A new image encryption method based on DNA strand displacement rule

Abstract

This invention relates to a novel image encryption method based on DNA strand displacement reaction rules, belonging to the field of information processing and encryption technology. The method involves constructing a cross-hybrid coupled mapping lattice chaotic system; generating a key using the original image, and then assigning the key to the chaotic system as an initial value; iterating the chaotic system to generate a chaotic sequence, and using the chaotic sequence to generate DNA strand displacement reaction rules; generating an S-box using a bijective function; scrambling the original image using the S-box; and performing DNA encryption on the scrambled image using the DNA strand displacement reaction rules to obtain a ciphertext image. This encryption algorithm effectively improves the information security of the ciphertext image and is resistant to brute force cracking and various statistical attacks.

Description

Technical Field

[0001] The present invention relates to the field of biological computing and image encryption technology, and in particular to a novel image encryption method based on DNA chain displacement reaction rules. Background Art

[0002] Digital images, as an important carrier of information dissemination, are widely used in education, commerce, military, and healthcare. These images may contain public or private data and are vulnerable to attacks during network transmission, leading to information leakage, theft, and tampering. Image encryption technology can ensure the secure transmission and storage of images. In recent years, DNA computing has been successfully introduced into information encryption methods. However, traditional DNA sequence calculations involve DNA addition, subtraction, and exclusive-OR (XOR) operations. These calculation rules have limited biological relevance, and the algorithms are simple and easily cracked. Therefore, new DNA computing methods are needed. DNA strand displacement reaction has been developed as a new biotechnology. By incorporating the DNA strand displacement reaction mechanism and developing new image encryption schemes, the biological relevance of DNA computing methods can be effectively enhanced, the diversity and complexity of DNA calculation rules can be increased, and the security of image encryption methods can be improved.

[0003] Due to the limited dynamical complexity of low-dimensional chaotic systems, insufficient computational precision can lead to dynamical degradation and short-cycle effects, reducing the security of chaotic encryption methods. The limited key space caused by the limited number of system variables also reduces the security of information encryption. Chaotic coupled map lattices, as high-dimensional chaotic systems, exhibit better chaotic dynamical behavior and a larger key space, as the dynamical behavior of system variables is related to both time and spatial position. Therefore, lower-dimensional chaotic systems have broad application prospects in information encryption.

[0004] In view of the above, the present application provides a novel image encryption method based on DNA strand displacement reaction rules to solve the above problems. Summary of the Invention

[0005] In view of the above situation, in order to overcome the defects of the existing technology, the present invention provides a new image encryption method based on DNA chain displacement reaction rules, including cross-hybrid coupling mapping lattice chaotic system design, DNA chain displacement reaction rule design and S-box structure design. This method constructs a new cross-hybrid coupling mapping lattice system, and successfully constructs an S-box by introducing a bijective function. The S-box can effectively scramble rectangular images; according to the DNA chain displacement reaction mechanism, a DNA chain displacement rule is constructed, which effectively supplements, enriches and develops the DNA computing method and enhances the security of image encryption.

[0006] A novel image encryption method based on DNA strand displacement reaction rules is characterized by comprising the following steps:

[0007] S1: Constructing a cross-hybrid coupled mapped lattice chaotic system;

[0008] S2: Generate a secret key using the original image. The secret key is used to generate the initial values ​​and parameters of the cross-hybrid coupled mapping lattice chaotic system.

[0009] S3: Iterative cross-hybrid coupling mapping lattice chaotic system generates chaotic sequences, and uses chaotic sequences to generate DNA strand displacement reaction rules;

[0010] S4: Generate S-box using bijective function;

[0011] S5: Use the S-box generated in S4 to perform multiple rounds of scrambling on the original image;

[0012] S6: Using DNA chain displacement reaction rules to diffuse the scrambled image to obtain an encrypted image;

[0013] S7: Decrypt the image according to the inverse process of image encryption to finally obtain the decrypted image.

[0014] The beneficial effects of the above technical solution are:

[0015] (1) Designed DNA strand displacement reaction rules, which effectively enriched and developed DNA computing operations and made DNA encryption algorithms more secure;

[0016] (2) An S-box is constructed using a bijective function, which can effectively scramble the plaintext image. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is the encryption flow chart of the present invention;

[0018] Figure 2 is the DNA strand displacement reaction rule of the present invention;

[0019] Figure 3 Lena (256×256) plaintext image and histogram of the present invention;

[0020] Figure 4 This is the Lena (256×256) ciphertext image and histogram of the present invention. DETAILED DESCRIPTION

[0021] The aforementioned and other technical contents, features and effects of the present invention will be clearly presented in the following detailed description of the embodiments with reference to the drawings of this application. The structural contents mentioned in the following embodiments are all referenced to the drawings in the specification.

[0022] 1. Construction of a Cross-Hybrid Coupled Mapping Lattice Chaotic System

[0023] The cross-hybrid coupled mapped lattice chaotic system is:

[0024]

[0025] Where p and q can be obtained from formula (2)

[0026]

[0027] The variable e is used as a coupling parameter to control the interaction between various lattices, subject to the constraint 0≤e≤1. Here, n represents time, k represents the number of lattices, fixed in the range 1≤k≤L, and the lattices indexed k+1 and k-1 are considered to be adjacent to the i-th lattice; the prescribed boundary conditions are as follows:

[0028]

[0029] Function f(x n (k))=μα n (k)(1-α n (k)) is a logical mapping.

[0030] 2. Generate a key using the original image and use it as the initial value. The secret key is a vector consisting of L+2 components. The key generation algorithm is shown in Table 1.

[0031] Table 1

[0032]

[0033] The function dec2bin(*) is used to generate a binary string to match a decimal integer *, length(*) is a function used to determine the length of a string or vector *, and the function randperm(*) is used to generate a random permutation of integers from 1 to *. L represents the number of mapping cells.

[0034] The key is used to generate the initial values ​​and parameters of the chaotic system:

[0035]

[0036] The subkey assigns an initial value α0(k) and parameters e and μ to each grid.

[0037] 3. Iteratively generate chaotic sequences and use them to generate DNA strand displacement reaction rules

[0038] Step 1: Convert the plaintext image into a decimal matrix M P , and then reconstructed according to the following formula

[0039] MP ←reshape(M P ,1,M×N)

[0040] Step 2: If the image size M×N is not divisible by 4, add 4-mod(M×N,4) pixels with a value of 0; otherwise, keep the plaintext image unchanged.

[0041] Step 3: Iterate the chaotic system times, remove the first s1 times, keep the remaining results, and obtain a size of The matrix Γ is reshaped as follows:

[0042]

[0043] in Represents a function used to obtain the smallest integer value greater than or equal to *.

[0044] Step 4: Select the M×N+mod(M×N,4) values ​​before the matrix Γ and form a new pseudo-random sequence Γ′. Use the formula to calculate the chaotic sequence Λ.

[0045] Λ=mod([Γ′×10 14 ],256) (6)

[0046] Step 5: Convert Λ from decimal to binary, and use DNA encoding rule 1 as shown in Table 2 (the second column in Table 2 is DNA encoding rule 1) to transform Λ into the DNA encoding matrix Λ D

[0047] Table 2 DNA coding rules

[0048] DNA coding rules 1 2 3 4 5 6 7 8 00 A A T T G G C C 01 G C G C A T A T 10 C G C G T A T A 11 T T A A C C G G

[0049] Step 6: From Λ D , we can get a long DNA chain containing (M×N+4-mod(M×N,4)) bases, and divide this long DNA chain into l short chains evenly, where Each short DNA strand R i (i=1,2,…,l) all consist of 16 bases.

[0050] Step 7: M P Convert from decimal to binary and use DNA encoding rule 1 to convert M P Convert to matrix M D .

[0051] Step 8: From M DWe can get another long chain containing 4×(M×N+4-mod(M×N,4)) bases, and divide this long DNA chain into l short chains, each short chain S i Contains 16 bases. For each 16-base fragment, design the following DNA strand displacement reaction rules:

[0052] (1) Take S i 1 The first 8 bases of t i 1 , the subsequent part serves as another foothold Toehold sequence t i 1 With chaotic sequence R i The first 8 sequences of λ are used to obtain another new toehold sequence λ through the DNA addition operation shown in Table 3. i 1 .

[0053] Table 3 DNA addition

[0054] DNA addition A G C T A A G C T G G C T A C C T A G T T A G C

[0055] (2) DNA chain S i 1 The paired chain with complementary bases, and the new toehold sequence λ i 1 Together to form a double strand of DNA Obviously, and S i 1 The conditions for DNA chain hybridization are met, allowing the DNA chain displacement reaction process to occur, thereby producing complete DNA waste chains and DNA single chains.

[0056] (3) The first 8 bases of The subsequent part serves as a foothold for the series λ i 1 ;Will Sequence foothold sequence With chaotic sequence R i Perform DNA addition operation on the first 8 sequences of i 2 .

[0057] (4) DNA chain Its complementary base-paired strand and the new toehold sequence λ i 2 Together to form a double strand of DNA It's obvious. and The conditions for DNA chain hybridization are met, allowing the DNA chain displacement reaction process to occur, resulting in a complete DNA waste chain and a DNA single chain ν i 2 , as a ciphertext chain.

[0058] 4. Use bijective function to generate S-box and use it to scramble the image

[0059] In order to enhance the scrambling effect on the plaintext image, the proposed S-box is used to perform multiple rounds of scrambling.

[0060] Step 1: Since the length and width of the plaintext image may not be equal, it is necessary to use the proposed S-box construction algorithm (as shown in Table 4);

[0061] Table 4

[0062]

[0063] Use the algorithm shown in Table 4 to construct the following two different S-boxes:

[0064]

[0065] Where W represents the total number of iterations.

[0066] Step 4: Use two different S-boxes Mbox and Nbox to perform multiple rounds of scrambling operations on the plaintext image using the algorithm shown in Table 5, where i′=1,2,…,M,j′=1,2,…,N,w=1,2,…,W.

[0067] Table 5

[0068]

[0069] Step 5: After W rounds of scrambling, the final scrambled image P1 can be obtained.

[0070] 5. Encrypting the scrambled image using DNA strand displacement reaction rules

[0071] Step 1: Convert the matrix P1 into a decimal matrix, then convert the decimal matrix into a binary representation, and use DNA encoding rule 1 (as shown in Table 2) to encode the binary matrix to obtain the transformed encoding matrix P1 D .

[0072] Step 2: Apply DNA strand displacement reaction rules to P1 D , generating matrix P2 D .

[0073] Apply DNA encoding rule 1 to DNA decoding matrix P2 D, convert it into a binary matrix, and finally convert the binary matrix into a decimal matrix to finally obtain the ciphertext image C.

[0074] As attached Figure 3 As shown, the histogram is used to represent the distribution of pixel values. Figure 3 (b) It can be seen that the distribution of pixel values ​​is uneven, which represents a certain characteristic of the pixel distribution of the plaintext image. Figure 4 (b) shows that the pixel values ​​of the ciphertext image are distributed relatively evenly, indicating that the ciphertext image has well concealed the pixel distribution characteristics of the plaintext image.

[0075] 6. Image Decryption

[0076] Step 1: Convert the matrix C into a decimal matrix, then convert the decimal matrix into binary representation, and use DNA encoding rule 1 to perform DNA encoding on the binary matrix to obtain the transformed encoding matrix

[0077] Step 2: Use the DNA subtraction elimination matrix shown in Table 6 The DNA encryption effect produced by the DNA strand displacement reaction rule is obtained, and the matrix

[0078] Table 6 DNA subtraction

[0079] DNA subtraction A G C T A A T C G G G A T C C C G A T T T C G A

[0080] Step 3: Transform the matrix Convert to a binary matrix, and then convert this matrix to a decimal matrix, denoted as E.

[0081] Step 4: Use Mbox and Nbox to reversely scramble the matrix E, thereby eliminating the effects of multiple rounds of scrambling and obtaining the decrypted image D.

[0082] The above description is only for illustrating the present invention. It should be understood that the present invention is not limited to the above embodiments, and various variations that conform to the concept of the present invention are within the scope of protection of the present invention.

Claims

1. A new image encryption method based on DNA strand displacement reaction rules, characterized in that: The following steps are involved: S1: Constructing a cross-hybrid coupled mapped lattice chaotic system; The cross-hybrid coupled mapped lattice chaotic system is expressed as: Where p and q are obtained by the following formula: where the variable e is used as a coupling parameter to control the interactions between various lattices and 0≤e≤1, α n (k) represents the lattice, where n represents time, k represents the number of lattices, and is fixed in the range 1≤k≤L, L is the total number of lattices, and the lattices with indices k+1 and k-1 are considered to be adjacent to the kth lattice. a and b represent the parameters of the cat mapping; The boundary conditions are as follows: Function f(α n (k))=μα n (k)(1-α n (k)) is a logical mapping; S2: Generate a secret key using the original image. The secret key is used to generate the initial values ​​and parameters of the cross-hybrid coupled mapping lattice chaotic system. The initial values ​​and parameters of the cross-hybrid coupled mapping lattice chaotic system generated by the secret key are expressed as follows: Where key represents the secret key, which is a vector consisting of L+2 components. The first component of key is key(1), the second component of key is key(2), and the remaining L components are represented by key(k+2), where k represents the number of grids k=1,2,…,L. The sub-key assigns an initial value α0(k) and parameters e and μ to each grid, that is, α0(k) and e and μ are all sub-keys. These sub-keys are generated from the secret key using formula (3). S3: Iterative cross-hybrid coupling mapping lattice chaotic system generates chaotic sequences, and uses chaotic sequences to generate DNA strand displacement reaction rules; The specific steps include: S3-1: Convert the plaintext image into a decimal matrix M P , and then reconstructed according to formula (4) M′ P ←reshape(M P ,1,M×N)(4)S3-2: If the image M×N is divisible by 4, then add mod(M×N,4) pixels with a value of 0; otherwise, keep the plaintext image unchanged; S3-3: Iterative Chaotic Systems times, remove the first s1 times, keep the remaining results, and obtain a size of The matrix Γ is reshaped as follows: in Represents a function used to obtain the minimum integer value greater than or equal to *; S3-4: Select the M×N+4-mod(M×N,4) value before the matrix Γ′ and form a new pseudo-random sequence Use formula (6) to find the chaotic sequence Λ; S3-5: Convert Λ from decimal to binary and use DNA encoding rules to transform Λ into DNA encoding matrix Λ D ; S3-6: By Λ D , we get a long DNA chain containing (M×N+4-mod(M×N,4)) bases, and divide this long DNA chain into l short chains evenly, where Each short DNA strand R i (i=1,2,…,l) all consist of 16 bases; S3-7: M′ P Convert from decimal to binary and use DNA encoding rules to convert M′ P Converted to DNA encoding matrix M D , where M P is the matrix reconstructed using formula (4); S3-8: From M D In the equation, we get another long chain containing 4×(M×N+4-mod(M×N,4)) bases, and divide this long DNA chain into l short chains S i 1 , each short chain contains 16 bases; S3-9: Based on the principle of DNA strand displacement reaction, design a DNA strand displacement reaction rule: (1) Take the short chain S in S3-8 i 1 The first 8 bases of t i 1 , the subsequent part serves as another foothold Toehold sequence t i 1 With chaotic sequence R i The first 8 sequences of λ are added by DNA to obtain another new toehold sequence λ i 1 ; (2) DNA chain S i 1 The paired chain with complementary bases, and the new toehold sequence λ i 1 Together to form a double strand of DNA Obviously, and S i 1 The conditions for DNA chain hybridization are met, allowing the DNA chain displacement reaction process to occur, thereby producing complete DNA waste chains and DNA single chains. (3) The first 8 bases of The subsequent part serves as a foothold for the series λ i 1 ;Will Sequence foothold sequence With chaotic sequence R i Perform DNA addition operation on the first 8 sequences of i 2 ; (4) DNA chain Its complementary base-paired strand and the new toehold sequence λ i 2 Together to form a double strand of DNA It's obvious. and The conditions for DNA chain hybridization are met, allowing the DNA chain displacement reaction process to occur, resulting in a complete DNA waste chain and a DNA single chain. As a ciphertext chain; S4: Generate two S boxes using bijective functions; S5: Use the two S-boxes generated in S4 to perform multiple rounds of scrambling on the original image; S6: Using DNA chain displacement reaction rules to diffuse the scrambled image to obtain an encrypted image; The specific steps include: S6-1: Convert the scrambled image P1 into a decimal matrix, then convert the decimal matrix into a binary representation, and use the DNA coding rule to encode the binary matrix to obtain the transformed coding matrix P1 D ; S6-2: Apply the DNA strand displacement reaction rule to P1 according to S3-9 D , generating the matrix S6-3: Applying DNA encoding rules to decrypt extended DNA chains Thus, the ciphertext image C is generated; S7: Decrypt the image according to the inverse process of image encryption to finally obtain the decrypted image.

2. The novel image encryption method based on DNA strand displacement reaction rule according to claim 1 is characterized in that: The specific steps of using the S-box to perform multiple rounds of scrambling in S5 include the following: S5-1: Use the S-box construction algorithm to construct the following two different S-boxes S5-2: Use two different S-boxes Mbox and Nbox to perform multiple rounds of scrambling iterations on the plaintext image; S5-3: After W iterations, the final scrambled image P1 can be obtained.

3. The novel image encryption method based on DNA strand displacement reaction rule according to claim 1 is characterized in that: The process of obtaining the decrypted image in S7 includes the following steps: S7-1: Convert the ciphertext image C into a decimal matrix, then convert the decimal matrix into binary representation, and encode the binary matrix using DNA encoding rules to obtain the transformed encoding matrix S7-2: Eliminate the matrix using DNA subtraction according to the DNA strand displacement reaction rules DNA encryption effect and obtain matrix S7-3: Matrix Convert to a binary matrix, and then convert this matrix to a decimal matrix, denoted as E; S7-4: Perform multiple rounds of reverse scrambling on the matrix E to eliminate the effects of multiple rounds of scrambling, and obtain the decrypted image D.

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