CN113837916A - Chaos system based recombinant scrambled DNA coding image encryption algorithm - Google Patents

Chaos system based recombinant scrambled DNA coding image encryption algorithm Download PDF

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CN113837916A
CN113837916A CN202111035206.4A CN202111035206A CN113837916A CN 113837916 A CN113837916 A CN 113837916A CN 202111035206 A CN202111035206 A CN 202111035206A CN 113837916 A CN113837916 A CN 113837916A
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叶汉民
苏可琴
黄仕明
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Guilin University of Technology
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Abstract

The invention discloses a chaos system-based recombinant scrambled DNA coding image encryption algorithm. And changing the pixel position of the carrier image through double scrambling operations of image random block recombination and cat face transformation. And (3) introducing the logistic mapping to generate a chaotic sequence as a diffusion sequence of an encryption algorithm, and respectively carrying out DNA coding and operation to obtain a final encrypted image. Experimental results show that the recombinant scrambling DNA coding image encryption algorithm based on the chaotic system can resist known plaintext attack and differential attack, the mean value of the pixel change rate (NPCR) of an encrypted image is 99.61%, the mean value of uniform average change strength (UACI) is 33.44%, and the encryption algorithm has good safety.

Description

Chaos system based recombinant scrambled DNA coding image encryption algorithm
Technical Field
The invention belongs to the crossing field of information security, digital image processing and secrecy, and the subject content is a recombinant scrambled DNA coding image encryption algorithm based on a chaotic system, and the encryption algorithm has good security.
Background
In the digital age, the storage and transmission of multimedia data become easy, but the issue of how to ensure the security of private information becomes more and more important. The image is the most intuitive and main way for people to obtain information, and the data transmitted by global internet users through the internet every day is huge, so the research focus in this document is the research on the method for the secret transmission and storage of digital images. The image encryption technology can prevent the plaintext information of the image from being disclosed, so that the privacy information is protected, and an attacker cannot acquire the image information under the condition of not knowing a decryption key, thereby achieving the effect of protecting the image information, and therefore, the image encryption technology can effectively ensure the safety of the information.
Disclosure of Invention
The traditional method has obvious defects, and the frequency domain encryption generally belongs to lossy encryption, so that the traditional image encryption algorithm has the risk of image information leakage, and the recombinant scrambling DNA coding image encryption algorithm based on the chaotic system is provided for solving the problems.
The main technical scheme comprises: according to the excellent encryption performance of scrambling-diffusing performance of the current encryption algorithm, preprocessing of random block recombination is carried out on a plaintext image, the position of each small block of image is changed, double encryption is carried out on the image through cat face transformation and logistic mapping chaos, the final encrypted image is obtained, and a new encryption scheme is provided for an image encryption method.
Experimental results show that the recombinant scrambling DNA coding image encryption algorithm based on the chaotic system can resist known plaintext attack and differential attack, the mean value of the pixel change rate (NPCR) of an encrypted image is 99.61%, the mean value of uniform average change strength (UACI) is 33.44%, and the encryption algorithm has good safety.
Drawings
Fig. 1 is a main architecture of an encryption algorithm.
Fig. 2 is a block recomposed image.
Fig. 3 is a graph of the encryption result of cat face transformation with different iteration numbers.
Fig. 4 is a graph of the face transform scrambling result.
Fig. 5 is a graph of chaotic encryption results.
Figure 6 is a flow chart of an encryption algorithm.
Fig. 7 is an experimental image.
Fig. 8 is an encrypted image.
FIG. 9 is (a-d) original image histogram (e-h) scrambled encrypted image histogram (i-l) chaotic encrypted image histogram (m-p) text encrypted image histogram.
FIG. 10 is (a-c) encrypted Lena neighbor correlation (d-f) encrypted Baboon neighbor correlation (g-i) encrypted Barbara neighbor correlation (j-l) encrypted Cameraman neighbor correlation.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
The main frame diagram of the invention is shown in figure 1, and the method is a chaos system-based recombinant scrambled DNA coding image encryption algorithm, and specifically comprises the following processes:
the method comprises the following steps: image block recombination
Firstly, preprocessing a plaintext image, averagely dividing an original plaintext image with the size of M multiplied by N into a plurality of parts with the same size, randomly disordering the divided parts, and then recombining the parts to obtain a recombined image.
Step two: arnold scrambling procedure
And (4) according to the set parameters a and b, carrying out movement with the iteration number of n1 on the recombined image pixel by using a scrambling formula.
And converting the pixel gray value of the scrambled image into a corresponding 8-bit binary sequence, scanning from left to right in an S-shaped mode from the first pixel of the image according to the coding rule of the table 1, carrying out DNA coding to obtain a 4-bit DNA sequence, and putting the 4-bit DNA sequence into an array with the length of M multiplied by N.
TABLE 1 DNA sequence coding rules
Figure RE-GDA0003375841490000021
And (3) cat face (Arnold) transformation, wherein all pixel coordinates in the image are replaced into new coordinates through cat face transformation, and the image pixel position is changed to realize image scrambling encryption. The formula is as follows:
Figure RE-GDA0003375841490000031
where (X, Y) is the pixel point of the image to be converted, (X, Y) is the converted coordinate of the pixel (X, Y), mod () is the modulo operation, and N is the order of the original image matrix (2):
Figure RE-GDA0003375841490000032
when the value of md-nc is 1, the transformation of the image pixel coordinate can be regarded as scrambling transformation in the same way. Selecting cat face transformation with simple operation to carry out scrambling process of the recombined image, and giving a to 3; and b is 5, namely m is 16, n is-3, c is-5, d is 1, the iteration number is selected for 10 times, and the reconstructed Lena image (256 × 256 pixels) is scrambled by cat face transformation through formula (1) to obtain the encrypted image.
Step three: logistic chaos mapping
Generating a Logistic chaotic sequence according to a set parameter u, selecting a number with the middle length of M multiplied by N in the sequence to obtain better randomness, converting the selected chaotic sequence into an integer within the range of 0-255, and then obtaining a corresponding 8-bit binary chaotic sequence.
The method selects a Logistic mapping as a diffusion sequence for image encryption, generates a Logistic chaotic sequence according to a formula (3) and set parameters, and introduces DNA codes in the diffusion stage of scrambling images.
m(k+1)＝u×m(k)(1-m(k)) (3)
Wherein m (k) belongs to (0, 1), 0< u < ═ 4, and by utilizing the characteristic that the logistic mapping is sensitive to the initial value, a chaos sequence with a long length can be obtained and can be used as an encryption sequence of a large-data-volume image.
The basic principle and the steps of image encryption by using the logistic chaotic mapping are as follows:
(1) generating a one-dimensional chaotic mapping sequence M (i) according to the basic definition of the logistic chaotic mapping, wherein the length is M multiplied by N;
(2) and performing exclusive or operation on the generated one-dimensional chaotic sequence m (i) and the preprocessed image pixel w (i) according to a formula (4):
Figure RE-GDA0003375841490000033
step four DNA encoding
DNA coding was performed sequentially according to the coding rules of Table 1, and the 4-bit DNA sequence was also obtained. The two obtained DNA coding sequences are divided into 8 groups of small segments with the same length, and the DNA sequence operation with the set number of times of n2 is carried out among the small segments according to a random key 2.
Fifthly, generating an encryption result graph
And finally, converting the operated DNA sequence into a pixel matrix with the pixel value of the same, and obtaining a final encrypted image.
Method test
In the simulation experiment, 6 gray images of 512 multiplied by 512Lena, Baboon, Barbara and the like are selected as processing images.
In order to verify the performance of the algorithm proposed by the experiment, the performances of the histogram of the encryption algorithm, UACI, NPCR, pixel correlation, key space and the like are analyzed respectively.
The image encryption algorithm should make the pixel gray value of the encrypted image uniformly distributed as much as possible, i.e. the histogram of the ciphertext image tends to be stable, and the pixel value distribution rule of the ciphertext image is covered, so that the difficulty of an attacker in constructing the transformation relation between the plaintext image and the ciphertext image is increased, and the security of the encryption algorithm is improved. FIG. 9 shows histograms of four original images, Lena, Baboon, Cameraman and Peppers, and histograms of encrypted images of chaotic and text encryption algorithms, respectively, by face transform, logistic mapping.
The differential attack means that an attacker slightly changes the original plaintext image M, and when the difference between the encrypted images A and B is extremely large, the attacker is particularly difficult to use the differential attack. Table 2 shows that the NPCR and UACI of six images obtained by recombining the scrambling DNA coding encryption algorithm based on the chaotic system are almost the same as the ideal values, which means that the encryption algorithm generates completely different encrypted images and the effect of resisting differential attack is ideal.
TABLE 2 NPCR and UACI for encryption algorithm
TABLE 1 NPCR and UACI for encryption algorithms
Figure RE-GDA0003375841490000041
The image pixel correlation coefficient is also an important evaluation index for evaluating an image encryption algorithm, and the pixel correlation refers to the relation between adjacent pixels of an image. Fig. 10 shows the correlation of adjacent pixels in the horizontal, vertical, diagonally opposite directions of the encrypted image Lena, Baboon, Barbara, Cameraman of the algorithm.
Key space refers to a range of encryption key sizes, typically counting unique keys in bits, i.e., by how many bits. The longer the bits of the key, the larger the key space, which is one of the important indicators to measure whether the encryption algorithm can resist the exhaustive attack.
In the process of reorganization and scrambling, a reorganized random key1, parameters a and b of a scrambled image, scrambling iteration times n1, a chaotic sequence parameter u, a coding rule and coding operation adopted need to be set, the random key2 and the diffusion times n2 are 64 bits of a computer used for an encryption simulation experiment, key1, a, b, n1, u, key2 and n2 are double-precision floating point type data, 8 selectable DNA coding rules and 3 DNA operation modes are provided, a key space of the reorganization and scrambling DNA coding encryption algorithm based on the chaotic system is calculated to be 3 multiplied by 2451 which is far larger than 2100, the possibility of exhaustively attacking and decrypting the image is almost eliminated by a super key space, and the security guarantee of image encryption is provided.

Claims (2)

1. A chaos system-based recombinant scrambled DNA coding image encryption algorithm is characterized in that the pixel position of a carrier image is changed through double scrambling operations of random block recombination and cat face transformation of an image; introducing a logistic mapping to generate a chaotic sequence as a diffusion sequence of an encryption algorithm, and respectively carrying out DNA coding and operation to obtain a final encrypted image; experimental results show that the recombinant scrambling DNA coding image encryption algorithm based on the chaotic system can resist known plaintext attack and differential attack, the mean value of the pixel change rate (NPCR) of an encrypted image is 99.61%, the mean value of uniform average change strength (UACI) is 33.44%, and the encryption algorithm has good safety.
2. The chaotic system-based recombinant scrambled DNA coded image encryption algorithm according to claim 1, characterized in that the method specifically comprises the following steps:
the method comprises the following steps: image block recombination
Firstly, preprocessing a plaintext image, averagely dividing an original plaintext image with the size of M multiplied by N into a plurality of parts with the same size, randomly disordering the divided parts, and then recombining the parts to obtain a recombined image;
step two: arnold scrambling procedure
Moving the recombined image pixels by a scrambling formula according to the set parameters a and b, wherein the iteration number of the recombined image pixels is n 1;
converting the pixel gray value of the scrambled image into a corresponding 8-bit binary sequence, scanning from left to right in an S shape from the first pixel of the image according to the coding rule of table 1, carrying out DNA coding to obtain a 4-bit DNA sequence, and putting the 4-bit DNA sequence into an array with the length of M multiplied by N;
transforming a cat face (Arnold), namely replacing all pixel coordinates in the image into new coordinates through cat face transformation, and changing the pixel positions of the image to realize image scrambling encryption; the formula is as follows:
Figure FDA0003246886230000011
where (X, Y) is the pixel point of the image to be converted, (X, Y) is the converted coordinate of the pixel (X, Y), mod () is the modulo operation, and N is the order of the original image matrix (2) is the 2 nd order matrix as shown in equation (2):
Figure FDA0003246886230000012
when the value of md-nc is 1, the transformation of the image pixel coordinate can be regarded as scrambling transformation in the same way; selecting cat face transformation with simple operation to carry out scrambling process of the recombined image, and giving a to 3; b is 5, namely m is 16, n is-3, c is-5, d is 1, the iteration number is selected for 10 times, and the reconstructed Lena image (256 × 256 pixels) is scrambled by cat face transformation through a formula (1) to obtain an encrypted image;
step three: logistic chaos mapping
Generating a Logistic chaotic sequence according to a set parameter u, selecting a number of sequences with the middle length of M multiplied by N to obtain better randomness, converting the selected chaotic sequence into an integer within the range of 0-255, and then obtaining a corresponding 8-bit binary chaotic sequence;
the method comprises the steps of selecting a Logistic mapping as a diffusion sequence for image encryption, generating a Logistic chaotic sequence according to a formula (3) and set parameters, and introducing DNA codes in a diffusion stage of scrambling an image;
m(k+1)＝u×m(k)(1-m(k)) (3)
wherein m (k) belongs to (0, 1), 0< u < ═ 4, and by utilizing the characteristic that the logistic mapping is sensitive to the initial value, a chaos sequence with a long length can be obtained and can be used as an encryption sequence of a large data volume image;
the basic principle and the steps of image encryption by using the logistic chaotic mapping are as follows:
(1) generating a one-dimensional chaotic mapping sequence M (i) according to the basic definition of the logistic chaotic mapping, wherein the length is M multiplied by N;
(2) and performing exclusive or operation on the generated one-dimensional chaotic sequence m (i) and the preprocessed image pixel w (i) according to a formula (4), wherein the formula is as follows:
Figure FDA0003246886230000021
step four DNA encoding
DNA coding is carried out according to the coding rule of the table 1 in sequence, and 4-bit DNA sequences are also obtained;
dividing the obtained two DNA coding sequences into 8 groups of small segments with the same length, and performing DNA sequence operation with set times of n2 according to a random key 2;
step five: generating an encrypted image
And finally, converting the operated DNA sequence into a pixel matrix with the pixel value of 0,255 to obtain the final encrypted image.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114615392A (en) * 2022-03-18 2022-06-10 东北大学 Image encryption method based on bit linkage

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CN108898025A (en) * 2018-06-25 2018-11-27 河南大学 New chaotic image encryption method based on dual scramble and DNA encoding
CN112287362A (en) * 2020-09-21 2021-01-29 南昌大学 Color image encryption algorithm based on DNA coding and double chaotic systems
CN113225449A (en) * 2021-05-27 2021-08-06 郑州轻工业大学 Image encryption method based on chaos sequence and DNA coding

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CN108898025A (en) * 2018-06-25 2018-11-27 河南大学 New chaotic image encryption method based on dual scramble and DNA encoding
CN112287362A (en) * 2020-09-21 2021-01-29 南昌大学 Color image encryption algorithm based on DNA coding and double chaotic systems
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