CN107437266A - Image encryption method based on chaos system Yu DNA chain displacement model - Google Patents

Abstract

The present invention relates to the image encryption method based on chaos system Yu DNA chain displacement model, belong to image encryption technical field.The present invention includes encoding original image；Chaos sequence (x, y, z) is produced using Lorenz chaotic maps：Give arbitrary initial value x₀,y₀,z₀, calculate the Hamming distance of sequence matrix obtained in S1, Hamming mends distance against distance and Hamming, and be 01 by its value, with x₀,y₀,z₀New initial value x is obtained after being added successively₁,y₁,z₁；Three chaos sequences are produced then in conjunction with systematic parameter；The basic thought of strand displacement system in biochemical reaction is introduced present invention formation DNA chain displacement model and image is encrypted by the present invention, due to the process energy parallel starting, with high degree of specificity recognition site, therefore Encryption Model has very strong computation capability and high storage density so that encryption efficiency is higher.

Description

Image Encryption Method Based on Chaotic System and DNA Chain Replacement Model

technical field

The invention relates to an image encryption method based on a chaotic system and a DNA chain replacement model, and belongs to the technical field of image encryption.

Background technique

In recent years, with the rapid development of the Internet, digital images are used more and more frequently by people. Whether it is social activities or online news media, medical institutions or government agencies, digital images as an information carrier are widely used by people because of their conciseness, expressiveness and intuitiveness. However, due to the openness of the network and the sharing of information and the continuous development of hacker technology, images in network transmission are likely to be intercepted by criminals and affect the commercial interests and privacy of individuals or organizations. For this reason, people have taken a series of measures To ensure the security of image transmission, image encryption is the most effective way. Due to the characteristics of image information redundancy and two-dimensional data, traditional text encryption methods such as DES, AES, IDEA, etc. are no longer suitable for image encryption. Therefore, the image encryption technology based on modern cryptosystem, the image encryption technology based on matrix transformation, the image encryption technology based on chaos, the image encryption technology based on secret sharing and the image encryption technology based on frequency domain appear one after another. However, with the rapid improvement of computer hardware capabilities and the continuous development of various new computer research, the security of these methods is facing severe challenges.

In 1963, the American meteorologist Lorenz proposed chaos theory (chaos), the diversity and multi-scale of nonlinear systems. Chaos theory explains that decision systems can produce random outcomes. In chaos theory, very small changes in the initial conditions, after continuous amplification, can cause extremely large differences in its future state. Therefore, chaotic systems are naturally related to cryptography.

Contents of the invention

In order to achieve the above object, the present invention provides an image encryption method based on a chaotic system and a DNA chain replacement model. In this paper, the chaotic system is used to generate three chaotic sequences to encrypt the image.

DNA strand displacement is a newly developed technique in DNA computing. In 2011, Science and Nature reported that the research group of Professor Winfree, Department of Computer Science, Caltech used DNA strand replacement technology to realize simple square root calculation. In the strand displacement reaction model, information can be encoded and hidden in single-stranded DNA. Each short DNA single strand (20-80nt) represents a logic signal, and only needs to change the sequence and length of the DNA single strand to represent another kind of information, and it is easy to realize the compilation of information. It can be considered to introduce the basic idea of this model into image encryption to produce good encryption effect.

In this paper, the DNA strand replacement model is introduced into the image encryption process. The mechanism of the strand displacement type is to control or induce the downstream strand displacement reaction by changing the length and sequence of the input signal molecule by utilizing the characteristic that the molecular hybridization free energy tends to be stable. The specific operation steps are as follows.

1. Two partially complementary DNA strands join together (strand A is longer than strand B);

2. At room temperature, to add chain C (its sequence is completely complementary to chain A), the specific recognition region first binds to the single-chain part of A;

3. The C chain gradually occupies the binding site of the A chain and the B chain, and the A chain and the B chain are gradually separated, and gradually reach the most stable state;

4. Finally, the C chain is completely combined with the A chain, and the B chain is completely separated from the A chain.

The object of the present invention is to propose an image encryption method based on a chaotic system and a DNA chain replacement model, using the chain replacement model to extract a key to scramble the pixel positions of the image, so that the encryption effect is good, thereby being able to resist the attack of intruders.

Technical scheme of the present invention comprises the steps:

S1. Obtain the pixel matrix of the input image, and encode it with DNA encoding rules;

S2. Use the Lorenz chaotic map to generate chaotic sequence (x, y, z): Given any initial value x ₀ , y ₀ , z ₀ , calculate the Hamming distance, Hamming inverse distance and Hamming distance of the sequence matrix obtained in S1 Clearly complement the distance, and convert its value to 0-1, and add it to x ₀ , y ₀ , z ₀ in turn to obtain a new initial value x ₁ , y ₁ , z ₁ ; then combine system parameters to generate three chaotic sequences;

S3, scrambling the pixel position of the image with the chaotic sequence (x, y): rounding down the chaotic sequence (x, y), and using the newly obtained sequence to scramble the pixel position of the image;

S4. Use the DNA chain replacement operation to obtain a string of keys, and use the key and XOR operation to change the pixel value;

The process of the step S4 is as follows:

First, the pixel matrix obtained in step S3 is divided into blocks, and the size of each small block is 2*4;

Then, the chain permutation reaction is applied to the key block, and four short DNA sequences are replaced as encryption keys; the obtained keys are used to encrypt the corresponding matrix blocks in turn, and the corresponding relationship is determined by the chaotic sequence (x, z): The 4 DNA chains in the key block are XORed with the partial DNA sequences in the encrypted matrix block, and a part of each DNA sequence in the matrix block is replaced accordingly to achieve the encryption effect; finally, the matrix is merged to complete Encryption for this step.

S5, using the chaotic sequence and the XOR operation to perform a diffusion operation on the value of the sequence matrix obtained in step S4;

S6. Perform DNA decoding on the sequence matrix obtained in S5 to obtain an encrypted image.

Compared with the prior art, the present invention has the following advantages:

1. The present invention introduces the basic idea of the strand displacement system in the biochemical reaction into the present invention to form a DNA strand displacement model to encrypt the image. Since the process can be started in parallel and has a highly specific recognition site, the encryption model has strong parallelism Computing power and high storage density make encryption more efficient.

2. The present invention not only considers the characteristics such as the sensitivity of the chaotic map to the initial value, but also applies the DNA chain replacement model in the encryption process. The combination of the two enables us to obtain a better encryption effect, and the encryption algorithm can effectively prevent The image is illegally cracked during transmission, which improves the security of digital image transmission.

Description of drawings

Figure 1 Eight encoding and decoding mapping rules for DNA sequences;

Figure 2 XOR operation of DNA sequence;

Figure 3 chain replacement reaction extraction key;

Figure 4 original image;

Figure 5 encrypted image;

Figure 6 decrypts the image;

The gray histogram of the original image of Fig. 7;

The grayscale histogram of Fig. 8 encrypted image;

The correlation of the horizontal direction of the original image in Fig. 9;

The correlation of the horizontal direction of the encrypted image in Fig. 10;

Fig. 11 is a schematic structural diagram of the present invention;

Figure 12 Basic process of strand displacement reaction.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings, and accompanying drawing 11 is the roadmap of the technical solution of the present invention.

The detailed steps are as follows:

Step 1: use the second coding rule as shown in accompanying drawing 1 to carry out DNA coding to the original image as shown in accompanying drawing 4;

Step 2: Calculate the Hamming distance, Hamming inverse distance and Hamming complement distance of the encoded matrix sequence, and convert the obtained values into decimals between 0 and 1; and then use the given initial values x ₀ , y ₀ , z ₀ are added together to generate new initial values x ₁ , y ₁ , z ₁ ; under the conditions of new initial values and system parameters, three chaotic sequences x, y, z are generated, rounded down and then multiplied by the pixel matrix the order of

Step 3: use the chaotic sequence (x, y) to scramble the pixel position of the image;

Step 4: Divide the matrix obtained in step 3 into blocks, the size of each block is 2*4, and use the DNA chain replacement model shown in Figure 12 to extract the key, using a DNA chain as shown in Figure 3 as For example, adopt the XOR operation encryption pixel matrix as shown in accompanying drawing 2;

Step 5: Merge the block matrices after the operation in step 4, and then use the chaotic sequence (y, z) and XOR operation to diffuse the pixel values of the obtained pixel matrix.

Step 6: Using the third DNA decoding rule shown in Figure 1 to decode the matrix sequence, the encrypted image shown in Figure 5 can be obtained.

Step 7: Perform the reverse operation of the encryption process on the encrypted image, and the decrypted image shown in Figure 6 is exactly the same as the original image.

Security analysis: the pixel value of the gray histogram of the original image shown in Figure 7 fluctuates greatly, that is, there are multiple peaks and troughs, indicating that the image is not encrypted and carries a large amount of information. After being encrypted by the algorithm of the present invention, Figure 8 shows the grayscale histogram of the encrypted image. It can be seen that the distribution of pixel values is very uniform and does not carry any useful information.

Figure 9 is a horizontal pixel correlation diagram of the original image, most of the pixels are located on both sides of the median line, indicating a strong correlation. Accompanying drawing 10 is the horizontal direction pixel correlation diagram of the encrypted image, and the distribution of its pixel points is loose, indicating that after encryption, the pixel correlation in the horizontal direction of the image becomes very weak.

Example 1

The embodiments of the present invention are implemented on the premise of the technical solutions of the present invention, and detailed implementation methods and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

Step 1: Convert the original grayscale image of size m*n into a binary matrix; encode the binary matrix according to the second rule of DNA sequence encoding, and obtain a DNA sequence matrix DA of size (m*n) , each element is a 4-digit base sequence;

Step 2: Given any initial value x ₀ , y ₀ , z ₀ , and then add it to Hamming distance, Hamming inverse distance, and Hamming complement distance respectively to obtain new initial values x ₁ , y ₁ , z ₁ , at x ₁ , y ₁ , z ₁ and system parameters σ, ρ, β (typical values σ=10, ρ=8/3, keep σ, ρ constant, and the Lorenz system enters a chaotic state when β>24.74) Under the conditions, use the Lorenz chaotic map to generate three chaotic sequences x=(x ₁ ,x ₂ ,...,x _n ), y=(y ₁ ,y ₂ ,...,y _n ), z=(z ₁ ,z ₂ ,...,z _n ). The equation of the Lorenz chaotic system is as follows:

The chaotic sequence (x, y) is rounded down, the formula is as follows:

Where x(i) is the value of the i-th position in the chaotic sequence x, y(j) is the value of the j-th position in the chaotic sequence y, m is the number of values in the chaotic sequence x, and n is the value in the chaotic sequence y The number of values makes the size of the chaotic sequence consistent with the order of the matrix, which is convenient for subsequent scrambling or diffusion matrices.

Step 3: Use the sequence (x, y) generated above to scramble DA to obtain sequence matrix SA. The formula is as follows:

Step 4: Divide the sequence matrix SA into equal blocks bR{i,j}, i=1,2,...m,j=1,2,...n, where the size of each block is 2* 4. Encrypt the obtained matrix according to the application of the DNA strand displacement model in the encryption process and the XOR operation. Firstly, chain replacement reaction is applied to the key block matrix, and a small part of each of the four DNA chains is replaced as the key block secret block, and then the key block and the encrypted matrix block are XORed to achieve the diffusion matrix sequence the goal of.

CA←secretBlock{}XORbR(i,j)i＝1,2,....m j＝1,2,...n

Combine the matrix blocks bR{i,j} to obtain the matrix sequence CA.

Step 5: Use the chaotic sequence (y, z) and the DNA XOR operation, and perform the XOR operation on the corresponding matrix elements according to the following formula.

XA←CA(i,j)XOR CA(y(i),z(j)); i=1,2...m j=1,2,...n

Step 6: Use the third encoding rule to decode HA to obtain a binary matrix, which is an encrypted image.

When the system parameters σ, ρ, β take the typical values σ=10, ρ=8/3, β=28, the chaotic system enters the chaotic state and can generate three chaotic sequences. Simultaneously take x ₀ =2, y ₀ =3, z ₀ =4 and combine Hamming distance, Hamming inverse distance and Hamming complementary distance to generate new initial values x ₁ , y ₁ , z ₁ .

In summary, this encryption algorithm utilizes the characteristics of the chaotic system being sensitive to the initial value and the highly parallel computing ability of the DNA computing model, and combines the chaotic system with the DNA chain replacement model to realize the encryption of digital images. The encryption effect of the algorithm is good, and the experimental simulation and simulation results show that the method can resist statistical attacks, differential attacks and exhaustive attacks, etc., and is suitable for image protection during image transmission.

The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Anyone familiar with the technical field within the technical scope disclosed in the present invention, according to the technical solution of the present invention Any equivalent replacement or change of its concepts shall fall within the protection scope of the present invention.

Claims (2)

1. the image encryption method based on chaos system Yu DNA chain displacement model, it is characterised in that：Comprise the following steps：

S1, the picture element matrix for obtaining input picture, and encoded with DNA encoding rule, obtain the DNA matrixes of original image；

S2, utilize Lorenz chaotic maps generation chaos sequence (x, y, z)：Give arbitrary initial value x₀,y₀,z₀, calculate in S1 The Hamming distance of obtained sequence matrix, Hamming mend distance against distance and Hamming, and are 0-1 by its value, with x₀,y₀,z₀Successively New initial value x is obtained after addition₁,y₁,z₁；Three chaos sequences are produced then in conjunction with systematic parameter；

S3, the location of pixels with chaos sequence (x, y) scramble image：Chaos sequence (x, y) is rounded downwards, with the sequence newly obtained The location of pixels of row scramble image；

S4, operated with DNA chain displacement to obtain a string of keys, utilize key and XOR diffusion pixel value；

S5, with chaos sequence and XOR operation is diffused again to the value of the obtained sequence matrix of step S4；

S6, the sequence matrix obtained to S5 carry out DNA decodings and can obtain encrypted image.

2. the image encryption method according to claim 1 based on chaos system Yu DNA chain displacement model, its feature exist In：The process of the step S4 is as follows：

First, picture element matrix piecemeal step S3 obtained, the size of each fritter is 2*4；Then, key block application chain is put Reaction is changed, displaces four short DNA sequence dnas as encryption key；Matrix-block is encrypted successively using obtained key： Partial dna sequence in 4 DNAs in key block and encrypted block is subjected to the effect that XOR reaches encryption respectively； Finally, matrix is merged to the encryption for the step for completing.