CN111723386A

CN111723386A - Dynamic DNA color image encryption method based on SHA-512

Info

Publication number: CN111723386A
Application number: CN202010513355.6A
Authority: CN
Inventors: 周士华; 何品言; 王宾
Original assignee: Dalian University
Current assignee: Dalian University
Priority date: 2020-06-08
Filing date: 2020-06-08
Publication date: 2020-09-29
Anticipated expiration: 2040-06-08
Also published as: CN111723386B

Abstract

The invention provides a dynamic DNA color image encryption method based on SHA-512, which comprises the following steps: generating a hash sequence of 512 bytes by utilizing SHA-512 and a plaintext image for calculating an initial value and intermittent parameters of the chaotic system, scrambling the converted plaintext color image by utilizing 2D-RT, and decomposing a scrambled result into three channels of red, green and blue; generating a chaotic sequence by using a four-wing chaotic system and a Lorenz system, and recombining the three channel matrixes and the chaotic matrix by combining intermittent parameters; calculating the Hamming distance of the DNA matrix, updating the initial values of the two chaotic systems, and generating a corresponding chaotic matrix to complete the diffusion operation of the DNA matrix; and decoding and decomposing the diffused DNA matrix, and scrambling the decomposed matrix to obtain an encrypted image. The invention adopts SHA-512 to generate the hash sequence, so that the method has enough key space to resist brute force attack.

Description

Dynamic DNA color image encryption method based on SHA-512

Technical Field

The invention relates to the field of bioinformatics and image encryption, in particular to a dynamic DNA color image encryption method based on SHA-512.

Background

With the advent of the internet age and big data age, research on images has attracted a large number of researchers. Images are extremely susceptible to copying, tampering, illegal distribution, and deliberate attack, and thus research demands for image security are increasing. Because image pixels have strong correlation, the effect and efficiency of directly applying the traditional encryption algorithm to the image are difficult to satisfy. The existing encryption technology for images mainly comprises a chaotic encryption technology, an encryption technology based on DNA coding, an information steganography technology, an encryption algorithm based on the optical field and the like. Although image encryption research has achieved a lot of results, some conventional encryption methods have serious security defects and cannot effectively resist a series of attacks such as statistical attack, plaintext attack, brute force attack and the like. Compared with other traditional methods, the encryption technology based on the DNA coding can better resist statistical attack and brute force attack, but some encryption systems based on the DNA coding also have the defects of incapability of resisting plaintext attack, time-consuming operation, incapability of fully playing DNA base relationship and the like. Aiming at the problems and the previous research results, the invention provides a dynamic DNA color image encryption method based on SHA-512, which can better solve the problems.

Disclosure of Invention

According to the technical problems that the existing encryption system based on the DNA coding can not resist the plaintext attack, is time-consuming in operation and can not give full play to the DNA base relationship, the dynamic DNA color image encryption method based on the SHA-512 is provided, a key space which is large enough to resist the brute force attack is possessed, meanwhile, the DNA matrix is diffused by adopting the unconventional operation, the algorithm complexity is reduced, and the operation time is saved.

The technical means adopted by the invention are as follows:

a dynamic DNA color image encryption method based on SHA-512 comprises the following steps:

sending a plaintext image into a first processing branch circuit to perform conversion operation based on an SHA-512 algorithm to generate a hash sequence, and calculating an initial value and intermittent parameters of a chaotic system according to the hash sequence, wherein the chaotic system comprises a four-wing chaotic system and a Lorentz chaotic system;

sending the plaintext image into a second processing branch to carry out scrambling operation based on a 2D-RT algorithm, and decomposing the obtained scrambling result into three channels of red, green and blue;

recombining the three channel matrixes of red, green and blue and the chaotic matrix generated by the four-wing chaotic system to generate a first intermediate matrix, wherein the chaotic matrix generated by the four-wing chaotic system is obtained by iterative conversion of an initial value of the four-wing chaotic system;

recombining chaotic matrixes generated by the Lorenz chaotic system to generate a second intermediate matrix, wherein the chaotic matrixes generated by the Lorenz chaotic system are obtained by iterative conversion of initial values of the Lorenz chaotic system;

respectively carrying out DNA encoding, DNA diffusion, DNA decoding and conversion on the first intermediate matrix and the second intermediate matrix to obtain a decimal matrix F and a decimal matrix X, and decomposing the decimal matrix F and the decimal matrix X;

and carrying out scrambling operation on the decomposition result so as to obtain an encrypted image.

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

1. according to the invention, the plaintext image is used for generating the hash sequence, and the hash sequence is used for determining the initial value and the intermittent parameter of the chaotic system, namely the initial value and the intermittent parameter of the system are indirectly determined by the plaintext image, so that the relation between the encryption system and the plaintext image is enhanced, the plaintext sensitivity is realized, and the encryption algorithm can more effectively resist plaintext attack.

2. The invention utilizes the hyperchaotic system and two rounds of scrambling-diffusing operations to effectively resist differential attack and eliminate the correlation among pixels, thereby leading the distribution histogram of each pixel value of the ciphertext image to be uniformly distributed and further effectively resisting statistical attack.

3. The invention adopts SHA-512 to generate the hash sequence, so that the method has enough key space to resist brute force attack.

4. The invention diffuses the DNA sequence operation different from the traditional DNA sequence operation on the DNA matrix, thereby reducing the complexity of the algorithm and saving the operation time.

5. The invention further strengthens the scrambling-diffusing effect of the image in the second round of scrambling-diffusing, thereby further improving the safety of the system.

For the above reasons, the present invention can be widely applied to the fields of image encryption and the like.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.

FIG. 1 is a flow chart of a method.

Fig. 2 shows the encryption and decryption effects of Lena images under 256 × 256 pixels: wherein (a) is an original image, (b) is an encrypted image, and (C) is a decrypted image.

Fig. 3 is a graph of the effect of encrypting an image of Lena under the condition of 256 × 256 pixels under the correct key and the incorrect key, wherein (a) the encryption effect is under the use of a brand-new hash sequence, (b) the encryption effect under the last byte is changed for the original hash sequence, and (c) the encryption effect is under the original hash sequence.

Fig. 4 is a graph of the effect of decoding an image by a Lena image under a correct key and an incorrect key under a condition of 256 × 256 pixels, wherein (a) the effect is to use an entirely new hash sequence to perform encryption, (b) the effect is to change the encryption effect under the last byte for the original hash sequence, and (c) the effect is to decrypt the original hash sequence.

Fig. 5 is an image correlation scatter diagram of the R channel of the Lena image under the condition of 256 × 256 pixels, where (a) - (c) are original image horizontal, vertical and diagonal correlation scatter diagrams, respectively, and (d) - (f) are ciphertext image horizontal, vertical and diagonal correlation scatter diagrams.

Fig. 6 is an image correlation scatter diagram of the G channel of the Lena image under the condition of 256 × 256 pixels, where (a) - (c) are original image horizontal, vertical and diagonal correlation scatter diagrams, respectively, and (d) - (f) are ciphertext image horizontal, vertical and diagonal correlation scatter diagrams.

Fig. 7 is an image correlation scatter diagram of Lena image under the condition of 256 × 256 pixels in the B channel, where (a) - (c) are original image horizontal, vertical and diagonal correlation scatter diagrams, respectively, and (d) - (f) are ciphertext image horizontal, vertical and diagonal correlation scatter diagrams.

Fig. 8 is a pixel histogram of an image phase of a Lena image under a 256 × 256 pixel condition, where (a) - (c) are histograms of channels R, G, and B of the original image, respectively, and (d) - (f) are histograms of corresponding encryption channels.

Fig. 9 is a graph of the decryption effect of Lena images under 256 × 256 pixel conditions under different noise attacks, wherein (a) (b) are respectively ciphertext images with 0.02 gaussian noise intensity and decryption images thereof; (c) (d) the ciphertext image and the decrypted image thereof with the Gaussian noise intensity of 0.2 are included; (e) (f) the ciphertext image and the decrypted image of the ciphertext image with the SPN noise intensity of 0.00002; (g) (h) the ciphertext image and the decrypted image thereof under the SPN noise intensity of 0.00005; (i) and (j) the ciphertext image and the decrypted image thereof under the SPN noise intensity of 0.0001.

Fig. 10 is a graph of the decryption effect of Lena images under 256 × 256 pixel conditions under different data loss attacks, where (a) (c) (e) (g) are ciphertext images under the loss of 1/4 pixels in the upper left corner, 1/4 pixels in the lower right corner, 1/8 pixels in the lower left corner and 1/8 pixels in the upper right corner, respectively, and (b) (d) (f) (h) are corresponding decrypted images.

FIG. 11 is a schematic diagram showing the operation of DNA cycle replacement in which (a) is clockwise replacement and (b) is counterclockwise replacement.

Detailed Description

In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.

As shown in FIG. 1, the invention provides a dynamic DNA color image encryption method based on SHA-512, when in execution, firstly, the SHA-512 and the plaintext image are utilized to generate a hash sequence of 512 bytes for calculating an initial value and an intermittent parameter of a chaotic system, the converted plaintext color image is scrambled by utilizing a 2D-RT, and the scrambled result is decomposed into three channels of red, green and blue; then, generating a chaotic sequence by using a four-wing chaotic system and a Lorenz system, and recombining the three channel matrixes and the chaotic matrix by combining intermittent parameters; calculating the Hamming distance of the DNA matrix, updating the initial values of the two chaotic systems, and generating a corresponding chaotic matrix to complete the diffusion operation of the DNA matrix; and decoding and decomposing the diffused DNA matrix, and scrambling the decomposed matrix to obtain an encrypted image.

Specifically, the method comprises the following steps:

step 1: reading in a plaintext picture P_M×N×3(M and N respectively represent the width and height of a single image channel), and an SHA-512 hash algorithm is used for operating P to generate a hash sequence K, so that an initial value and intermittent parameters of the hyper-chaotic system are calculated.

(1) Reading a plaintext image P, and generating a hash sequence K of 512 bytes [ K ] by using SHA-512₁，k₂，...，k₆₄]K is a value in the range of [0,255 ]]Decimal integer of (c).

(2) Calculating a parameter h for obtaining an initial value of the chaotic system₁-h₇The process is as follows:

(3) utilizing h in (2)₁-h₄Calculating an initial value x of the four-wing chaotic system₀，y₀，z₀And w₀The process is as follows:

utilizing h in (2)₅-h₇Calculating an initial value c of the Lorenz chaotic system₁，c₂And c₃The process is as follows:

(4) calculating intermittent parameter index₁-index₈The process is as follows:

step 2: transforming a plaintext image P using a matrix-shaped reconstruction function_M×N×3Conversion to P_M×3NPerforming the 2D-RT operation t times on P to generate a scrambled matrix PST_M×3NAnd decomposing it into R₁，G₁And B₁。

The specific operation process of the 2D-RT is as follows:

encryption:

PST(x′，y′)＝P(x，y) (6)

and (3) decryption:

P(x，y)＝PST(x′，y′) (7)

where t is 5, a is 1, b is 3, c is 5, d is 16, rm is 4, and rn is 7, resulting in the scrambled matrix PST_M×3N。

And step 3: and 7 chaotic sequences are generated by utilizing a four-wing hyper-chaotic system and a Lorenz hyper-chaotic system.

(1) Using an initial value x₀，y₀，z₀，w₀Iterative four-wing hyper-chaotic system 4MN + l₀(l₀1000) times, and remove the first l₀Entry, four sequences X, Y, Z and W of length 4MN are generated. Next, using the sequences X, Y, Z, an isometric sequence X is generated₁，Y₁And Z₁The process is as follows:

(2) using an initial value c₁，c₂And c₃Iterative Lorenz hyper-chaotic system MN + l₀Then (l)₀1000) and remove the first l₀Term, generating three sequences C of length MN₁，C₂And C₃. Subsequently, using the sequence C₁，C₂And C₃Generating equal length sequences L₁，L₂And L₃The process is as follows:

and 4, step 4: and recombining the scrambled image and the chaotic matrix.

(1) R is to be₁，G₁And B₁Binary matrices R respectively converted into M × 8N_bin，G_binAnd B_bin. Using intermittent parameter index₁Determining the value of the first intermediate matrix T, the size of which is 3M × 8N, and the process is as follows:

T＝T_i(i ═ 1, 2.., 6), where i ═ index₁And is and

(2) will sequence L₁，L₂And L₃Conversion into three chaotic matrices of M × NL _1, L _2, and L _3 Next, L _1, L _2, and L _3 are converted into three binary matrices L1 of M × 8N by a matrix reconstruction function_bin，L2_binAnd L3_bin. Finally, the intermittent parameter index is utilized₃The value of the second intermediate matrix CT, CT being 3M × 8N in size, is determined as follows:

CT＝CT_i(i ═ 1, 2.., 6), where i ═ index₃

And 5: matrices T and CT are DNA encoded.

(1) Respectively using the matrix reconstruction function to obtain the sequences X in the step 3₁，Y₁And Z₁Converted into three chaotic matrices X _1, Y _1 and Z _1 of M × 4N by using intermittent parameter index₂And mod (index)₃6) +1 DNA coding matrices ER _ T and ER _ CT are selected as follows:

ER_T＝ER_i，ER_CT＝ER_j，i＝index₂，′j＝mod(index₂6) +1, i ═ 1, 2., 6}, j ═ 1, 2., 6}, where

(2) The matrix T and the matrix CT are encoded.

1) The first bit plane and the eighth bit plane in the matrix T are reorganized as follows: the first column of the first bit plane and the first column of the eighth bit plane are combined together left and right to form the first two columns of the new bit plane matrix T18, the second column of the first bit plane and the second column of the eighth bit plane are combined together left and right to form the third and fourth columns of the new bit plane matrix T18, and so on to form the whole new bit plane matrix T18; then, the same operations are performed on the second and seventh bit planes to constitute a matrix T27, the third and sixth bit planes to constitute a matrix T36, and the fourth and fifth bit planes to constitute a matrix T45. Similarly, the same operation is performed on the binary matrix CT to obtain four matrices CT18, CT27, CT36, and CT 45. The 8 new matrices are all 3 mx 2N in size.

2) T18, T27, T36 and T45 were encoded using the DNA coding matrix ER _ T, where ER _ T (: ,1: n) encoding T18 yields the matrix T _ DNA18, ER _ T (: n + 1: 2N) encoding T27 resulting in matrix T _ DNA27, ER _ T (: 2N + 1: 3N) encoding T36 yields matrix T _ DNA36, and ER _ T (: 3N + 1: 4N) encoding T45 resulting in matrix T _ DNA 45. The same operation was performed for encoding CT18, CT27, CT36, CT45 using the DNA encoding matrix ER _ CT, resulting in four matrices CT _ DNA18, CT _ DNA27, CT _ DNA36, and CT _ DNA 45. Finally, two 3M × 4N matrices, i.e., DNA _ T ═ T _ DNA18, T _ DNA27, T _ DNA36, T _ DNA45, were constructed using the above matrices

And DNA _ CT ═ CT _ DNA18, CT _ DNA27, CT _ DNA36, CT _ DNA 45.

The appropriate coding rules are selected and are shown in table 1.

Table 1: DNA encodes 8 rules

Step 6: the function HD is defined and the Hamming distance between DNA matrices is calculated.

The HD function is defined as follows:

wherein, A and B represent two different DNA matrixes respectively, and 3M and N represent the width and height of the DNA matrix respectively.

Next, Hamming distances d of the DNA matrices T _ DNA18, T _ DNA27, T _ DNA36, T _ DNA45, CT _ DNA18, DT _ DNA27, CT _ DNA36 and CT _ DNA45 are calculated according to the formulas (12) and (13)₁-d₈。

Then, the chaos system initial value parameter is updated by the formula (14).

And 7: and calculating a new chaotic sequence by using the updated initial value.

(1) From x'₀，y′₀，z′₀And w'₀Iterative four-wing chaotic system 4MN + l₁(l₁1000), remove the first l₁The term yields four sequences of length 4MN, X ', Y', Z ', and W'. The sequences X ', Y ' and Z ' are then used to generate three sequences X of equal length₂，Y₂And Z₂。

(2) From c'₁，c′₂And c'₃4MN + l iteration Lorenz chaotic system₁Next, and abandon the first₁Item, generating three sequences C 'all 4MN in length'₁，C′₂And C'₃. Subsequently, utilize C'₁，C′₂And C'₃Generation of three equal length sequences L'₁，L′₂And L'₃。

(3) Using an initial value of x ″)₀，y″₀，z″₀And w ″)₀Updating iterative four-wing hyper-chaotic system 4MN + l₂(l₂1000) times, and abandon the first l₂Four sequences X ', Y', Z 'and W' were generated at a time, all 4MN in length. Subsequently, three isometric sequences X are generated using the sequences X ', Y ' and Z '₃Y and Z₃。

And 8: the DNA matrices DNA _ T and DNA _ CT were subjected to a diffusion operation.

(1) The sequences W, W 'and W' are converted into three matrices W _1, W _2 and W _3 of size M × 4N, respectively, and then the interval parameter index is used₅The time matrix constituting a 3M × 4N matrix forms a matrix of the number of Times DNA base complementation operations are performed.

Times＝{Times_i}，i＝index₅(i＝1，2，...，6)

Times＝mod(floor(Times-fix(Times))×10¹⁴，4)+1 (19)

(2) The sequences X ', Y ' and Z ' are converted into three matrices X _3, Y _3 and Z _3, respectively, each of size M × 4N, then the pause parameter index is used₆The three matrices are constructed into a matrix CR of size 3M × 4N.

CR＝{CR_i}，i＝index₆(i＝1，2，...，6)

(3) DNA complementation operation is performed on the matrix DNA _ T, resulting in DNA matrix DNA _ N.

(4) Sequence L'₁，L′₂And L'₃Respectively converted into three matrixes L _1 ', L _2 ' and L _3 ' with the size of M × 4N, and the interval parameter index is utilized₇A matrix Cycle of size 3M × 4N was constructed.

Cycle＝{Cycle_i}，i＝index₇，i＝1，2，...，6

(5) A DNA cycle replacement operation is performed on the matrix DNA _ CT, resulting in matrix DNA _ C.

1) And (5) DNA base complementation operation. The 6 DNA base complementary operation rules are defined as follows:

Rule 1：(AT)(TC)(CG)(GA)Rule 2：(AT)(TG)(GC)(CA)Rule 3：(AC)(CT)(TG)(GA)

Rule4：(AC)(CG)(GT)(TA)Rule 5：(AG)(GT)(TC)(CA)Rule 6：(AG)(GC)(CT)(TA)

from the above 6 rules, the DNA base complementation procedure has the following properties:

that is, only when the minor axis 4 is operated to 0, the base is not changed after the base complementation operation.

The DNA base complementary operation function is shown in formula (21)

DNA_N(i，j)＝

DNA_complementary_operation(DNA_T(i，j)，Times(i，j)，CR(i，j)) (21)

Wherein, i is 1,2,. 3M; j is 1, 2.

2) DNA cycle replacement operation

In order to solve the problem that the relationship between 4 bases cannot be sufficiently realized by a single substitution rule, a DNA cycle substitution operation is adopted, as shown in FIG. 11. The defined DNA cycle replacement procedure is as follows:

DNA_C(i，j)＝DNA_cycle_operation(DNA_CT(i，j)，Cycle(i，j)) (22)

the Cycle matrix is defined in (4) of step 8. Additionally, i is 1, 2.., 3M; j is 1, 2.

And step 9: the decoding operation is performed on the matrices DNA _ N and DNA _ C.

(1) Will sequence X₂，Y₂And Z₂Conversion into three matrices X _2, Y _2 and Z _2 of M × N, using the pause parameter index₄And mod (index)₄6) +1 to select the DNA decoding matrices DR _ T and DR _ CT.

DR_T＝DR_i1，DR_CT＝DR_i2，i₁＝index₄，i₂＝mod(index₄，6)+1(i₁＝1，2，...，6；i₂1, 2.., 6), wherein

(2) The matrixes DNA _ N and DNA _ C are respectively decoded by using the decoding matrixes DR _ T and DR _ CT, and are converted into corresponding decimal matrixes F and matrixes X, and the sizes of the decimal matrixes F and the matrixes X are 3M multiplied by N.

Step 10: the matrix F and the matrix X are decomposed separately.

(1) Using intermittent parameter index₈Decomposition of matrix F into R₂，G₂And B₂The sizes are both M × N.

F_1＝F(1：M，：)F_2＝F(M+1：2M，：)F_3＝F(2M+1：3M，：)

(2) Using the intermittent parameter mod (index)₈6) +1 decomposes the matrix X, resulting in three matrices X _1, X _2, and X _3 of size M × N.

X_1＝X(1：M，：)X_2＝X(M+1：2M，：)X_3＝X(2M+1：3M，：)

Step 11: and carrying out scrambling operation on the decomposed matrix to obtain an encrypted image.

Using M to R₂，G₂And B₂Performing a conditional cyclic shift operation to generate R₃，G₃And B₃。

Regarding the Mandelbrot set M and cyclic shift, the specific flow is as follows:

(1) mandelbrot set

W(i，j)＝(i*j)+C(i＝1，2，...，M，j＝1，2，...，N) (23)

Wherein C is 10¹⁴。

(2) And (3) a conditional cyclic shift algorithm:

where i is 1, 2.., N, where i is the width of the matrix M. Let the maximum value of the ith column of the M set be max_iAnd a channel R₂，G₂And B₂The maximum value of the ith row is max_ri，max_giAnd max_bi. Then, if max_iLess than max_bi. Then to R₂Cycle i left shift max_iUnit, otherwise to R₂Cyclically shift right max_iA unit; if max_iLess than max_riThen to G₂Cycle i left shift max_iUnit, otherwise for G₂Cyclically shift right max_iA unit; if max_iLess than max_giThen to B₂Cycle i left shift max_iUnit, otherwise pair B₂Cyclically shift right max_iUnit of unit

Step 12: to R₃，G₃And B₃Performing a second diffusion operation to obtain C_R，C_GAnd C_BAnd A is combined to generate a final ciphertext image C.

The scheme and effect of the present invention will be further explained by specific application examples.

Example 1

This embodiment will be described using a color drawing of Lena 256 × 256.

(1) Reading in the image Lena, combining with SHA-512, generating 512 byte sequence

h＝9f63791ec64b3bb5bcf1d6e1272557c9779b37575f33a72e0fbf73a8339bba94d0e3de2ab82ae305ee0a71a122123407227708ff0bc0296768566c2cc59e7d37。

Thus, the four initial values of the four-wing hyper-chaotic system generated according to the definition of the inventive method are expressed as

key1 ═ 1.8175, 1.6275, 2.3765, 2.1882. And three Lorenz chaotic system initial values are expressed as

key2 ═ 1.2824, 1.1429, 2.3939. There are also 8 intermittent parameters index ═ 6, 4, 2, 2, 3, 3, 1, 1.

(2) Lena is decomposed into R after 5 times of 2D-RT operations₁，G₁，B₁Passages, i.e.

(3) By using key1 and key2 to respectively iterate the four-wing chaotic system 4 × 256 × 256+1000 times and 256 × 256+1000 times, the first 1000 times are discarded, and the following six sequences are generated:

X1＝[3，3，6...，1]，Y1＝[4，2，6，...，6]，Z1＝[5，2，7，...，3]

L1＝[223，229，18，...，227]，L2＝[214，184，184，...，138]，

L3＝[194，126，64，...，78]

(4) handle channel R₁，G₁，B₁Converted to binary format and formed into a new matrix T using index1 ═ 6, i.e.

Subsequently, the sequence L₁，L₂，L₃Respectively converted into M × N matrixes L _1, L _2 and L _3, further converted into binary matrixes by index₃Constructing the matrix CT2, i.e.

(5) Using index ₂4 and mod (index)₂+1, 6) +1 ═ 5, two groups of coding matrices ER are selected₄And ER₅Encoding T and CT separately yields:

(6) calculating the Hamming distance by using the DNA matrix, and updating the initial value of the system to obtain a new secret key:

key1’＝[1.282，1.1882，1.5269，1.4685]，

key2’＝[0.9265，0.8804，1.2794]，

key1”＝[0.5082，0.484，0.5782，0.5545]

(7) the four-wing chaotic system and the Lorenz system are iterated by using key1 ' and key2 ' for 4 multiplied by 256 plus 1000 times respectively, and the first 1000 times are abandoned, so that seven sequences of the sequences X ', Y ', Z ', W ' and Z1 ', Z2 ', Z3 ' are generated respectively. The four-wing chaotic system is iterated by using key1 ' for 4 multiplied by 256+1000, and the first 1000 times are abandoned, so that the sequences X ', Y ', Z ' and W ' are generated.

1) Calculating a new sequence X using the sequence₂，Y₂，Z₂，X₃，Y₃，Z₃And L'₁，L′₂，L′₃Here, only X is shown₂

X₂＝[7，2，7，...，4]

2) The sequence is converted into an M × 4N matrix X _2, Y _2, Z _2, X _3, Y _3, Z _3, L _1 ', L _2 ', L _3 '. Here, X _2 and L _1 'are shown'

(8) The DNA matrices DNA _ T and DNA _ CT were subjected to a diffusion operation.

1) Converting the sequence W, W 'and W' into matrices W _1, W _2 and W _3 of an M × 4N matrix, using the pause parameter index₅Construct and process the resulting matrix Times as 3, i.e.

2) Using intermittent parameter index₆The matrix CR is constructed from 3 and the matrices X _3, Y _3 and Z _3, i.e.

3) Using intermittent parameter index₇The matrices L _1 ', L _2 ' and L _3 ' form a matrix Cycle, i.e. the matrix Cycle is formed

4) Performing DNA replacement operation on DNA _ T by using Times and CR matrix, performing DNA cyclic replacement operation on DNA _ CT by using matrix Cycle, and generating new matrices DNA _ N and DNA _ C, namely

(9) Using index₄＝2，mod(index₄6) +1 ═ 3 and X _2, Y _2 and Z _2 two sets of decryption matrices DR are selected₂And DR₃And decodes DNA _ N and DNA _ C, respectively, to generate matrices F and X, i.e.

(10) Using the intermittent parameter index ₈1 and mod (index)₈F, X is decomposed 6) +1 ═ 2, yielding the matrix R₂，G₂，B₂And X_R，X_G，X_B. Wherein the content of the first and second substances,

(11) computing Mandelbrot set M, for R₂，G₂And B₂Performing conditional shift operation to generate matrix R₃，G₃And B₃Wherein

(12)R₃And X_R，G₃And X_GAnd B₃And X_BAnd respectively XOR-ing and merging into a final image C. The R, G, B channels of C are as follows:

the decryption method only needs to execute the encryption method in a reverse order, only needs to pay attention to the fact that DNA complementary operation and DNA cyclic replacement operation need to be executed reversely in the decryption process, and the 2D-RT is the same. This achieves the effect of the implementation of fig. 2.

The safety of the present invention was analyzed as follows:

1. a key space. The key space mainly consists of system parameters of SHA-512, four-wing chaotic system k and 2D-RT, the size of the key space is 2512 × 214 × 5 × (102)6 is 1.0984 × 10171, which is far greater than 2100, so that the method can be considered to resist brute force attacks.

2. Key sensitivity. This method can be considered to be key sensitive if the keys and the encryption system are in one-to-one correspondence. In the present invention,

K1＝a1100bff91ac78cb8910aafcea1290fc99a3001cbbac73ef31ff23dd1347f90c60ad23fe26bd4133bad0501a273f0170adfe301261dc3df034ad00ff127526ff

K2＝9f63791ec64b3bb5bcf1d6e1272557c9779b37575f33a72e0fbf73a8339bba94d0e3de2ab82ae305ee0a71a122123407227708ff0bc0296768566c2cc59e7d38

and correct key

K＝9f63791ec64b3bb5bcf1d6e1272557c9779b37575f33a72e0fbf73a8339bba94d0e3de2ab82ae305ee0a71a122123407227708ff0bc0296768566c2cc59e7d37。

As can be seen from fig. 4, the present invention has key sensitivity.

3. And (5) performing correlation research. If the strong correlation exists directly in the pixels of the encrypted ciphertext image after the image is encrypted, the encryption system cannot resist statistical attack. As shown in table 1 and fig. 5 to 7, the absolute values of the correlation coefficients of R, G, and B channels of the ciphertext image are all lower than 0.02, and it can be considered that the correlation of the ciphertext image of the present invention is eliminated, so that the ciphertext image can withstand statistical attacks.

4. Image pixel histograms. The image histogram reflects the gray value distribution, and if the ciphertext image histogram is uniformly distributed, the encryption system is considered to be safe. As shown in table 2 and fig. 8, the gray values of the ciphertext image under the present invention are uniformly distributed, and the variance is less than 293, so that the present invention is safe.

5. The entropy of the information. The gray value of the encryption system is uniformly distributed, and the information entropy of the encryption system is further explained to be necessarily close to the theoretical value, namely the gray value digit. The gray value of the image is 8 bits, so if the entropy of the information is close to 8, the encryption system can be considered to be safe and reliable. As shown in Table 3, the entropy of the information of the invention is close to 8, and the information is safe and reliable.

6. And (5) differential attack analysis. The differential attack is that an attacker slightly changes an original image and then attacks the original image according to the original encryption method, and if the attacker can find the association between the original image and the encrypted image, the encryption system cannot resist the differential attack. The common detection indexes of the differential attack are NPCR and UACI, and the theoretical safety values of the NPCR and the UACI are 99.6% and 33.4%. As can be seen from Table 4, the NPCR and UACI values of the present invention are close to the theoretical values, i.e. the present invention can withstand the differential attack

7. Noise attacks and brute force attacks. The image is inevitably subjected to noise and pixel value loss in the transmission process. If the decrypted image can still be identified under the condition that noise and pixel loss exist in image transmission, the system can be considered to resist noise attack and violent attack. As shown in table 5 and fig. 9-10, the decrypted image can still be distinguished when the ciphertext image suffers from different intensity noises and different degrees of pixel value loss, and the PSNR values are both greater than 27, so that the invention can be considered to resist noise attack and brute force attack.

Table 1: the color picture pixel is 256 multiplied by 256 relative numbers

Table 2: the image pixel is 256 multiplied by 256 of variance size of pixel distribution in the plaintext image and the ciphertext image

Table 3: information entropy size when image pixel is 256 multiplied by 256

Table 4: the image pixel has NPCR and UACI values of 256 × 256

Table 5: the Lena pixels of the image are 256 multiplied by 256 to obtain different noise intensities and different noise intensities under different data loss quantities

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic DNA color image encryption method based on SHA-512 is characterized by comprising the following steps:

2. The image encryption method according to claim 1, wherein the hash sequence is K ═ K [ K ═ K-₁,k₂,…,k₆₄]Wherein k is₁,k₂,…,k₆₄Is a value range of [0,255]Decimal integer of (1);

the step of calculating the initial value and the intermittent parameter of the chaotic system according to the Hash sequence mainly comprises the following steps:

(1) calculating a parameter h for obtaining an initial value of the chaotic system₁-h₇：

(2) Calculating an initial value x of the four-wing chaotic system₀,y₀,z₀And w₀：

(3) Calculating an initial value c of the Lorenz chaotic system₁,c₂And c₃：

(4) Calculating intermittent parameter index₁-index₈：

3. The image encryption method according to claim 2, wherein the three channel matrices of red, green and blue and the chaotic matrix generated by the four-wing chaotic system are recombined to generate a first intermediate matrix, and specifically comprises:

performing binary conversion on the red, green and blue channel matrixes to obtain a matrix R_bin,G_binAnd B_bin；

Generating a first intermediate matrix T using the pause parameters according to the following calculation:

T＝T_i(i ═ 1,2, …,6), where i ═ index₁And is and

4. the image encryption method according to claim 2, wherein the reconstructing of the chaotic matrix generated by the lorentz chaotic system to generate the second intermediate matrix specifically comprises:

after the initial value iteration Lorenz chaotic system is utilized, an isometric sequence L is generated by processing₁,L₂And L₃；

For the sequence L₁,L₂And L₃Binary conversion is carried out to obtain a matrix L1_bin,L2_binAnd L3_bin；

Generating a second intermediate matrix CT using the intermittent parameters according to the following calculation:

CT＝CT_i(i ═ 1,2, …,6), where i ═ index₃

5. The image encryption method according to claim 1, wherein the DNA encoding is performed on the first intermediate matrix and the second intermediate matrix respectively, and specifically comprises:

acquiring DNA coding matrixes ER _ T and ER _ CT;

coding the first intermediate matrix T and the second intermediate matrix CT to obtain corresponding DNA matrixes:

DNA_T＝[T_DNA18,T_DNA27,T_DNA36,T_DNA45]

and DNA _ CT ═ CT _ DNA18, CT _ DNA27, CT _ DNA36, CT _ DNA 45;

calculating the Hamming distance between the DNA matrixes, and updating the initial value parameters of the chaotic system by using the Hamming distance;

and calculating a new chaotic sequence by using the updated initial value.

6. The image encryption method according to claim 5, wherein the obtaining of the DNA coding matrices ER _ T and ER _ CT specifically comprises:

after the initial value iteration four-wing chaotic system is utilized, an isometric sequence X is generated by processing₁,Y₁And Z₁；

Respectively reconstructing the sequence X by using a matrix reconstruction function₁,Y₁And Z₁Converting into three chaotic matrixes X _1, Y _1 and Z _ 1;

using intermittent parameter index₂And mod (index)₃6) +1 DNA coding matrices ER _ T and ER _ CT are obtained according to the following calculation:

ER_T＝ER_i,ER_CT＝ER_j,i＝index₂,j＝mod(index₂6) +1, i ═ 1,2, …,6, and j ═ 1,2, …,6, where

7. The image encryption method according to claim 1, wherein the DNA diffusion operation includes: performing DNA complementary operation on the first intermediate matrix; and performing DNA cycle replacement operation on the second intermediate matrix.