CN108122188B - Image encryption method - Google Patents

Image encryption method Download PDF

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CN108122188B
CN108122188B CN201810031169.1A CN201810031169A CN108122188B CN 108122188 B CN108122188 B CN 108122188B CN 201810031169 A CN201810031169 A CN 201810031169A CN 108122188 B CN108122188 B CN 108122188B
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dna
image
scrambling
dna sequence
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CN108122188A (en
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陈建铭
吴祖扬
范晓宁
王景行
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Shenzhen Graduate School Harbin Institute of Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T1/00—General purpose image data processing
    • G06T1/0021—Image watermarking
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2201/00—General purpose image data processing
    • G06T2201/005—Image watermarking
    • G06T2201/0053—Embedding of the watermark in the coding stream, possibly without decoding; Embedding of the watermark in the compressed domain

Abstract

The invention discloses an image encryption method, which combines chaotic mapping and DNA coding to encrypt a plaintext image and comprises the following steps: generating an initial key; generating a chaotic sequence and a scrambling vector by using an initial key; scrambling and encrypting the plaintext image by using the scrambling vector to obtain a scrambled image; performing DNA coding on the chaotic sequence to obtain a first DNA sequence, and performing DNA coding on the scrambled image to obtain a second DNA sequence; performing diffusion encryption on the DNA sequence by using the first DNA sequence to obtain a third DNA sequence; and performing DNA decoding on the third DNA sequence to obtain a ciphertext image.

Description

Image encryption method
Technical Field
The present application relates to an image encryption processing technique.
Background
In modern life, with the rapid development of the internet, people can publish information through the network all the time, and although great convenience is brought to our life, we are also faced with the situation that a large amount of data is leaked and tampered. Especially, the use and dissemination of a large amount of image information causes more and more people to pay attention to the information security problem. Secure image encryption techniques are relied upon in scenarios such as military operations, electronic commerce, medical systems, and real-time monitoring. Therefore, how to ensure the security of the image information has become an important issue of public attention.
There is no algorithm in cryptography that is specific to the particular data type, digital image, that is, encryption. The encryption algorithm is used for encrypting plaintext data into ciphertext data, so that an attacker cannot obtain useful information from the ciphertext data, and the purpose of confidentiality is achieved. However, mainstream Encryption algorithms such as Advanced Encryption Standard (AES) and International Data Encryption Algorithm (IDEA) are mainly used for encrypting text Data. For digital images, it is necessary to convert an encrypted image into one-dimensional binary data and then perform data encryption processing as a binary stream. However, the digital image has the characteristics of two-dimensional distribution, high redundancy between adjacent pixels, large data volume and the like, so the characteristics of the digital image per se should be fully considered in the encryption process. The mainstream encryption algorithm is slow in encryption speed and low in efficiency for images with large data volume, and is not suitable for real-time encryption.
In recent years, chaos mapping (Chaotic Map) has characteristics of ergodicity, pseudo-randomness, high sensitivity to initial conditions and control parameters, and the like, and is low in implementation cost. These characteristics make chaotic mapping widely accepted by a large number of scholars as being suitable for image encryption techniques. With the development of DNA research, a large number of scholars have applied DNA sequences as information carriers in the field of image encryption. Therefore, the use of chaotic mapping and DNA coding in image encryption is gaining more and more attention.
Disclosure of Invention
The invention aims to provide an image encryption algorithm which is realized in the aspects of safety and time efficiency.
The invention provides an image encryption method, which combines chaotic mapping and DNA coding to encrypt a plaintext image, and preferably comprises the following steps:
generating an initial key;
generating a chaotic sequence and a scrambling vector by using an initial key;
scrambling and encrypting the plaintext image by using the scrambling vector to obtain a scrambled image;
performing DNA coding on the chaotic sequence to obtain a first DNA sequence, and performing DNA coding on the scrambled image to obtain a second DNA sequence;
performing diffusion encryption on the second DNA sequence by using the first DNA sequence to obtain a third DNA sequence; and
and performing DNA decoding on the third DNA sequence to obtain a ciphertext image.
Preferably, the chaotic sequence is generated based on a first initial key, a third control parameter and a first constant, and the scrambling vector is generated based on a second initial key, a fourth control parameter and a second constant.
Preferably, the initial key for generating the plaintext image P (m, n) is calculated by formula (1)
Figure BDA0001546508660000025
Figure BDA0001546508660000021
Wherein alpha is1And beta1First and second control parameters, respectively, w can be obtained by equation (2):
Figure BDA0001546508660000022
preferably, the chaotic sequence is generated by the following steps
Figure BDA0001546508660000023
The first initial key (y)1(0),y2(0),y3(0),y4(0) And a first set of control parameters a, b, c, d, k as input values to equation (3), iterate the Gao hyperchaotic map to produce a first discrete sequence yk(k＝1,2,3,4)；
Figure BDA0001546508660000024
The first discrete sequence yk(k ═ 1,2,3,4) the first pseudorandom sequence is obtained by combining equation (4)
Figure BDA0001546508660000031
And
Figure BDA0001546508660000032
applying the first pseudo-random sequence
Figure BDA0001546508660000033
The first N1 pseudo random numbers are truncated and the result is expressed by equation (5)
Figure BDA0001546508660000034
The first m x n number of (a) is converted into an integer sequence between 0 and 255
Figure BDA0001546508660000035
Figure BDA0001546508660000036
Preferably, the scrambling vectors are generated by the following steps, including a row scrambling vector H and a column scrambling vector L:
second initial key
Figure BDA0001546508660000037
And a second set of control parameters a, b, c, d, k as input values to the hyperchaotic mapping equation (3), iterating the hyperchaotic mapping to produce a second discrete sequence
Figure BDA0001546508660000038
Figure BDA0001546508660000039
The second discrete sequence is divided into
Figure BDA00015465086600000310
The second pseudo-random sequence is obtained by combining the following formula (6)
Figure BDA00015465086600000311
Figure BDA00015465086600000312
Applying the second pseudo-random sequence
Figure BDA00015465086600000313
Front N of2A pseudo-random sequence is dropped, to
Figure BDA00015465086600000314
And
respectively to be provided with
Figure BDA00015465086600000315
Sorting according to ascending order, and sorting the sorted sourcesThe sequence of starting subscript values are stored separately as row scrambling vectors
Figure BDA00015465086600000316
Sum and column scrambling vectors
Figure BDA00015465086600000317
Preferably, the scrambling vector includes a row scrambling vector and a column scrambling vector, and scrambling and encrypting the plaintext image using the scrambling vector includes: scrambling the plaintext image by using the line scrambling vector; and performing row scrambling processing on the image subjected to the row scrambling processing by using the row scrambling vector.
Preferably, the DNA encoding of the chaotic sequence comprises: converting the chaotic sequence into a first binary sequence; and DNA encoding the first binary sequence according to a first mapping relation of a predetermined DNA encoding rule;
DNA encoding the scrambled image comprises: converting the scrambled image into a second binary sequence according to a predetermined conversion rule; and carrying out DNA coding on the second binary sequence according to a second mapping relation of the DNA coding rule.
Preferably, the performing diffusion encryption on the second DNA sequence using the first DNA sequence comprises:
using the first DNA sequence R by the formulae (7) and (8)eAnd a predetermined addition and XOR operation rule on the second DNA sequence Pe'performing a diffusion operation to obtain a third DNA sequence C':
Figure BDA0001546508660000041
Figure BDA0001546508660000042
preferably, the DNA decoding of the third DNA sequence comprises:
performing DNA decoding on the DNA sequence according to a third mapping relation of the DNA coding rule, and converting the DNA sequence into a one-dimensional binary sequence; and
and converting the one-dimensional two-step processing sequence into a pixel value of a ciphertext image according to the preset conversion rule.
The embodiment of the invention has the advantages of safety, time efficiency, large key space, strong key sensitivity, strong capability of resisting statistical attack and differential attack, low possibility of information leakage, low time complexity and the like.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments of the present invention will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without inventive exercise.
FIG. 1 illustrates an image encryption method according to an embodiment of the present invention;
FIG. 2 illustrates an image encryption method according to another embodiment of the present invention;
FIG. 3 is a graph of key sensitivity testing for the method of FIG. 2;
fig. 4 is a histogram of a plaintext image and a ciphertext image of the method shown in fig. 2.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar components or components having the same or similar functions throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The invention provides an image encryption method (IEHDC for short) based on hyperchaotic mapping and DNA coding, which combines the hyperchaotic mapping and the DNA coding and has higher safety than the single use of one of the technologies.
An embodiment of the present invention provides an image encryption method, including: and (4) encrypting the plaintext image by combining the chaotic mapping with the DNA coding. Referring to fig. 1, the encrypting the plaintext image by combining the chaos mapping and the DNA encoding includes:
ST1, generating an initial key;
ST2, generating a chaos sequence and a scrambling vector by using the initial key;
ST3, scrambling and encrypting the plaintext image by using the scrambling vector to obtain a scrambled image;
ST4, carrying out DNA coding on the chaotic sequence to obtain a first DNA sequence, and carrying out DNA coding on the scrambled image to obtain a second DNA sequence;
ST5, diffusion-encrypting the second DNA sequence by using the first DNA sequence to obtain a third DNA sequence; and
ST6, and carrying out DNA decoding on the third DNA sequence to obtain a ciphertext image.
Fig. 2 shows an image encryption method according to another embodiment of the present invention, in which a plaintext image to be encrypted is P (m, n), the method includes:
s1, generating partial initial key
Figure BDA0001546508660000051
Part of the initial key can be calculated by formula (1)
Figure BDA0001546508660000052
Figure BDA0001546508660000053
Wherein alpha is1And beta1For controlling the parameter, w can be obtained by equation (2).
Figure BDA0001546508660000054
S2, generating chaos sequence
Figure BDA0001546508660000055
The chaotic sequence may be generated through the following steps S21-S23
Figure BDA0001546508660000056
S21, the first initial key (y)1(0),y2(0),y3(0),y4(0) And a first set of control parameters a, b, c, d, k as input values to equation (3), iterate the Gao hyperchaotic map to produce a first discrete sequence yk(k is 1,2,3, 4). Wherein the first initial key (y)1(0),y2(0),y3(0),y4(0) ) may be custom generated.
Figure BDA0001546508660000061
In one example, the mapping may enter a hyper-chaotic state when a-36, b-3, c-28, d-16, and-0.7 ≦ k ≦ 0.7.
S22, mapping the iteration Gao hyperchaotic to generate a first discrete sequence yk(k is 1,2,3,4), and the first pseudo-random sequence is obtained by combining the formula (4)
Figure BDA0001546508660000062
Figure BDA0001546508660000063
S23, converting the first pseudo-random sequence into a first pseudo-random sequence
Figure BDA0001546508660000064
The first N1 pseudo random numbers are truncated and the result is expressed by equation (5)
Figure BDA0001546508660000065
The first m x n number of (a) is converted into an integer sequence between 0 and 255
Figure BDA0001546508660000066
Figure BDA0001546508660000067
S3, generating scrambling vectors H and L; the scrambling vectors H and L may be generated through steps S31 to S34.
S31, second initial key
Figure BDA0001546508660000068
And a second set of control parameters a, b, c, d, k as input values to the hyperchaotic mapping equation (3), iterating the hyperchaotic mapping to produce a second discrete sequence
Figure BDA0001546508660000069
Wherein the second initial key
Figure BDA00015465086600000610
May be custom generated.
S32, generating a second discrete sequence by mapping the iteration Gao hyperchaotic
Figure BDA00015465086600000611
Obtaining a second pseudo-random sequence by combining the formula (6)
Figure BDA00015465086600000612
Figure BDA00015465086600000613
S33, converting the second pseudo-random sequence
Figure BDA0001546508660000071
Front N of2A pseudo-random sequence is dropped, to
Figure BDA0001546508660000072
S34, respectively
Figure BDA0001546508660000073
Sorting according to ascending order, and respectively storing the sorted sequences of the original subscript values as row scrambling vectors
Figure BDA0001546508660000074
Sum and column scrambling vectors
Figure BDA0001546508660000075
S4, scrambling and encrypting the plaintext image P (m, n) by using the scrambling vectors H and L to obtain an encrypted scrambled image P' (m, n); the scramble encryption may be performed through steps S41 and S42.
S41, line scrambling: using line scrambling vectors
Figure BDA0001546508660000076
Moving each line H (i) in the plaintext image P (m, n) to the i ∈ [1, m ]]A row;
s42, a column scrambling process: using column scrambling vectors
Figure BDA0001546508660000077
Moving each column L (j) in the row-scrambled image to the j ∈ [1, n ]]And (4) columns.
S5, aiming at the chaotic sequence
Figure BDA0001546508660000078
And DNA encoding the scrambled images P' (m, n) to obtain a first DNA sequence ReAnd a second DNA sequence Pe′；
Wherein, for the chaotic sequence
Figure BDA0001546508660000079
Performing DNA encoding includes: will chaos sequence
Figure BDA00015465086600000710
Conversion into binary sequences RbThen the binary sequence RbFirst mapping map according to Table 11Carrying out DNA coding to obtain a first DNA sequence Re。
The DNA encoding of the scrambled image P' (m, n) includes: converting P '(m, n) into a one-dimensional binary sequence P in the order of' from top to bottom and from left to rightb', then the binary sequence Pb' second mapping map according to Table 12Carrying out DNA coding to obtain a second DNA sequence Pe′。
Wherein, map is more than or equal to 11,map2≤8，map1And map2May be optional from the 8 encoding rules of table 1, and may or may not be the same.
TABLE 1 8 coding rules for DNA coding
Figure BDA00015465086600000711
S6, Using the first DNA sequence ReFor the second DNA sequence Pe'performing diffusion encryption to obtain a third DNA sequence C';
p can be paired by formula (7) and formula (8)e'conducting a diffusion operation to obtain C'. The rules of addition and exclusive-or after DNA encoding are shown in tables 2 and 3.
Figure BDA0001546508660000081
Figure BDA0001546508660000082
TABLE 2 rules of addition of DNA sequences
Figure BDA0001546508660000083
TABLE 3 rule of XOR operation for DNA sequences
Figure BDA0001546508660000084
S7, carrying out DNA decoding on the third DNA sequence C' to obtain a ciphertext image C (m, n); the DNA decoding may be performed through steps S71 and S72.
S71, according to the third mapping relation map of Table 13And performing DNA decoding on the third DNA sequence C' and converting into a one-dimensional binary sequence. Wherein map is3May be optionally selected from the 8 coding rules of Table 1, with map1Or map2May be the same or different.
S72, converting the binary sequence subjected to the DNA decoding conversion into pixel values; the ciphertext image C (m, n) with the size of m × n may be converted in the order of "from top to bottom, left to right".
The embodiment of the invention has the advantages of large key space, strong key sensitivity, strong capability of resisting statistical attack and differential attack, low possibility of information leakage, low time complexity and the like.
(1) Key space
A good image encryption algorithm should be able to resist brute force attacks. Since an attacker cannot decrypt the ciphertext by exhausting all keys for a limited time only if the key space is large enough. At this point, the algorithm is fully resistant to brute force attacks. In this algorithm, the initial key has y1(0),y2(0),y3(0),y4(0),map1,map2,map3,k1,k2,N1,N2,α1,
Figure BDA0001546508660000091
And the like. If the key precision is set to be 10-15, the key space of the algorithm is at least 1015×14×83≈2709. In general, we consider that when the key space of an algorithm is greater than 2100The encryption algorithm can resist brute force attacks. But with the rapid development of computer hardware, the larger the key space, the higher the security against brute force attacks. Thus, the key space of IEHDC is large enough to resist brute force attacks.
(2) Key sensitivity
To ensure to addThe security of the cryptosystem should be analyzed in both the encryption phase and the decryption phase. A good encryption system should be extremely sensitive to the key. That is, small changes in the key can cause differences in image encryption and decryption. To test IEHDC, the plaintext is encrypted in an encryption phase using a set of keys G, one of which is a key
Figure BDA0001546508660000092
The ciphertext is decrypted using a key set K that is slightly different from G, where
Figure BDA0001546508660000093
The other keys are not changed and the resulting decrypted image should be very different from the original image.
In this regard, we performed a key sensitivity test in which the encryption algorithm of IEHDC was tested, taking "Flower", "Fruit", "Girl" and "Tree" as examples. And encrypting the plaintext image by using the key group of G, and decrypting the ciphertext image by using the key group of K. The results of the experiment are shown in FIG. 3. It follows that the image decrypted using a key that differs only slightly from the correct key is completely different from the original image, yielding hardly any useful information. And the image decrypted using the correct key is identical to the original image. This shows that our proposed encryption algorithm is very sensitive to the key.
(3) Histogram analysis
Histogram analysis is a very important feature in image analysis. Theoretically, a good image encryption algorithm can withstand various statistical attacks. The histogram reflects the distribution of the number of pixels of the image at the gray level. The smoother the histogram of the ciphertext image, the better the encryption effect. Therefore, the ciphertext image and the original image have almost no statistical similarity, and the information of the original image can be effectively prevented from being leaked through statistical attack. As shown in fig. 4, histograms of plaintext images exemplified by "Boats", "Fruit", "Tree", and "Baboon" and histograms of corresponding ciphertext images encrypted by IEHDC. It is clear that the histograms of all plaintext images have significant pixel value characteristics and are therefore vulnerable to statistical attacks. The histogram distribution of the ciphertext image is not uneven and is very uniform, and the characteristics contained in the plaintext image are effectively eliminated. Thus, the ciphertext image may not provide any useful information to an attacker for use in a statistical attack analysis process. This shows that the IEHDC proposed by the present invention has a strong ability to resist statistical attacks.
(4) Correlation analysis
In image processing, correlation analysis is often used to test the correlation between two adjacent pixels. We know that there is a high correlation between adjacent pixels in the plaintext image. Therefore, a good image encryption algorithm should be able to eliminate this correlation to resist various statistical attacks. Table 4 shows correlation coefficients of adjacent pixels in each plaintext image and the corresponding ciphertext image encrypted by IEHDC calculated by equations (9) to (12). It can be seen that all plaintext images have correlation coefficients close to 1, while their ciphertext images have correlation coefficients almost equal to 0. When the correlation coefficient of the image is closer to 0, the encryption effect of the algorithm is better. Therefore, IEHDC has a good effect in eliminating the correlation between pixels.
Figure BDA0001546508660000101
Figure BDA0001546508660000102
Figure BDA0001546508660000103
Figure BDA0001546508660000104
TABLE 4 correlation coefficient between adjacent pixels of IEHDC plain text and corresponding cipher text
Figure BDA0001546508660000105
Figure BDA0001546508660000111
Taking "Baboon", "barbarbara", "Flower", "Dog", "Fruit", and "Girl" as examples, table 5 shows the pixel distribution of each plaintext image and the corresponding ciphertext image encrypted by IEHDC in the horizontal, vertical, and diagonal directions. It can be seen that the pixel value distribution of all the plaintext images in different directions is dense, which shows that the plaintext has high correlation and obvious characteristics. The pixel value distribution of the ciphertext image is scattered, which shows that the correlation of the ciphertext image is very low. The encryption algorithm successfully eliminates high correlation in a plaintext image, and can effectively resist various statistical attacks.
TABLE 5 correlation of neighboring pixels
Figure BDA0001546508660000112
Figure BDA0001546508660000121
Table 5 (continuation watch)
Figure BDA0001546508660000122
Figure BDA0001546508660000131
(5) Information entropy analysis
In information theory, information entropy is the most important randomness measure. The calculation formula of the information entropy can be expressed as formula (13):
Figure BDA0001546508660000132
assuming 28 states for the information source, then:
Figure BDA0001546508660000133
where n represents the number of pixel values to be counted, mi represents the pixel value, and p (mi) represents the probability of occurrence of the symbol mi. From the above formula, we can know that in a gray image in units of pixels, when all pixel values are uniformly distributed, the pixels are independent of each other, and the information entropy is 8 at maximum. Therefore, the ideal value of the information entropy of the encrypted image should be 8. The closer to 8, the less likely an attacker will crack.
As can be seen from table 6, the entropy of the IEHDC-encrypted image is close to 8, which indicates that the randomness of the pixel value distribution of the ciphertext image is very strong. Therefore, the possibility of leaking information is very small.
TABLE 6 information entropy of plaintext and corresponding ciphertext images of IEHDC
Figure BDA0001546508660000134
(6) Differential attack
The differential attack means that when the original image is slightly changed, the encrypted ciphertext is compared with the ciphertext encrypted by the original image and analyzed, and the relation between the original image and the encrypted image is obtained. If an original image is slightly changed, the obtained ciphertext is different from the original ciphertext, and the algorithm can resist differential attack. Table 7 shows the NPCR and UACI values of ciphertexts encrypted by the IEHDC encryption algorithm for different images through the calculations of equations (15) and (17). From the above, we can find that the values of the NPCR and UACI parameters of the ciphertext encrypted by the IEHDC are close to 100% and 33.5%, respectively, which indicates that the IEHDC has a good encryption effect, and when the IEHDC is used to encrypt two slightly different plaintext images, the two obtained ciphertext images have a great difference. This effectively avoids the possibility that an attacker wants to obtain valid information of the plaintext by comparing the ciphertext differences.
Figure BDA0001546508660000141
Figure BDA0001546508660000142
Figure BDA0001546508660000143
TABLE 7 comparison of different algorithms for each image NPCR
Figure BDA0001546508660000144
(7) Temporal complexity analysis
The time complexity is mainly used for testing the time required by the algorithm to encrypt the image. On the premise of algorithm safety, the time complexity of the encryption algorithm should be as small as possible, so that the encryption speed can be increased, and the user experience can be improved. In IEHDC, the scrambling encryption process needs to generate m + n pseudo-random keystream. In the diffusion encryption process (m × n) pseudo-random key streams are required. Both processes require only one cycle to complete. Therefore, IEHDC has a temporal complexity of o (n).
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" or the like, mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing is a more detailed description of the present invention that is presented in conjunction with specific embodiments, and the practice of the invention is not to be considered limited to those descriptions. It will be apparent to those skilled in the art that a number of simple derivations or substitutions can be made without departing from the inventive concept.

Claims (6)

1. An image encryption method, characterized in that a chaos mapping is combined with a DNA coding to encrypt a plaintext image, wherein the combining the chaos mapping with the DNA coding to encrypt the plaintext image comprises:
generating an initial key, and calculating and generating a partial initial key by formula (1)
Figure FDA0002980028230000011
Figure FDA0002980028230000012
Wherein alpha is1And beta1First and second control parameters, respectively, w can be obtained by equation (2):
Figure FDA0002980028230000013
generating a chaotic sequence and a scrambling vector by using the initial key;
scrambling and encrypting the plaintext image by using the scrambling vector to obtain a scrambled image;
performing DNA coding on the chaotic sequence to obtain a first DNA sequence, and performing DNA coding on the scrambled image to obtain a second DNA sequence;
performing diffusion encryption on the second DNA sequence by using the first DNA sequence to obtain a third DNA sequence; and
performing DNA decoding on the third DNA sequence to obtain a ciphertext image;
wherein the chaotic sequence is generated by the following steps
Figure FDA0002980028230000014
The first initial key (y)1(0),y2(0),y3(0),y4(0) And a first set of control parameters a, b, c, d, k as input values to equation (3), iterate the Gao hyperchaotic map to produce a first discrete sequence yk(k＝1,2,3,4)；
Figure FDA0002980028230000015
The first discrete sequence yk(k ═ 1,2,3,4) the first pseudorandom sequence is obtained by combining equation (4)
Figure FDA0002980028230000016
And
Figure FDA0002980028230000021
applying the first pseudo-random sequence
Figure FDA0002980028230000022
The first N1 pseudo random numbers are truncated and the result is expressed by equation (5)
Figure FDA0002980028230000023
The first m x n number of (a) is converted into an integer sequence between 0 and 255
Figure FDA0002980028230000024
Figure FDA0002980028230000025
Wherein N1 is a constant;
the scrambling vector is generated by the following steps, including a row scrambling vector H and a column scrambling vector L:
second initial key
Figure FDA0002980028230000026
And a second set of control parameters a, b, c, d, k as input values to the hyperchaotic mapping equation (3), iterating the hyperchaotic mapping to produce a second discrete sequence
Figure FDA0002980028230000027
Figure FDA0002980028230000028
The second discrete sequence is divided into
Figure FDA0002980028230000029
The second pseudo-random sequence is obtained by combining the following formula (6)
Figure FDA00029800282300000210
Figure FDA00029800282300000211
Applying the second pseudo-random sequence
Figure FDA00029800282300000212
Front N of2A pseudo-random sequence is dropped, to
Figure FDA00029800282300000213
And
respectively to be provided with
Figure FDA00029800282300000214
Sorting according to ascending order, and respectively storing the sorted sequences of the original subscript values as row scrambling vectors
Figure FDA00029800282300000215
Sum and column scrambling vectors
Figure FDA00029800282300000216
2. The method of claim 1, wherein the chaotic sequence is generated based on a first initial key, a third control parameter, and a first constant, and the scrambling vector is generated based on a second initial key, a fourth control parameter, and a second constant.
3. The method of any of claims 1 to 2, wherein the scrambling vectors comprise row scrambling vectors and column scrambling vectors, and wherein scrambling the plaintext image with the scrambling vectors comprises: scrambling the plaintext image by using the line scrambling vector; and performing row scrambling processing on the image subjected to the row scrambling processing by using the row scrambling vector.
4. The method of claim 3, wherein:
DNA encoding of the chaotic sequence comprises: converting the chaotic sequence into a first binary sequence; and DNA encoding the first binary sequence according to a first mapping relation of a predetermined DNA encoding rule;
DNA encoding the scrambled image comprises: converting the scrambled image into a second binary sequence according to a predetermined conversion rule; and carrying out DNA coding on the second binary sequence according to a second mapping relation of the DNA coding rule.
5. The method of claim 4, wherein diffusion encrypting the second DNA sequence using the first DNA sequence comprises:
using the first DNA sequence R by the formulae (7) and (8)eAnd a predetermined addition and XOR rule to the second DNA sequence P'ePerforming a diffusion operation to obtain a third DNA sequence C':
Figure FDA0002980028230000031
Figure FDA0002980028230000032
6. the method of claim 5, wherein DNA decoding the third DNA sequence comprises:
performing DNA decoding on the DNA sequence according to a third mapping relation of the DNA coding rule, and converting the DNA sequence into a one-dimensional binary sequence; and
and converting the one-dimensional two-step processing sequence into a pixel value of a ciphertext image according to the preset conversion rule.
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