CN101706946A - Digital image encryption method based on DNA sequence and multi-chaotic mapping - Google Patents

Abstract

The invention discloses a novel digital image encryption method belonging to the field of DNA calculation and image encryption, and provides a digital image encryption method based on a DNA sequence and multi-chaotic mapping. The traditional encryption algorithm based on chaos has the defects that a key space is small, a chaos system is easy to analyze and forecast, and the like; and almost of the current encryption systems based on DNA need complex biological operation and are hard to realize. In order to overcome the defects, the invention provides the digital image encryption method based on a DNA sequence and multi-chaotic mapping, comprising the following steps of: firstly, scrambling the positions of pixels of images by utilizing a two-dimension chaotic sequence generated by Cubic mapping and Haar wavelet functions, and then disrobing the pixel values of the images under the action of a chaotic sequence generated by the DNA sequence and the Logistic mapping. The experimental result shows that the algorithm is easy to realize, has better encryption effect on images, large key space and high sensitivity to keys and can effectively resist exhaustive attack and statistical attack.

Description

Digital image encryption method based on dna sequence dna and many chaotic maps

Technical field

The present invention relates to the field that DNA calculates field and digital image encryption, particularly a kind of digital image encryption method mainly is to utilize the encoding characteristics of dna sequence dna to realize the encryption of digital picture in conjunction with many chaotic maps.

Background technology

In current society, computer network has changed people's communication mode, and people can be transmitted various multimedia messagess easily by network.Because network opening, multi-media information security more and more causes people's attention with maintaining secrecy.Digital picture is the important information carrier in the multimedia communication, thereby how to protect image information to become question of common concern.

Since chaos have class at random, initial value susceptibility and be difficult to characteristic such as prediction, become the focus that researchers pay close attention to.Object according to scramble divides, and can be divided into two classes based on the image encryption method of chaos: location of pixels scramble and pixel value scramble.The characteristics of location of pixels scramble are the encryption efficiency height, and are effective, but the security of algorithm is not high, are difficult to resist statistical attack; The characteristics of pixel value scramble are the algorithm security height, but cipher round results is bad, and efficient is low.In addition, the cryptographic algorithm of traditional pixel value based on chaos all be the chaos sequence that produces with single chaotic maps directly and the gray-scale value of pixel superpose and realize the encryption of image.Shortcomings such as lot of documents points out, the image encryption algorithm that utilizes single chaotic maps to realize has security lower, and chaos sequence is easily decoded and key space is little.

The DNA encryption system is to be accompanied by the research that DNA calculates in recent years and the cryptography frontier that occurs, be characterized in DNA being information carrier, with the modern biotechnology is implementation tool, excavates advantages such as intrinsic high storage density of DNA and high concurrency, realizes cryptographic functions such as encryption, deciphering.The existing algorithm of encrypting based on DNA will be operated with Bioexperiment mostly, because the Bioexperiment apparatus expensive, experimental situation is difficult to control, and shortcomings such as experiment sensitivity height are still theoretical more than practice based on the research that DNA encrypts at present.

Summary of the invention

In order to overcome the shortcoming of above-mentioned encipherment scheme, the present invention proposes a kind of digital image encryption method based on dna sequence dna and many chaotic maps, broken away from the complex biological operation during DNA encrypts, the simple characteristic of utilizing dna encoding also realizes the scramble that location of pixels and pixel are put simultaneously in conjunction with many chaos sequences, and improve digital image encryption algorithm effects and security.This algorithm is better to the cipher round results of image, and key space is big, and is strong to the susceptibility of key, can resist exhaustive attack and statistical attack effectively.

Technical scheme of the present invention is: the location of pixels of the chaos sequence scramble image that this algorithm at first produces by Cubic mapping and wavelet function, utilize then dna sequence dna coding, get the pixel value that chaos sequence that rules combinations such as benefits, decoding shine upon generation by Logistic is upset image.

Accompanying drawing 1 is depicted as algorithm flow chart of the present invention, and it specifically comprises following sport technique segment:

1. the generation of chaos sequence

In the algorithm of the present invention, shine upon with Cubic mapping, wavelet function mapping and Logistic and to realize image encryption.Wherein the characteristic of Cubic mapping and Logistic mapping is that scholars are well-known.Here we highlight the characteristic of wavelet function.

(1) Cubic mapping

The Cubic mapping definition is as follows:

x _n-1＝μx _n ³+(1-μ)x _n???????????????(1)

X wherein _n∈ [1,1], n=0,1,2 ..., when μ ∈ [3.2,4], produce chaos sequence.

(2) wavelet function mapping

Wavelet function iteration under certain conditions also can produce chaos phenomenon.In the iterative formula (2) that an one dimension wavelet function constitutes:

$x_{n+1}=k(1-x_n^2)\exp (-0.5{(x_n+\mathrm{\μ})}^2)---\left(2\right)$

Work as k=1.33, x ∈ (0,1), μ ∈ chaos phenomenon can occur when [0.77 ,-0.29].The bifurcation diagram and the Lyapunov index map of wavelet function mapping are seen Fig. 2.

(3) Logistic mapping

The Logistic mapping is a kind of typical chaotic maps, and it is defined as follows:

x _n+1＝μx _n(1-x _n)?????????????(3)

μ ∈ [0,4] wherein, x _n∈ (0,1), n=0,1,2 ...When 0＜μ≤3.569945, this power system produces doubling time from the steady state (SS) bifurcated; When 3.569945＜μ≤4, this power system enters chaos state.

Among the present invention,, be directly by initial value x by Cubic mapping and the chaos sequence that wavelet function produces ₀, y ₀The real number chaos sequence that produces, and, must convert binary sequence to by the chaos sequence that the Logistic mapping produces in order to act on mutually with dna sequence dna.Define a threshold function table f (x) according to all chaos sequence of real numbers that is produced by any initial value, getting threshold value is 0.5, and then f (x) is defined as follows:

$f\left(x\right)=\left\{\begin{array}{cc}0,& 0<x\&le;0.5;\\ 1,& 0.5<x\&le;1;\end{array}\right.---\left(4\right)$

Just can convert the chaos sequence of real numbers to binary sequence by f (x).

2.DNA sequential encryption

The single stranded DNA sequence is made up of four kinds of base A (adenine), C (cytosine), G (guanine), T (thymine), wherein A and T, C and G complementation.Respectively four bases in the dna sequence dna are carried out binary coding with 00,01,10,11, total 4!=24 kinds of coded combinations.Because binary digit 0 and 1 complementation, thereby 00 and 11 complementations, 01 and 10 complementations so in 24 kinds of numerical codings, have 8 kinds of codings to satisfy base complementrity pairing criterion, see Table 1.

8 kinds of codings of table 1DNA sequence, decoding mapping criterion

??1	??2	??3	??4	??5	??6	??7	??8
								??00---A??01---C??10---G??11---T	??00---A??01---G??10---C??11---T	??00---C??01---A??10---T??11---G	??00---C??01---T??10---A??11---G	??00---G??01---A??10---T??11---C	??00---G??01---T??10---A??11---C	??00---T??01---C??10---G??11---A	??00---T??01---G??10---C??11---A

At first, these 8 kinds of rules are mapped in 8 sub regions between (0,1), for example: (0,0.125] region representation rule 1, (0.125,0.25] expression rule 2 Then, (key1, the key2) random number between the generation at random two (0,1) are selected different dna encodings, decoding rule with this, and different codings, decoding rule make the encryption and decryption difference of image with two seeds; At last, convert original image to binary sequence,, realize the encryption of image according to the coding of selecting, decoding criterion.

Example: as first pixel value of original image is that [01001011] is encoded with dna encoding mapping criterion 1 and obtained dna sequence dna [CAGT], and above-mentioned dna sequence dna is decoded with DNA decoding mapping criterion 5 obtains binary sequence [11010010] then.

3. based on the image encryption algorithm of dna sequence dna and many chaotic maps

Concrete steps are as follows:

(1) 8 gray level image A of input (m, n), m, n are the ranks dimension of image A;

(2) utilize Cubic mapping and wavelet function respectively with initial value x ₀, y ₀, systematic parameter μ ₁, μ ₂Produce two chaos sequence { x _m, { y _n;

(3) these two sequences are arranged by ascending order, obtain two new sequence { x _m', { y _n';

(4) with { x _m', { y _n' value of the position at each element place replaces former sequence { x _m, { y _nIn this element, obtain two new sequence { x _m" }, { y _n";

(5) with row address and the column address of these two sequences, image pixel positions is carried out scramble with this matrix as the scramble matrix, obtain gray level image B (m, n);

(6) image B is changed into the binary sequence M of one dimension, because each pixel value can be by 8 binary representations, so length (M)=m * n * 8;

(7) with sequence M, encode according to the DNA mapping ruler that seed key1 chooses, obtaining length is the dna sequence dna N of m * n * 8/2;

(8) utilizing the Logistic chaotic maps, is z at initial value ₀, systematic parameter is μ ₃Condition under, generation length is the chaos sequence z of m * n * 8/2 _i

(9) utilize threshold function table f (x) that chaos sequence is changed into binary sequence, work as z _i=1 o'clock, the base of this position was got benefit, otherwise constant;

(10) dna sequence dna after will changing carries out decode operation according to the DNA mapping ruler that seed key2 chooses, and is reduced into binary sequence, reconstructed image matrix, the gray level image after obtaining encrypting.

Wherein, step (1)-(5) are the scramble processes of image pixel positions, and step (6)-(10) are that the pixel value of image is upset process.The decrypting process of image is the inverse process of encrypting, and is no longer burdensome here.

Beneficial effect of the present invention: from above-mentioned Algorithm Analysis, the assailant must possess 8 key parameters of four group keys, i.e. Cubic mapping initial value (x ₀), systematic parameter (μ ₁), wavelet function initial value (y ₀), systematic parameter (μ ₂), Logistic mapping initial value (z ₀), chaos system parameter (μ ₃), dna encoding key (key1), DNA decoding key (key2), could be decrypted image smoothly, improved the security of image greatly; With traditional encipherment scheme ratio based on chaos, the present invention has that cipher round results is good, and key space is big, the high and advantages such as anti-exhaustive attack and statistical study attack of key sensitivity; With the encipherment scheme ratio based on the DNA cryptographic system, the present invention can encrypt digital picture, and with respect to the biology operation of complexity, this algorithm is easy to realize and control.

Description of drawings

Fig. 1 algorithm flow chart of the present invention;

The bifurcation diagram of Fig. 2 wavelet function and exponent index map;

Fig. 3 figure as a result of the present invention;

Fig. 4 key sensitivity test pattern;

The histogram of Fig. 5 original image and encrypted image;

Correlogram between Fig. 6 original image and encrypted image horizontal direction pixel.

Embodiment

In conjunction with the accompanying drawings implementation process of the present invention is done detailed explanation, but be not limited to present embodiment.

Under the MATLAB7.1 environment, the lena gray level image to 128 * 128 is at x ₀=0.3, y ₀=0.1, z ₀=0.36, μ ₁=3.6, μ ₂=-0.5, μ ₃=3.9, key1=1986 carries out emulation experiment under the condition of key2=1.Experiment flow as shown in Figure 1.

Step 1: (m n), sees accompanying drawing 3 (a) to input lena gray level image A, and m, n are the ranks dimension of image A, m=128 wherein, n=128.Image A can be expressed as matrix form and see formula (5);

$\left\{\begin{array}{c}[X^{\&prime;},X^{\&prime;\&prime;}]=\mathrm{Sort}\left(X\right)\\ [Y^{\&prime;},Y^{\&prime;\&prime;}]=\mathrm{Sort}\left(Y\right)\end{array}\right.---\left(5\right)$

Step 2: utilize Cubic mapping and wavelet function respectively with initial value x ₀=0.3, y ₀=0.1, systematic parameter μ ₁=3.6, μ ₂=-0.5, produce two chaos sequence X=x ₁x ₂X _m, Y=y ₁y ₂Y _n

Step 3: utilize formula (6) to sequence X, Y carries out ascending order and arranges;

$A={\left(\begin{array}{cccc}101& 107& ...& 203\\ 100& 106& ...& 202\\ ...& ...& ...& ...\\ 66& 57& ...& 129\end{array}\right)}_{\mathrm{mn}}---\left(6\right)$

Function S ort () is the index order function, and X ', Y ' are sequence X, the new sequence that obtains after the Y ascending order, X ", Y " is its corresponding index value;

Step 4: come the position of scramble image A with formula (7), (m n), sees accompanying drawing 3 (b) to obtain image B behind the scramble;

$A(i,j)\&LeftRightArrow;A(X^{\&prime;\&prime;}\left(i\right),Y^{\&prime;\&prime;}\left(j\right))---\left(7\right)$

I=1 wherein, 2 ... m, j=1,2 ... n;

Step 5: convert image B the binary sequence M of one dimension to, the length of M is m * n * 8;

Step 6: the DNA mapping ruler of being chosen by seed key1=1986 is a rule 7, and 7 couples of sequence M carry out dna encoding with rule, obtain dna sequence dna N, length (N)=m * n * 4;

Step 7: utilizing the Logistic chaotic maps, is z at initial value ₀=0.36, systematic parameter is μ ₃Under=3.9 the condition, generation length is the chaos sequence Z={z of m * n * 8/2 ₁z ₂Z _{M * n * 4};

Step 8: utilize threshold function table f (x) that chaos sequence is changed into binary sequence, work as z _i=1 o'clock, the base of N (i) was got benefit, otherwise N (i) is constant;

Step 9: the dna sequence dna after will changing, the DNA mapping ruler of choosing according to seed key2=1 6 carries out decode operation, is reduced into binary sequence, the reconstructed image matrix, the gray level image after obtaining encrypting is seen accompanying drawing 3 (c).

The image deciphering is the inverse process of encrypting, and deciphering figure sees accompanying drawing 3 (d).

For the better security of this cryptographic algorithm of explanation, the present invention is respectively to key space, the sensitivity of key, and the correlativity between grey level histogram and the pixel etc. is analyzed.

1. key space analysis

In the present invention, having 8 keys, is respectively x ₀, μ ₁, y ₀, μ ₂, z ₀, μ ₃, key1, key2, wherein x ₀∈ [1 ,-1], μ ₁∈ [3.2,4], y ₀∈ [0,1], μ ₂∈ [0.77 ,-0.29], z ₀∈ [0,1], μ ₃∈ [3.569945,4], key1, key2 are random numbers.If computational accuracy is 10 ^-14, calculating the key space of removing outside the random number is 10 ¹⁴* 10 ¹⁴* 10 ¹⁴* 10 ¹⁴* 10 ¹⁴* 10 ¹⁴=10 ⁸⁴, as seen this algorithm has enough big key space and resists exhaustive attack.

2. key sensitivity analysis

For the sensitivity of test key, use the key of fine difference to be decrypted, accompanying drawing 4 is the result after deciphering.Fig. 4 (a) represents x ₀=0.30000000000001, the deciphering figure that other key is constant; The same with Fig. 4 (a), Fig. 4 (b), Fig. 4 (c) represent y respectively ₀=0.10000000000001, z ₀=0.36000000000001, the deciphering figure that other key is constant; Deciphering figure under the wrong DNA mapping ruler of Fig. 4 (d) expression.Fig. 4 (a) and (b), (c) can illustrate, as long as have small difference in the key, all can not recover original image.As seen, this algorithm has stronger key sensitivity, can effectively resist exhaustive attack.

3. grey level histogram analysis

We analyze the change of image statistics characteristic before and after encrypting by histogrammic comparison.From accompanying drawing 5 (a) and (b) as can be seen, bigger variation has taken place in the histogram of image before and after the encryption.Image pixel before encrypting is more concentrated, promptly distributes fewer at the two ends of (0,255) pixel, and intermediate distribution is more, and the distribution of the image pixel after encrypting is more even, and two image similarities are lower, and the assailant is difficult to utilize the statistical property of grey scale pixel value to recover original image.This shows that this algorithm has well resists the statistical study ability.

4. correlation analysis

Correlativity between original image pixels is very high, in order to destroy statistical attack, must reduce the correlativity of encrypted image.Our being chosen at horizontal direction, vertical direction and, utilizing the correlativity between formula (8)-(11) calculating pixel then at random from original image and encrypted image to 3000 pairs of neighbor pixels on the angular direction.

$r_{\mathrm{xy}}=\frac{\mathrm{cov}(x,y)}{\sqrt{D\left(x\right)}\&times;\sqrt{D\left(y\right)}}---\left(8\right)$

$E\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i---\left(9\right)$

$D\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(x_i-E\left(x\right))}^2---\left(10\right)$

$\mathrm{cov}(x,y)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(x_i-E\left(x\right))(y_i-E\left(y\right))---\left(11\right)$

Wherein x and y are the gray-scale values between two adjacent pixels.

	Original image	Encrypted image
			Horizontal direction	??0.9248	??0.0023
Vertical direction	??0.9547	??-0.0161

	Original image	Encrypted image
			To the angular direction	??0.8886	??0.0015

The related coefficient of two adjacent pixels in table 2. original image and the encrypted image

The correlativity of original image and encrypted image horizontal direction is seen accompanying drawing 6 (a) and (b), related coefficient be respectively 0.9248 and the related coefficient of other direction of 0.0023. see Table 2.Correlativity between the pixel of encrypted image is very low as can be seen from Fig. 6 (b) and table 2, almost near 0, and explanation once more, this algorithm has very strong anti-statistical attack ability.

Data in this example are the process of cryptographic algorithm for convenience of description only, and this working of an invention and cipher round results do not rely on concrete numerical value.

Claims (4)

1. based on the digital image encryption method of dna sequence dna and many chaotic maps, it is characterized in that this method comprises the steps:

(1) 8 gray level image A of input (m, n), m, n are the ranks dimension of image A;

(2) utilize Cubic mapping and wavelet function respectively with initial value x ₀, y ₀, systematic parameter μ ₁, μ ₂Produce two chaos sequence { x _m, { y _n;

(3) these two sequences are arranged by ascending order, obtain two new sequence { x _m', { y _n';

(4) with { x _m', { y _n' value of the position at each element place replaces former sequence { x _m, { y _nIn this element, obtain two new sequence { x _m" }, { y _n";

(5) with row address and the column address of these two sequences, image pixel positions is carried out scramble with this matrix as the scramble matrix, obtain gray level image B (m, n);

(6) image B is changed into the binary sequence M of one dimension, each pixel value is by 8 binary representations, length (M)=m * n * 8;

(7) with sequence M, encode according to the DNA mapping ruler that seed key1 chooses, obtaining length is the dna sequence dna N of m * n * 8/2;

(8) utilizing the Logistic chaotic maps, is z at initial value ₀, systematic parameter is μ ₃Condition under, generation length is the chaos sequence z of m * n * 8/2 _i

(9) utilize threshold function table f (x) that chaos sequence is changed into binary sequence, work as z _i=1 o'clock, the base of this position was got benefit, otherwise constant;

(10) dna sequence dna after will changing carries out decode operation according to the DNA mapping ruler that seed key2 chooses, and is reduced into binary sequence, reconstructed image matrix, the gray level image after obtaining encrypting.

2. the digital image encryption method based on dna sequence dna and many chaotic maps according to claim 1 is characterized in that, the DNA mapping ruler of choosing according to seed key1 in the described step (7) carries out Methods for Coding and is:

At first, set up the dna encoding, the decoding mapping ruler that satisfy the base complementrity pair principle, see Table 1;

8 kinds of codings of table 1 dna sequence dna, decoding mapping ruler

??1 ??2 ??3 ??4 ??5 ??6 ??7 ??8 ??00---A??01---C??10---G??11---T ??00---A??01---G??10---C??11---T ??00---C??01---A??10---T??11---G ??00---C??01---T??10---A??11---G ??00---G??01---A??10---T??11---C ??00---G??01---T??10---A??11---C ??00---T??01---C??10---G??11---A ??00---T??01---G??10---C??11---A

Secondly, be 8 sub regions with (0,1) area dividing, the corresponding a kind of mapping ruler of each subregion:

(0,0.125] mapping ruler 1

(0.125,0.25] mapping ruler 2

(0.25,0.375] mapping ruler 3

(0.375,0.5] mapping ruler 4

(0.5,0.625] mapping ruler 5

(0.625,0.75] mapping ruler 6

(0.75,0.875] mapping ruler 7

(0.875,1] mapping ruler 8

Once more, utilize random function to produce a random number between (0,1) as seed, choose corresponding DNA mapping ruler with this random number again with integer k ey1;

At last, with the DNA mapping ruler of choosing the image that step (6) obtains being encoded, at first is the binary matrix of one dimension with image transitions during coding, utilizes the DNA mapping ruler of choosing to encode then and obtains the dna sequence dna matrix N.

3. the digital image encryption method based on dna sequence dna and many chaotic maps according to claim 1 is characterized in that, the method that the middle base of described step (9) is got benefit is:

At first, with the chaos sequence { z that produces in the step (8) _i, i=1,2 ... m * n * 8/2 changes into binary sequence according to threshold function table f (x), sees formula (a):

$f\left(x\right)=\left\{\begin{array}{cc}0,& 0<x\&le;0.5;\\ 1,& 0.5<x\&le;1;\end{array}\right.---\left(a\right)$

Then, judge z _iWhether equal 1, if equal 1 then to N _i, i=1,2 ... benefit is got in m * n * 8/2, otherwise N _iConstant, the benefit of A is T here, and the benefit of C is G, and vice versa;

At last, obtain getting dna sequence dna matrix after the benefit.

4. the digital image encryption method based on dna sequence dna and many chaotic maps according to claim 1 is characterized in that, the method that the DNA mapping ruler of choosing according to seed key2 in the described step (10) carries out decode operation is:

At first, described according to claim 2, utilize random function to produce a random number between (0,1) with integer k ey2 as seed;

Secondly, described according to claim 2, choose the DNA mapping ruler according to the random number that produces;

At last, according to the DNA mapping ruler of choosing the sequence matrix that step (9) obtains is decoded, obtain a binary one dimension matrix, be converted into the matrix of size again, this matrix is carried out obtaining the big or small (m * n that is after the decimal system conversion for (m * n, 8), 1) matrix, obtain encrypted image by matrix reconstruct, its size be (m, n).

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