downwards, to obtain the matrix P3.

[0066] (4) Perform row cyclic shift on matrix P3, and shift the i-th column by (-1) i+1 S1(i) positions, where i = 1, 2, ..., m. If i is an odd number, the row is cyclically shifted to the right, and if i is an even number, the row is cyclically shifted to the left, to obtain the matrix P4.

[0067] Step 3: DNA manipulation

[0068] (1) Convert the matrix P4 to binary, and you get a binary matrix B of size m×8n. Each value in the matrix P4 corresponds to an 8-bit binary value in B. From right to left, take the 1st, 7th, and 8th binary values ​​to form a new 3-bit binary value, which can represent a range of 0 to 7, and get a corresponding matrix G of size m×n.

[0069] (2) Each value in the matrix G corresponds to the DNA encoding rule of the 8-bit binary value in B. According to the corresponding rule, the matrix B is DNA encoded to obtain a DNA matrix R of size m×4n.

[0070] (3) Matrix A is operated on matrix R, and the operation rules follow the special DNA operation constructed above, that is, A·R, to obtain matrix O.

[0071] (4) Decode the matrix O according to A-00, C-01, G-10, T-11 to obtain the ciphertext image C.

Claims

1. An image encryption method based on two-dimensional Sine-Polynomial chaotic mapping and DNA operation, characterized by: (1) Construct a two-dimensional Sine-Polynomial (2D-SPN) chaotic system, which is defined as follows: Where a, b∈R are system parameters. The chaotic system is obtained by coupling the Sine map with the polynomial. And when a=100, b∈[20,100, the 2D-SPN map is in a chaotic state. (2) Construct a cyclic scrambling method based on random sequences. The specific scrambling process is as follows: Assume a 4×4 matrix M, Step 1: Change the order of each row in the matrix M to obtain the matrix M1. Specifically, the i-th row of the matrix M1 is the ni-th row of the matrix M, where i=1,2,…,n, and n represents the number of rows of the matrix M. Step 2: If the matrix M is a square matrix, then transpose the matrix M1 to obtain the matrix M2. Specifically, the element G2(i,j) in the matrix M2 is equal to the element G1(j,i) in the matrix M1. Where i = 1, 2, ..., n, j = 1, 2, ..., n. If the matrix M is not a square matrix, then skip this step and directly execute the operation in (3). Step 3: Circularly move the jth column in matrix M2 vertically (-1) j V(j) positions are used to get the matrix M3. V is a random sequence and V(j) represents the kth element in the sequence. For ease of demonstration, assume a sequence of length 4: V＝1,2,3,4 get: (-1) j V=-1,2,-3,4, where The positive and negative represent the direction of the circular movement. If it is positive, it moves upward, and if it is negative, it moves downward. Correspondingly, -1 represents moving one position downward, and 2 represents moving two positions upward, and M3 is obtained as follows. Step 4: Circularly move the i-th row in matrix M3 horizontally (-1) i+1 W(i) positions are used to get the matrix M4. Where W is a random sequence and W(i) represents the i-th element in the sequence. Assume that: (-1) i+1 W＝1,-2,3,-4 The positive and negative represent the direction of the circular movement. If it is positive, it moves to the right, and if it is negative, it moves to the left. Correspondingly, 1 represents moving one position to the right, and -2 represents moving two positions to the left, and M4 is obtained as follows. (3) Construct a DNA operation rule as follows: Common DNA operation rules include addition, subtraction, XOR and XOR, as follows: Construct a special DNA operation, denoted as ·, and the specific operation rules are as follows: (4) Construct an image encryption method based on 2D-SPN and DNA operation. The image encryption method is mainly divided into two parts. The first part is that the 2D-SPN chaotic system generates the random sequence required in the encryption process. The initial value of the system is related to the plaintext image. Therefore, for different plaintext images, the random sequence generated by 2D-SPN is different. The second part is the image encryption process, which mainly includes the cyclic scrambling process and DNA operation. The detailed workflow is shown in Figure 1, and the specific steps are as follows: Step 1: Calculate the initial plaintext image P through SHA-256 m×( The 256-bit hash value K is then divided into 8 groups, each with 32 bits, recorded as: K = k1k2,…,k $ , where i = 1, 2, ..., 8, k $ ∈[0,255=。 Step 2: Set the key key = {a, b, x1, y1, x2, y2, z1, z2} and update the initial value of the 2D-SPN chaotic map according to the following formula: Step 3: Iterate the 2D-SPN system mn+z1 times using the initial values ​​x′1, y′1, and discard the first z1 values ​​of each sequence. Get two sequences X and Y of length mn, and take the first m and n values ​​of sequences X and Y to form new sequences S1 and S2. Finally, perform modulo operation on S1 and S2: S1=mod(S1×10 8 , m); S2 = mod(S2 × 10 8 , n). Step 4: Use the initial values ​​x′2, y′2 to iterate the 2D-SPN system 2mn+z2 times, and discard the first z2 values ​​of each sequence. Get two sequences K and Z of length 2mn, and concatenate the two sequences to get a sequence S3 of length 4mn. Perform a modulus operation on S3: S3=mod(S3×10 8 , 4). Finally, S3 is converted into a matrix A of size m×4n. Step 5: Change the order of the rows in the initial plaintext image P to obtain the matrix P1. The i-th row of the matrix P1 is the mi-th row of P, where i = 1, 2, ..., m. Step 6: If m=n, transpose the matrix P1 to obtain P2. Otherwise, let P2=P1. Step 7: Circularly shift the columns of matrix P2, and move the jth column by (-1) j S2(j) positions, where j = 1, 2, ..., n. If j is an even number, the column is cyclically shifted upwards, and if j is an odd number, the column is cyclically shifted downwards, to obtain the matrix P3. Step 8: Circularly shift the rows of matrix P3 and move the i-th column by (-1) i+ 1S1(i) positions. Where i = 1, 2, ..., m. If i is an odd number, the row is cyclically shifted to the right, and if i is an even number, the row is cyclically shifted to the left, to obtain the matrix P4. Step 9: Convert the matrix P4 to binary, and you will get a binary matrix B of size m×8n. Each value in the matrix P4 corresponds to an 8-bit binary value in B. From right to left, take out the 1st, 7th, and 8th binary values ​​to form a new 3-bit binary value, which can represent a range of 0 to 7, and get a corresponding matrix G of size m×n. Step 10: There are 8 rules for DNA coding: Then each value in the matrix G corresponds to the DNA encoding rule of the 8-bit binary value in B. According to the corresponding rule, DNA encoding is performed on the matrix B to obtain a DNA matrix R of size m×4n. Step 11: Operate the matrix A obtained in step 4 with the matrix R obtained in step 10. The operation rules follow the special DNA operation constructed above, namely A·R, to obtain the matrix O. Step 12: Decode the matrix O according to A–00, C–01, G–10, T–11 to obtain the ciphertext image C.

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