CN115037845B - Color image reversible hiding method based on Hachimoji DNA and Julia fractal - Google Patents

Color image reversible hiding method based on Hachimoji DNA and Julia fractal Download PDF

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CN115037845B
CN115037845B CN202210506487.5A CN202210506487A CN115037845B CN 115037845 B CN115037845 B CN 115037845B CN 202210506487 A CN202210506487 A CN 202210506487A CN 115037845 B CN115037845 B CN 115037845B
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CN115037845A (en
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高铁杠
王坤姝
夏晓帆
桂苏颖
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Nankai University
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Abstract

A reversible color image hiding method based on Hachimoji DNA and Julia fractal. Watermark embedding firstly encrypts a watermark image by using an HDNA sequence containing 8 bases, TSS-CML and Julia set image to obtain an encrypted HDNA watermark. Then, the carrier image is decomposed into non-overlapping blocks with equal size, and the blocks are randomly selected from the non-overlapping blocks to be subjected to singular value decomposition. And then, carrying out HDNA watermark embedding by a method of modifying the first row elements of the singular value matrix, and carrying out SVD inverse operation on all the selected blocks to finally obtain a carrier image containing the watermark. Watermark extraction is the inverse of embedding. Compared with the existing image encryption method, the method can recover the watermark from the image which is possibly attacked without depending on the original image, has good imperceptibility, has strong robustness to common image processing attack, geometric attack and some compound attacks, and can be widely applied to the fields of biological genes, medicine, military affairs and the like.

Description

Color image reversible hiding method based on Hachimoji DNA and Julia fractal
Technical Field
The invention belongs to the technical field of information security, relates to a color image information hiding scheme utilizing a Hachimoji DNA technology, julia fractal, spatiotemporal chaos and singular value decomposition, and particularly relates to a reversible color image hiding algorithm based on the Hachimoji DNA and Julia fractal.
Background
With the rapid development of computer networks, digital images are favored due to their unique characteristics of intuition, image, rich information, and the like, and it has become very common to use networks for digital image transmission in daily life. However, due to the openness of the network and some defects in the own protocol, the security problem of digital image transmission over the network has become an important research topic in the field of information security. Digital watermarking techniques are used to protect intellectual property rights by hiding logos, timestamps and other proprietary information in text, images, audio and video, among others. With the frequency of exposure events and intrusions, the importance of privacy protection and intellectual property rights is becoming increasingly prominent in the multimedia information industry.
In recent years, information hiding methods based on DNA technology and chaos theory have attracted much attention and intensive research. Due to the characteristics of high parallelism, large storage space and ultra-low power consumption, a large number of researchers apply DNA structures to the fields of biology, chemistry, mathematics, computer science, and the like. The method based on the chaos theory has the advantages of large key space, high sensitivity to initial values, more complex chaos characteristics and the like, and is also widely applied to image privacy protection. However, in the traditional DNA technology, 4 bases are used for DNA coding and DNA operation, the rule is simple, and the length after coding is long, so that the safety of the algorithm is low, and the required storage space is large. The introduction of the novel Hachimoji DNA can strengthen the complexity of coding and operation, shorten the sequence length and effectively improve the defects of the traditional technology. In addition, the chaotic degree of encryption can be further improved and the safety and the robustness can be enhanced by combining Julia fractal and an improved space-time chaotic system.
Disclosure of Invention
The invention aims to overcome the defects of the conventional image privacy protection algorithm based on a DNA technology and a chaotic system, and provides a reversible color image hiding method based on Hachimoji DNA and Julia fractal by combining the relevant knowledge of the cryptography theory and image processing. The algorithm is high in safety, strong in robustness and good in imperceptibility and reversibility.
Technical scheme of the invention
A reversible color image hiding method based on HachimojiDNA and Julia fractal is realized by using the technologies of HachimojiDNA technology, julia fractal, spatiotemporal chaos, singular value decomposition and the like. Fig. 1 is a flow chart of the color image reversible concealment algorithm of the present invention, which specifically includes the following steps:
step 1: for color carrier image I with size of M multiplied by N multiplied by 3 and color watermark image W with size of M multiplied by N multiplied by 3, red, green and blue three primary color components of the carrier image I and the watermark image W are respectively separated to obtain three carriers with size of M multiplied by NVolume image matrix I R 、I G 、I B And three watermark image matrixes W with the size of m multiplied by n R 、W G 、W B Wherein M, N > M, N. Combining keys alpha, beta, u 1 (0)、u 2 (0)、u 3 (0) Generating parameters and initial values of a TSS coupling mapping grid, and generating a key stream K by iterating the space-time chaotic system 1 、K 2 、K 3 And pseudo random number RN 1 、RN 2 、RN 3 。
Step 2: using the key initial complex parameter c, the target resolution r, the iteration number s, and the image center coordinate (x) 0 ,y 0 ) Obtaining a local Julia image by parameters such as a scaling factor z, randomly intercepting two coordinate points by using a mouse, taking the obtained local Julia image as a key image J, and separating red, green and blue three primary colors to obtain a Julia matrix J R 、J G 、J B 。
And 3, step 3: pseudo-random number RN obtained by step 1 1 、RN 2 、RN 3 Watermarking an image matrix W R 、W G 、W B And Julia matrix J R 、J G 、J B Selecting any one rule from 384 coding rules to carry out HachimojiDNA coding, carrying out XOR operation on three watermarking HachimojiDNA matrixes and three Julia HachimojiDNA matrixes by utilizing a HachimojiDNA XOR algorithm to obtain three HachimojiDNA XOR-operated matrixes with the size of m multiplied by 3n, and using w to obtain three HachimojiDNA XOR-operated matrixes with the size of m multiplied by 3n i,ψ Base elements of the matrix are represented, where i = R, G, B represents color components, ψ = a, T, C, G, P, Z, S, B represents hacimojidna bases. Table 1 lists 8 encoding rules, and table 2 lists an exclusive or algorithm.
TABLE 1 HachimojiDNA coding rules
Figure BDA0003637518620000021
Figure BDA0003637518620000031
TABLE 2 Hachimoji DNA XOR algorithm
Exclusive OR A B C G P S T Z
A C P A T B Z G S
B P C B S A G Z T
C A B C G P S T Z
G T S G C Z B A P
P B A P Z C T S G
S Z G S B T C P A
T G Z T A S P C B
Z S T Z P G A B C
And 4, step 4: matrix I of carrier images R 、I G 、I B Decomposing the image into non-overlapped pixel blocks with the size of 8 multiplied by 8, randomly selecting 3mn blocks from the non-overlapped pixel blocks, performing singular value decomposition operation on the non-overlapped pixel blocks to obtain a singular value matrix V, and embedding the watermark into the carrier image by the following method on a first row of the singular value matrix: order to
Figure BDA0003637518620000032
f is an embedding quantity threshold value, and the relation of numerical values of elements in the first row in the matrix V is modified:
1) When w = a, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure BDA0003637518620000033
Figure BDA0003637518620000034
2) When w = T, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure BDA0003637518620000035
Figure BDA0003637518620000036
3) When w = C, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | > f; executing the following steps:
Figure BDA0003637518620000037
Figure BDA0003637518620000038
4) When w = G, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | > f; executing:
Figure BDA0003637518620000041
Figure BDA0003637518620000042
5) When w = P, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure BDA0003637518620000043
Figure BDA0003637518620000044
6) When w = Z, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure BDA0003637518620000045
Figure BDA0003637518620000046
7) When w = S, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | > f; executing:
Figure BDA0003637518620000047
Figure BDA0003637518620000048
8) When w = B, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing the following steps:
Figure BDA0003637518620000049
Figure BDA00036375186200000410
and 5: and finally, carrying out inverse singular value decomposition operation on the block embedded with the watermark information, recovering the non-overlapped block split by the carrier image, and combining the red component, the green component and the blue component to obtain the carrier image finally embedded with the watermark.
Step 6: the watermark extraction process is the inverse process of watermark embedding, and can be extracted only by carrying out operation according to the sequence inverse to the process.
The TSS mapping grid used in step 1 is described as follows:
u n+1 (j)＝(1-α)f(u n (j))+αf(u n (j-1))，
here, the first and second liquid crystal display panels are,
Figure BDA00036375186200000411
j＝1,2,3…，α∈(0，1)，β∈(0,4]；
incorporating the original carrier image matrix I R 、I G 、I B And a watermark image matrix W R 、W G 、W B As a secret key, discarding the first 600 values to obtain three chaotic sequences S with the length of 3mn t Wherein t =1,2,3;
chaotic sequence S t The optimization processing method comprises the following steps: s t ′＝10 θ ×S t -round(10 θ ×S t )，[～,K t ]＝sort(S t '), round (x) takes the integer closest to x, sort (x) in increasing order.
Generating pseudo random numbers RN 1 、RN 2 、RN 3 The method comprises the following steps: RN (radio network node) t ＝fix(mod((K t (m, n)), 384)) +1, wherein t =1,2,3; here, fix (x) is a rounding function in the 0 direction, and mod (x) is a remainder function.
In step 3, the watermark image matrix W is processed R 、W G 、W B And Julia matrix J R 、J G 、J B The method for performing Hachimoji DNA coding is: hachimojiDNA is a synthetic genetic system consisting of adenine a, thymine T, cytosine C, guanine G, as well as purine analogs P and B, pyrimidine analogs Z and S, wherein the pairing relationship between bases is: a is complementary to T, C is complementary to G, S is complementary to B, and P is complementary to Z; converting decimal pixel values into octal numbers with three-bit length, converting the octal numbers into binary numbers with nine-bit length, and finally generating pseudo random numbers RN through a chaotic system 1 、RN 2 、RN 3 And (3) selecting a rule for coding, and eliminating repeated coding according to a base complementary pairing principle to obtain 384 available coding rules in total.
The method for performing DNA exclusive OR on the watermark image matrix and the Julia matrix after the HachimojiDNA coding comprises the following steps: generating a corresponding HachimojiDNA exclusive or operation rule according to a HachimojiDNA coding rule; under the same rule, after the binary system represented by the base is subjected to exclusive-or operation, the base is expressed by the operated base, and the obtained new base is the exclusive-or operation result.
The invention has the advantages and beneficial effects that:
the invention provides a new thought and method for image information hiding research, and has the advantages of high safety, strong robustness, high key sensitivity, imperceptibility and the like. By utilizing a novel HachimojiDNA technology, a DNA coding rule and an operation rule based on 8-bit basic groups are designed. Compared with the traditional 24 coding rules of 4-bit nucleic acid base, the coding rule of the Hachimoji DNA designed by using 8-bit base is as high as 384, and the length of a pixel converted into a DNA sequence is shortened from the original 4 bits to 3 bits. The technology can not only improve the safety and complexity of a cryptosystem, but also reduce the length of a DNA sequence and reduce the required storage space. Compared with the traditional scheme, the chaotic system and Julia fractal are used for generating the key, so that the safety is higher, and the robustness is stronger. The color image information hiding scheme provided by the invention can be widely applied to the fields of military affairs, medicine, biological genes and the like.
Drawings
FIG. 1 is a flow chart of the color image encryption algorithm of the present invention.
FIGS. 2 (a) - (h) are respectively color plaintext images Lena, baboon, airplane, boat, goat, butterfly, tower, and Tiger.
Fig. 3 (a) - (b) show color watermark image Number, IEEE.
Fig. 4 (a) - (d) are carrier images with embedded watermarks IEEE, respectively, and (e) - (h) are carrier images with embedded watermarks Number, respectively.
Fig. 5 (a) - (h) are watermark images extracted from fig. 4 (a) - (d), respectively.
Fig. 6 (a) shows watermark images extracted with correct keys, and (b) to (c) show watermark images extracted with incorrect keys.
Fig. 7 (a) is a Number watermark image extracted after 25% of the attack is cut, (b) is a Number watermark image extracted after 3 × 3 gaussian low-pass filtering attack, (c) is a Number watermark image extracted after 2 times of amplification and 2 times of reduction, and (d) is a Number watermark image extracted after histogram mean square attack.
Detailed Description
Example 1:
the following detailed description of the embodiments of the present invention is provided in connection with the accompanying drawings and examples. The present embodiment is implemented on the premise of the technical solution of the present invention, so that a person skilled in the relevant field can better understand the technical features and functional features of the present invention, but the scope of the present invention is not limited to the following embodiments.
A reversible color image hiding algorithm based on HachimojiDNA and Julia fractal is shown in figure 1, which is a flow chart of the reversible color image hiding algorithm of the invention. In this embodiment, the programming tool is MatlabR2018b, the operating environment is intel xeon cpu e3-1231 v33.40ghz, ram10.0gb, the standard color image shown in (a) of fig. 2 with the size of 512 × 512 is selected as the carrier image, and the standard color image Number shown in (a) of fig. 3 is the watermark image.
The specific process is as follows:
1. inputting a color carrier image with the size of 512 x 512, marked as I, a color watermark image with the size of 32 x 32, marked as W, separating red, green and blue three primary color components of the two images to obtain three carrier image matrixes I with the size of 512 x 512 R 、I G 、I B And three watermark image matrices W of size 32 x 32 R 、W G 、W B 。
2. Combining keys alpha, beta, u 1 (0)、u 2 (0)、u 3 (0) Generating parameters and initial values of a TSS coupling mapping grid, and generating a key stream K by iterating the space-time chaotic system 1 、K 2 、K 3 And pseudo random number RN 1 、RN 2 、RN 3 The method comprises the following steps:
iterative TSS coupled mapping trellis u n+1 (j)＝(1-α)f(u n (j))+αf(u n (j-1)) 3672 times, j =1,2,3 \ 8230, where,
Figure BDA0003637518620000061
u∈(0,1)，α∈(0，1)，β∈(0,4]. U =0.053217834876451, β =3.803881733267997 1 (0)＝0.590282398735162，u 2 (0)＝0.477083823287224，u 3 (0) = 0.28356413228, and original carrier image matrix I R 、I G 、I B And a watermark image matrix W R 、W G 、W B As a key, and discarding the first 600 values to obtain three chaos sequences S with length of 3072 1 、S 2 、S 3 。
3. For the above chaos sequence S t Carrying out optimization treatment: s t ′＝10 θ ×S t -round(10 θ ×S t )，[～,K t ]＝sort(S t '). Here t =1,2,3, θ =6, round (x) is taken as the nearest integer to x, sort (x) being in increasing order. Then, using the keystream K t Generating pseudo random numbers RN t ：RN t ＝fix(mod((K t (m, n)), 384)) +1. Here, theFix (x) is a rounding function towards zero, mod (x) is a remainder function.
4. Obtaining a local Julia image by using the parameters of key initial complex parameter c =0.1+0.7i, target resolution r =512, iteration number s =200, image center coordinate (x 0=0, y0= 0), scaling factor z =1 and the like, arbitrarily selecting the coordinates by using a mouse to obtain a key image J with the size of 32 x 32, and separating the key image J by red, green and blue three primary colors to obtain three Julia matrixes J with the size of 32 x 32 R 、J G 、J B 。
5. By pseudo-random numbers RN 1 、RN 2 、RN 3 Selecting coding rule to make watermark image matrix W R 、W G 、W B And Julia matrix J R 、J G 、J B HachimojiDNA encoding from Table 1 was performed, and the three watermarked HachimojiDNA matrices and the three Juliania HachimojiDNA matrices were subjected to XOR operation using the XOR algorithm of Table 2 to obtain three 32X 96 HachimojiDNA XOR-operated watermark matrices W' R 、W′ G 、W′ B 。
TABLE 1 HachimojiDNA coding rules
Base Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 Rule 7 Rule 8
A 000 000 001 001 010 010 011 011
B 001 100 011 010 000 111 110 010
C 010 110 000 011 100 011 101 110
G 101 001 111 100 011 100 010 001
P 011 010 101 000 001 001 111 000
S 110 011 100 101 111 000 001 101
T 111 111 110 110 101 101 100 100
Z 100 101 010 111 110 110 000 111
TABLE 2 Hachimoji DNA XOR algorithm
Exclusive OR A B C G P S T Z
A C P A T B Z G S
B P C B S A G Z T
C A B C G P S T Z
G T S G C Z B A P
P B A P Z C T S G
S Z G S B T C P A
T G Z T A S P C B
Z S T Z P G A B C
6. To further improve the safety, W' R 、W′ G 、W′ B The matrix is transformed into a one-dimensional sequence of length 3072 using a keystream K 1 、K 2 、K 3 Scrambling the sequence, changing the scrambled one-dimensional sequence into 32 × 96 encryption matrix, and using w i,ψ Base elements representing the matrix, where i = R, G, B represents color components, ψ = a, T, C, G, P, Z, S, B represents hacimoji DNA bases.
7. Matrix I of carrier images R 、I G 、I B Decomposing into 4096 non-overlapping blocks of pixels of size 8 x 8, performing a singular value decomposition operation on each of the randomly selected 3072 blocks from each of the color components, and embedding the watermark in the carrier image on the resulting singular value matrix V by:
1) Order to
Figure BDA0003637518620000081
f is an embedding quantity threshold value, and the relation of numerical values of elements in a first row in the matrix V is modified by the following method to realize the embedding of the watermark: when w = a, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | > f; executing the following steps:
Figure BDA0003637518620000082
Figure BDA0003637518620000083
2) When w = T, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure BDA0003637518620000084
Figure BDA0003637518620000085
Figure BDA0003637518620000086
3) When w = C, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure BDA0003637518620000087
Figure BDA0003637518620000091
Figure BDA0003637518620000092
4) When w = G, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure BDA0003637518620000093
Figure BDA0003637518620000094
Figure BDA0003637518620000095
5) When w = P, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | > f; executing the following steps:
Figure BDA0003637518620000096
Figure BDA0003637518620000097
Figure BDA0003637518620000098
6) When w = Z, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure BDA0003637518620000099
Figure BDA00036375186200000910
Figure BDA00036375186200000911
7) When w = S, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing the following steps:
Figure BDA00036375186200000912
Figure BDA00036375186200000913
Figure BDA00036375186200000914
8) When w = B, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | > f; executing the following steps:
Figure BDA00036375186200000915
Figure BDA00036375186200000916
Figure BDA00036375186200000917
8. and finally, carrying out inverse singular value decomposition operation on the block embedded with the watermark information, recovering the non-overlapped block split by the carrier image, and combining the red component, the green component and the blue component to obtain the carrier image embedded with the watermark finally.
9. The watermark extraction process is the inverse process of watermark embedding, and can be extracted only by carrying out operation according to the sequence inverse to the process.
The effects of the invention can be verified by the following performance analysis:
1. imperceptibility
Fig. 4 (a) - (d) are carrier images with embedded watermarks IEEE, respectively, and (e) - (h) are carrier images with embedded watermarks Number, respectively.
The human visual system can visually see that the method has better imperceptible watermark and meets the requirement of imperceptibility. Objectively, we use the Universal Image Quality Index (UIQI) to measure the quality difference before and after embedding the watermark in the carrier image, which is calculated as follows:
Figure BDA0003637518620000101
wherein the content of the first and second substances,
Figure BDA0003637518620000102
and
Figure BDA0003637518620000103
representing the mean, σ, of the image 1,2 Representing the covariance of the two. Generally, the performance index of UIQIThe closer to 1, the more consistent the two test images are, the better the watermark imperceptibility is, and the correlation loss, the brightness distortion and the contrast distortion are smaller than those of the original main image.
2. Reversibility
Fig. 5 (a) - (h) are watermark images extracted from fig. 4 (a) - (d), respectively.
The invention can be visually seen by naked eyes, and can better extract the watermark information. Objectively, the extraction effect of the watermark is evaluated by using an index of a Normalized Coefficient (NC), and the calculation is as follows:
Figure BDA0003637518620000104
where W and W' represent the original watermark image and the extracted watermark image, respectively. It is easy to find that an NC value of 1 indicates that the extracted watermark is completely lossless. Through calculation, the NC values of the eight extracted watermark images in fig. 5 all reach an ideal value of 1, that is, the algorithm of the invention can extract hidden information completely without loss, that is, the invention meets the reversibility requirement.
3. Key space analysis
In the algorithm of the present invention, the calculation accuracy is 10 -15 The system parameters alpha, beta, and the initial value u are set 1 (0)、u 2 (0)、u 3 (0) As a key, the key space is greater than 2 249 Therefore, the key space of the image encryption algorithm provided by the invention is large enough and can completely resist exhaustive attack.
4. Key sensitivity analysis
Fig. 6 (a) shows watermark images extracted with correct keys, and (b) to (c) show watermark images extracted with incorrect keys.
To test the sensitivity of the encryption algorithm to the key, a small change is made to any one of the keys, for example, let α' = α -10 -15 The other keys remain unchanged. Fig. 6 (b) - (c) are the decrypted images with only minor changes to the key alpha. It is easy to see that when the key is wrong, no plaintext information can be obtained, i.e. the information hiding algorithm provided by the present invention is highly sensitive to the key.
5. Known plaintext/chosen plaintext attack analysis
In our algorithm, some efficient procedures are designed to prevent these common attacks. Firstly, calculating the sum of a common image and a watermark image to generate an initial value and a parameter of a chaotic system, and generating a chaotic sequence to replace and diffuse the watermark image. Thus, small changes to the ordinary host image may result in a completely different keystream and embedded image, which means that the proposed encryption algorithm is highly dependent on the ordinary image and the watermark image. In addition, the HDNA values are obtained from random numbers, which are associated with chaotic systems. Thus, the position of each insertion is different. In general, even if an attacker has access to a plaintext image and a cryptographic image pair, the resulting cryptographic images are only related to their corresponding plaintext images. Therefore, the encryption algorithm provided by the invention can effectively resist known plaintext/selected plaintext attacks.
6. False positive detection assay
In watermarking schemes based on singular value decomposition, only insignificant parts of the watermark image are embedded in the carrier image, which often leads to false positive problems. The watermark information may be extracted from a library of images that have not been downloaded by the user, such as the internet or public sources. Embedding the entire watermark into the host image is therefore a good way to avoid the problem of false positives. In the present invention, the watermark images are all embedded completely in the carrier image in a blind manner, which means that we propose a method that avoids the false positive problem.
7. Analysis of resistance to attack
Fig. 7 (a) is a Number watermark image extracted after 25% of attack is cut, fig. 7 (b) is a Number watermark image extracted after 3 × 3 gaussian low-pass filtering attack, fig. 7 (c) is a Number watermark image extracted after 2 times of amplification and 2 times of reduction, and fig. 7 (d) is a Number watermark image extracted after histogram mean-square attack.
It can be seen that when the carrier image embedded with the watermark is subjected to shearing, gaussian low-pass filtering, resizing attack and histogram mean-square attack, most of the hidden watermark image information can still be correctly recovered by using the extraction method of the invention, which shows that the encryption algorithm provided by the invention has better robustness and common attack resistance.

Claims (5)

1. A color image reversible hiding method based on Hachimoji DNA and Julia fractal is characterized by comprising the following steps:
step 1: for color carrier image I with size of M multiplied by N multiplied by 3 and color watermark image W with size of M multiplied by N multiplied by 3, red, green and blue three primary color components are respectively separated to obtain three carrier image matrixes I with size of M multiplied by N R 、I G 、I B And three watermark image matrices W of size mxn R 、W G 、W B Wherein M, N > M, N; binding keys alpha, beta, u 1 (0)、u 2 (0)、u 3 (0) Generating parameters and initial values of a TSS coupling mapping grid, and generating a key stream K through an iterative space-time chaotic system 1 、K 2 、K 3 And pseudo random number RN 1 、RN 2 、RN 3 ；
Step 2: using the key initial complex parameter c, the target resolution r, the iteration number s, and the image center coordinate (x) 0 ,y 0 ) Obtaining a local Julia image by a scaling factor z, randomly intercepting two coordinate points by using a mouse, taking the obtained local Julia image as a key image J, and separating red, green and blue primary colors to obtain a Julia matrix J R 、J G 、J B ；
And step 3: pseudo-random number RN obtained by step 1 1 、RN 2 、RN 3 Watermarking an image matrix W R 、W G 、W B And Julia matrix J R 、J G 、J B Selecting any one rule from 384 encoding rules to carry out Hachimoji DNA encoding, carrying out XOR operation on three watermark Hachimoji DNA matrixes and three Julia Hachimoji DNA matrixes to obtain three matrixes with the size of m multiplied by 3n after the XOR operation of the Hachimoji DNA matrixes, and expressing base elements in the Hachimoji DNA matrixes by w;
and 4, step 4: matrix I of carrier images R 、I G 、I B Decomposing the image into non-overlapped pixel blocks with the size of 8 multiplied by 8, randomly selecting 3mn pixel blocks from the non-overlapped pixel blocks to execute singular value decomposition operation to obtain a singular value matrix V, and embedding the watermark into the carrier image by the following method for the first line of the singular value matrix:
order to
Figure FDA0004046123080000011
And f is an embedding quantity threshold value, and the numerical relation of the first row elements in the matrix V is modified:
1) When w = a, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | > f; executing the following steps:
Figure FDA0004046123080000012
Figure FDA0004046123080000013
Figure FDA0004046123080000014
2) When w = T, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing the following steps:
Figure FDA0004046123080000015
Figure FDA0004046123080000016
Figure FDA0004046123080000021
3) When w = C, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure FDA0004046123080000022
Figure FDA0004046123080000023
Figure FDA0004046123080000024
4) When w = G, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＞0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure FDA0004046123080000025
Figure FDA0004046123080000026
Figure FDA0004046123080000027
5) When w = P, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure FDA0004046123080000028
Figure FDA0004046123080000029
Figure FDA00040461230800000210
6) When w = Z, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＞0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure FDA00040461230800000211
Figure FDA00040461230800000212
Figure FDA00040461230800000213
7) When w = S, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＞0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure FDA00040461230800000214
Figure FDA00040461230800000215
Figure FDA00040461230800000216
8) When w = B, if the following algebraic relation is not satisfied: v 1,1 -V 1,3 ＜0，V 1,2 -V 1,4 ＜0，V 1,5 -V 1,7 ＜0，|V 1,1 -V 1,3 |≥f，|V 1,2 -V 1,4 |≥f，|V 1,5 -V 1,7 | ≧ f; executing:
Figure FDA00040461230800000217
Figure FDA00040461230800000218
Figure FDA00040461230800000219
and 5: and finally, carrying out inverse singular value decomposition operation on the block embedded with the watermark information, recovering the non-overlapped block split by the carrier image, and combining the red component, the green component and the blue component to obtain the carrier image embedded with the watermark finally.
2. The method of claim 1, wherein: the TSS coupling map grid used in step 1 is described as follows:
u n+1 (j)＝(1-α)f(u n (j))+αf(u n (j-1))，
here, the first and second liquid crystal display panels are,
Figure FDA0004046123080000031
u∈(0,1)，j＝1,2,3，α∈(0，1)，β∈(0,4]；
incorporating the original carrier image matrix I R 、I G 、I B And a watermark image matrix W R 、W G 、W B As a key, discarding the first 600 values to obtain three chaotic sequences S with the length of 3mn t Wherein t =1,2,3;
chaotic sequence S t The optimization processing method comprises the following steps: s t ′＝10 θ ×S t -round(10 θ ×S t )，[～,K t ]＝sort(S′ t ) Round (x) is taken as the nearest integer to x, sort (x) is increasing order.
3. The method of claim 2, wherein: generating pseudo random numbers RN 1 、RN 2 、RN 3 The method comprises the following steps: RN (radio network node) t ＝fix(mod((K t (m, n)), 384)) +1, wherein t =1,2,3; here, fix (x) is a rounding function in the 0 direction, and mod (x) is a remainder function.
4. The method of claim 1, wherein: in step 3, the watermark image matrix W is processed R 、W G 、W B And Julia matrix J R 、J G 、J B The method for performing Hachimoji DNA coding is: hachimoji DNA is a synthetic genetic system composed of adenine a, thymine T, cytosine C, guanine G, as well as the purine analogs P and B, the pyrimidine analogs Z and S, wherein the pairing relationship between bases is: a is complementary to T, C is complementary to G, S is complementary to B, and P is complementary to Z; converting decimal pixel values into octal numbers with three-bit length, converting the octal numbers into binary numbers with nine-bit length, and finally generating pseudo random numbers RN through a chaotic system 1 、RN 2 、RN 3 And determining a coding rule, and eliminating repeated coding according to a base complementary pairing principle to obtain 384 available coding rules.
5. The method of claim 1, wherein: the method for performing DNA XOR on the watermark image matrix and the Julia matrix after the Hachimoji DNA coding in the step 3 comprises the following steps: generating a corresponding Hachimoji DNA exclusive or operation rule according to a Hachimoji DNA coding rule; under the same rule, after the binary number represented by the base is subjected to exclusive OR operation, the binary number is represented by the operated base, and the obtained new base is the exclusive OR operation result.
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