CN105913369A - Three dimensional cat face transformation and hyper-chaotic system-based fractional domain image encryption method - Google Patents

Abstract

The invention discloses a three dimensional cat face transformation and hyper-chaotic system-based fractional domain image encryption method which is mainly used for solving problems of low scrambling degrees, low sensitivity of secret keys and poor robustness in technologies of the prior art. The method comprises the following steps: 1, after an original image is decomposed, a three dimensional matrix set is obtained; 2, each element in the three dimensional matrix set is subjected to three dimensional cat face transformation operation, and a scrambled three dimensional matrix set is obtained; 3, the scrambled three dimensional matrix set is reconstructed, and a scrambled image is obtained; 4, the scrambled image is subjected to fraction Fourier transforming operation, and a transformed image is obtained; 5, a Clifford hyper-chaotic system is used for generating a chaotic sequence and processing the chaotic sequence, and a row and column scrambled address set is obtained; 6, the row and column scrambled address set is used for subjecting the transformed image to secondary scrambling operation, and a final encrypted image is obtained. The three dimensional cat face transformation and hyper-chaotic system-based fractional domain image encryption method is high in scrambling degree, strong in sensitivity and good in robustness; security of image transmission is improved, and the method can be applied to information safety.

Description

Score field image encryption method based on three-dimensional cat face conversion with hyperchaotic system

Technical field

The invention belongs to technical field of image processing, particularly to a kind of image encryption method, can be used for information security.

Background technology

Along with the fast development of network technology, substantial amounts of view data is transmitted on the internet and exchanges.Due to figure As information is vivid, comprised contains much information, and it becomes the mankind and transmits the important means of information.Image information is directed not only to To individual privacy, some also relates to national security, thus image encryption is increasingly by the most attention of society.In recent years, Fractional fourier transform and chaos is used to be encrypted to cause to image and pay close attention to widely.

Changing image pixel positions is the method commonly using image encryption.Arnold conversion, is commonly called as " conversion of cat face ", is The class cutting conversion that Russia mathematician V.J.Arnold proposes in the research of ergodic theory.Because the chaos of cat face conversion is special Property, it is incorporated into image encryption and digital watermarking has good effect.Three-dimensional cat face conversion has good decorrelation, due to This conversion is three-dimensional, thus has certain space complexity in actual applications, and it has bigger close than the conversion of two-dimentional cat face Key space, faster diffusion velocity.But, owing to three-dimensional cat face conversion has periodically, and parameter only has 6, therefore is used for counting It is easily subject to attack during according to encryption.

Chaos phenomenon is the performance of the similar stochastic process a kind of that determine, inherent occurred in nonlinear dynamic system.Mixed The chaotic signal that ignorant system produces has similar white noise, structure complexity, is difficult to analyze and to initial condition and control parameter The characteristics such as extreme sensitivity.Hyperchaotic system is a kind of special chaos system, is generally of two or more positive The chaos system of Lyapunov index is referred to as hyperchaotic system.Positive Lyapunov index is the most, the side that system track is unstable To the most, the randomness of system is the strongest, and its antidecoding capability is the strongest.Use Clifford hyperchaotic system that image is added Close, its key has good sensitivity.Utilize Clifford hyperchaotic system encrypted image simply in the spatial domain of image Converting, if cipher text part information dropout, then decrypted image also can lose part information therewith, so robustness compares Difference.

Fractional fourier transform can make the energy of image different along with the difference of conversion order.When order is by 0 convergence In changing in 1, image is gradually reduced in time domain energy, and frequency domain energy is gradually increased, and vice versa.So fractional order Fourier becomes Change and there is time domain and the feature in frequency-domain combined territory.Therefore, in transform domain, the distribution of the energy of picture signal is change.It along with The changing above each pixel of Energy distribution to spatial domain of conversion order, thus it is effectively guaranteed that the safety of encrypted image Property, make encrypted image have stronger antinoise signal and process and the ability of malicious attack.But it is single use fractional fourier transform The sensitivity of the key being encrypted image is the highest, there is certain risk being decrypted.

Summary of the invention

Present invention aims to the deficiency of above-mentioned prior art, it is provided that one converts with super mixed based on three-dimensional cat face The score field image encryption method of ignorant system, the sensitivity of safety and key to improve image transmitting.

The technical scheme is that first treating encrypted image carries out three-dimensional cat face conversion, then carries out mark to it Fourier transformation, finally uses Clifford hyperchaotic system that image is carried out scramble, obtains encrypted image.Implementation step bag Include as follows:

(1) the gray level image F of a width M × N is inputted, it is thus achieved that and the two-dimensional matrix f of this gray level image (s, t), and to this two dimension Matrix decomposes, and obtains the three-dimensional matrice set omega of gray level image_n={ A₁,A₂,...,A_n, wherein A_nRepresent three-dimensional matrice collection Close Ω_nIn the n-th three-dimensional matrice, M >=N；

(2) transformation matrix parameter and the iterations m of three-dimensional cat face conversion are chosen, to three-dimensional matrice set omega_nIn each Three-dimensional matrice makees m three-dimensional cat face conversion respectively, obtains the three-dimensional matrice set omega ' after scramble_n={ A '₁,A′₂,...,A′_n, Again by the three-dimensional matrice set omega ' after scramble_nReconstruct the image array f after two dimension scramble₁(s,t)；

(3) fractional fourier transform conversion exponent number p in x, y direction is chosen₁、p₂, to the image array f after two dimension scramble₁ (s t) carries out two dimension fractional fourier transform, the image array after being converted

(4) x is chosen respectively₀、y₀、z₀As the initial value of Clifford hyperchaotic system, and this initial value is substituted into Clifford Hyperchaotic system equation is iterated, obtains three chaos sequence { x_i}、{y_i}、{z_i, i=0,1,2 ..., 9999+M；

(5) respectively by first chaos sequence { x_iAnd second chaos sequence { y_iFront 10000 numerical value remove, and It is re-started numbering, obtains acting on the final chaos sequence in x directionWith the original chaotic sequence acting on y direction {y′_i′, j₁=0,1,2 ..., M-1, i '=0,1,2 ..., M-1；

(6) choose and act on the original chaotic sequence { y ' in y direction_i′Top n element and rename, acted on The final chaos sequence in y directionj₂=0,1,2 ..., N-1；

(7) the final chaos sequence in x directionFinal chaos sequence with y directionBy order from small to large It is ranked up, obtains two orderly new chaos sequencesWithAnd record the new chaos sequence in x direction respectivelyy The new chaos sequence in directionIn each element final chaos sequence in x directionFinal chaos sequence with y directionIn Position Number, obtain line shuffle address setWith row scramble address setWhereinRepresent the new chaos sequence in x directionIn r₁+ 1 element is in x direction Whole chaos sequenceIn Position Number,Represent the new chaos sequence in y directionIn r₂+ 1 element is in y direction Final chaos sequenceIn Position Number, r₁=0,1,2 ..., M-1, r₂=0,1,2 ..., N-1；

(8) image array after the conversion that will obtain in step (3)Row, column successively according to line shuffle address Element in set Q and row scramble address set P carries out scramble, and image array g after being encrypted (u, v).

The invention have the benefit that

1. the present invention utilizes three-dimensional cat face conversion and Clifford hyperchaotic system to carry out overall situation pixel permutation, and with dividing Number Fourier transformation processes, and greatly reduces the dependency between ciphertext pixel；

2. the present invention carries out preliminary scrambling encryption first with three-dimensional cat face conversion, then utilizes fractional fourier transform to enter Row secondary is encrypted, and finally utilizes Clifford Hyperchaotic Sequence scramble to carry out Tertiary infilling, and this multi-level encryption makes encryption method There is the highest safety；

3. the present invention uses fractional fourier transform, enhances the robustness of image encryption；

4. the present invention uses Clifford hyperchaotic system, has the key parameter that sensitivity is higher.

Accompanying drawing explanation

Fig. 1 is the flowchart of the present invention；

Fig. 2 is the original image that the present invention uses；

Fig. 3 is the image after encrypting Fig. 2；

Fig. 4 is the grey level histogram of Fig. 2；

Fig. 5 is the grey level histogram of Fig. 3

Key sensitivity analysis figure when Fig. 6 is that in the present invention, change combined by two chaos initial values；

Key sensitivity analysis figure when Fig. 7 is that in the present invention, two fractional fourier transform exponent numbers combine change；

Fig. 8 is that the image after Clifford hyperchaotic system method and the inventive method encryption is suffering sanction in various degree Image after cutting and the deciphering figure of correspondence thereof.

Detailed description of the invention

With reference to Fig. 1, the present invention to be embodied as step as follows:

Step 1, inputs image to be encrypted, it is thus achieved that and its two-dimensional matrix f (s, t).

Call imread function and read in the gray level image of M × N of an entitled liftingbody as image to be encrypted, As shown in Figure 2, it is thus achieved that and its two-dimensional matrix f (s, t), now M=N=512.

Step 2, to two-dimensional matrix f, (s, t) decomposes, and obtains the three-dimensional matrice set omega of gray level image_n。

(2a) the three-dimensional matrice set omega after decomposition is determined_nNumber n of middle element:

(2a1) total number S of element of image is calculated₀=M × N=512 × 512=262144, to S₀Open cube and to knot Fruit rounds, and obtains line number value a of the three-dimensional matrice of first cubic₁=64, make n=1；

(2a2) the element number S of image after n-1 three-dimensional matrice before calculating is removed_n-1Scheme after deducting the n-th three-dimensional matrice The element number a of picture_n ³Value, obtain removing the element number S of image after the n-th three-dimensional matrice_n；

(2a3) the element number S of image after the n-th three-dimensional matrice is removed in judgement_nWhether ＞ 100 sets up: if setting up, the most right Remove the element number S of image after the n-th three-dimensional matrice_nOpen cube and result is rounded, making n=n+1, returning step (1a2)；If being false, then make remaining element number a₀For S now_n, end loop；

Now S₁=0, it is clear that no more than 100, and remaining element number a₀=S₁=0, end loop, therefore after decomposing Three-dimensional matrice set omega_nNumber n=1 of middle element；

(2b) by two-dimensional matrix f, (s t) resolves into the three-dimensional matrice set omega of 1 three-dimensional matrice composition₁:

(2b1) by two-dimensional matrix f, (s t) reconstructs one-dimension array B [262144], according to order from left to right by each column Element be placed in one-dimension array, the element in each column is placed from the top down, obtains one containing 262144 elements One-dimension array B [262144]；

(2b2) element of the n-th=1 fragment is placed in the n-th=1 three-dimensional matrice of correspondence, will the n-th=1 section In 262144 elements place according to the order from bottom-up layer, element is placed into each column by every layer from left to right, then Element in each column is arranged from the top down, obtains the three-dimensional matrice A that size is 64 × 64 × 64₁, by this three Dimension matrix obtains three-dimensional matrice set omega_n={ A₁}。

Step 3, to three-dimensional matrice set omega₁In each three-dimensional matrice make m=10 three-dimensional cat face conversion respectively, put Three-dimensional matrice set omega ' after unrest₁。

Three-dimensional cat face transformation for mula is as follows:

$\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\\ z^{\′}\end{array}\right]=A\left[\begin{array}{c}x\\ y\\ z\end{array}\right]\mathrm{mod}\left(N\right),$

WhereinIt is referred to as Transformation matrix, a_x、a_y、a_zIt is respectively two dimension cat face transformation matrix a expansion parameter in the x, y, z-directions, b_x、b_y、b_zFor two dimension Cat face transformation matrix b expansion parameter in the x, y, z-directions；X, y, z is respectively the abscissa before conversion, vertical coordinate, ordinate； X ', y ', z ' are the abscissa after three-dimensional cat face change action, vertical coordinate, ordinate；Mod represents modular arithmetic.

Choose transformation matrix parameter a of three-dimensional cat face conversion_x=a_y=a_z=b_x=b_y=b_z=1 and iterations m=10, Utilize above-mentioned three-dimensional cat face transformation for mula to three-dimensional matrice set omega₁In a three-dimensional matrice convert, its step is as follows:

(3a) three-dimensional matrice A is obtained₁In coordinate (x, y, z) pixel value at place of each pixel；

(3b) by three-dimensional matrice A₁In the coordinate of each pixel (x, y, z) according to above-mentioned three-dimensional cat face conversion Carry out coordinate transform, obtain coordinate (x ', y ', z ')；

(3c) original pixel value is composed on new coordinate (x ', y ', z '), thus complete once three-dimensional cat face conversion；

(3d) repeat above-mentioned conversion 9 times, obtain the three-dimensional matrice A ' after scramble₁, by the three-dimensional matrice A ' after scramble₁, Obtain the three-dimensional matrice set omega ' after scramble₁={ A '₁}。

Step 4, by the three-dimensional matrice set omega ' after scramble₁Reconstruct the image array f after two dimension scramble₁(s,t)。

(4a) by the n-th=1 three-dimensional matrice A₁In h₁The h of page₂Row h₃The element of row is placed on one-dimension array B₁'s TheIndividual position, obtains n=1 one-dimension arrayh₁=1,2, 3 ..., 64, h₂=1,2,3 ..., 64, h₃=1,2,3 ..., 64；

(4b) by n=1 one-dimension array B₁[262144] new one-dimension array B ' it is emitted on successively according to the size of array [262144], in, the new one-dimension array B ' [262144] containing 262144 elements is obtained；

(4c) by 262144 elements in new one-dimension array B ' [262144] according to being subsequently placed at from left to right Image array f after two dimension scramble₁(s, t) in each column, the element in each column places from the top down, obtains two dimension scramble After image array f₁(s,t)。

Step 5, by the image array f after the scramble of two dimension₁(s t) carries out two dimension fractional fourier transform, is converted After image array

Two dimension fractional fourier transform formula is as follows:

$F_{p_1,p_2}(u,v)=F^{p_1,p_2}\[f_1(s,t)\]={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{f}_1(s,t)K_{p_1,p_2}(s,t,u,v)dsdt,$

WhereinBeing the core of two dimension fractional fourier transform, this conversion can be equivalent to respectively by x, y two Individual direction carries out fractional fourier transform, therefore its transformation kernel can be write asNow two The kernel function of dimension fractional fourier transform is:

$K_{p_1,p_2}(x,t,u,v)=\frac{\sqrt{(1-j\cot \mathrm{\α})}\sqrt{(1-j\cot \mathrm{\β})}}{2\mathrm{\π}}\×\exp (\frac{j(s^2+u^2)}{2\tan \mathrm{\α}}-\frac{jsu}{\sin \mathrm{\α}})\exp (\frac{j(t^2+v^2)}{2\tan \mathrm{\β}}-\frac{jtv}{\sin \mathrm{\β}})$

Whereinp₁、p₂It is respectively the exponent number of fractional form；

Choose the fractional fourier transform conversion exponent number p in x, y direction₁=0.6, p₂=0.4, after the scramble of two dimension Image array f₁(s t) brings above-mentioned two dimension fractional fourier transform formula into, carries out two dimension fractional fourier transform, converted After image array

Step 5, chooses the initial value of Clifford hyperchaotic system, and this initial value is substituted into Clifford hyperchaotic system side Journey is iterated, obtains three chaos sequence { x_i}、{y_i}、{z_i}。

(5a) input initial value x₀=-0.98765, y₀=0.435678, z₀=-0.0000029884, makes k=0；

(5b) first chaos sequence { x is calculated_i+ 1 element x of kth_k+1, x_k+1=sin (ay_k)-z_kcos(bx_k), its Middle a=2.24, b=0.43；

(5c) second chaos sequence { y is calculated_i+ 1 element y of kth_k+1, y_k+1=z_ksin(cx_k)-cos(dy_k) its Middle c=-0.65, d=-2.43；

(5d) the 3rd chaos sequence { z is calculated_i+ 1 element { z of kth_i, z_k+1=ecos (bx_k), wherein e=1.0；

(5e) numerical value of k is increased by 1, it is judged that the magnitude relationship of k and 10511, if k≤10511, return (5b)；Otherwise, Jump out circulation, terminate calculating, obtain three chaos sequence { x_i}、{y_i}、{z_i, wherein i=0,1,2 ..., 10511.

Step 6, respectively by first chaos sequence { x_iAnd second chaos sequence { y_iFront 10000 numerical value remove, And it is re-started numbering, obtain acting on the final chaos sequence in x directionWith the original chaotic sequence acting on y direction Row { y '_i′, j₁=0,1,2 ..., 511, i '=0,1,2 ..., 511.

Step 7, chooses the original chaotic sequence { y ' acting on y direction_i′Front N=512 element and rename, To the final chaos sequence acting on y directionj₂=0,1,2 ..., 511.

Step 8, the final chaos sequence to x directionFinal chaos sequence with y directionProcess, obtain Line shuffle address set Q and row scramble address set P.

(8a) the final chaos sequence in x directionFinal chaos sequence with y directionBy order from small to large It is ranked up, obtains two orderly new chaos sequencesWith

(8b) the new chaos sequence in x direction is recordedIn each element final chaos sequence in x directionIn Position Number, obtains line shuffle address setWhereinRepresent the new chaos sequence in x directionIn r₁+ 1 element final chaos sequence in x directionIn Position Number, r₁=0,1,2 ..., 511；

(8c) the new chaos sequence in y direction is recordedIn each element final chaos sequence in y directionIn Position Number, obtains row scramble address set Represent the new chaos sequence in y directionIn R₂+ 1 element final chaos sequence in y directionIn Position Number, r₂=0,1,2 ..., 511.

Step 9, to the image array after conversionCarry out scramble, and image array g after being encrypted (u, v).

By the image array after conversion in step 5R₁+ 1 line replacement is toOK；By image arrayR₂+ 1 column permutation is toRow, image array g after being encrypted (u, v), as it is shown on figure 3, r₁=0, 1,2 ..., 511, r₂=0,1,2 ..., 511.

The effect of the present invention can be further illustrated by following emulation experiment:

In order to illustrate advantage and the feature of the present invention, below this invention and prior art are emulated, analyze it Cipher round results.

1. experimental situation

The hardware test platform of this experiment is: Inter (R) Core (TM) i5-4200U CPU, dominant frequency 1.6Ghz, internal memory 4.0GB；Software platform is: Windows 7 operating system and Matlab2012a.Emulating image uses gray level to be 256, size It it is the liftingbody figure of 512 × 512.

2. experiment content

Experiment 1, the grey level histogram of image before and after contrast the inventive method encryption.

Statistical nature grey level histogram between the frequency that in digital picture, each gray level and this gray level occur Representing, grey level histogram is an important statistical nature of image.

The pixel of each gray scale treating encrypted image is added up, and obtains encrypting the grey level histogram of front image, such as Fig. 4 Shown in；The pixel of each gray scale of the image after encrypting by the inventive method is added up, the ash of the image after being encrypted Degree rectangular histogram, as shown in Figure 5.

The grey level histogram of the image before and after encryption is compared, finds that the grey level histogram of the image after encryption is with former There is the biggest difference between the grey level histogram of beginning image, illustrate that the inventive method masks the statistics spy of original image Property, thus significantly increase the image resistance to Statistical Analysis Attacks.

Experiment 2, contrast the inventive method and the scramble degree of three-dimensional cat face alternative approach.

Being encrypted Fig. 2 by the inventive method, result is as shown in Figure 3；

With existing three-dimensional cat face alternative approach, Fig. 2 is encrypted, obtains three-dimensional cat face alternative approach encryption figure.

Randomly choose in level, vertical both direction from Fig. 2, Fig. 3 and three-dimensional cat face alternative approach encryption figure respectively 5000 pairs of neighbors, to investigating dependency, substitute into below equation and are calculated the pixel phase relation at different directions of each image Number:

$\left\{\begin{array}{c}E\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{x}_i\\ D\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{(x_i-E(x\left)\right)}^2\\ \mathrm{cov}(x,y)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}(x_i-E(x\left)\right)(y_i-E(y\left)\right)\\ r_{x,y}=\frac{\mathrm{cov}(x,y)}{\sqrt{D\left(x\right)}\sqrt{D\left(y\right)}}\end{array}\right.$

Wherein x and y refers to the gray value of two neighbors of image, and E (x) is the estimated value of the mathematic expectaion of x, D (x) Being the estimated value of the variance of x, (x y) is the estimated value of covariance of x and y, calculates with the image of two kinds of encryption method gained cov At the pixel correlation coefficient of different directions, result is as shown in table 1.

The existing three-dimensional cat face conversion of table 1 and the pixel correlation coefficient of the inventive method encrypted image

	Artwork	Only three-dimensional cat face conversion	The inventive method
				Horizontal direction	0.8661	0.0920	0.0342
Vertical direction	0.9578	0.0427	0.0405

As it can be seen from table 1 original image is bigger at the pixel correlation coefficient of different directions, show original image Dependency between neighbor pixel is the highest；After three-dimensional cat face conversion is encrypted, the phase between neighbor pixel Closing property substantially diminishes, but the dependency between the neighbor pixel after being encrypted by the inventive method is lower.So, the present invention Method is abundant to the comparison of image slices vegetarian refreshments scramble, and the safety of encryption is higher.

Experiment 3, contrast the inventive method and the key sensitivity of existing fractional fourier transform.

Note original image is I, and encrypted image is Q, is R by the image of deciphering encrypted image gained, thenMSE represent through deciphering image with encrypt before image equal Side's error, MSE value is the biggest, and the information difference of the image before showing the image after deciphering and encrypting is the biggest.

In order to describe the encryption method effectiveness to key in detail, describe with the MSE of decrypted image with original image.

For the hyperchaotic system in the inventive method, fixing z₀=-0.0000029884, makes initial value x₀、y₀Associating change During change on the impact of MSE as shown in Figure 6；

For fractional fourier transform method, two exponent number p of fractional fourier transform₁、p₂To MSE's during associating change Impact is as shown in Figure 7.

Comparison diagram 6 and Fig. 7 understands, and in the present invention, the change of chaos initial value makes MSE curved surface only in one piece of minimum region Interior change is fairly obvious, and the encryption method of fractional fourier transform make MSE curved surface significant change Parameters variation scope very Greatly, thus the present invention has the key that sensitivity is the strongest, outside the scope that the key parameter of input is minimum around right value, Now decrypted image then can not obtain original image.

Experiment 4, the robustness that contrast the inventive method is encrypted with Clifford hyperchaos method.

By existing Clifford hyperchaos method, liftingbody figure is encrypted, then by encryption figure shearing 20%, 30%, 40%, obtain the cutting figure after the encryption as shown in Fig. 8 (a), Fig. 8 (b), Fig. 8 (c)；Again the image after cutting is carried out Deciphering, obtains the deciphering figure of Clifford hyperchaos encryption method as shown in Fig. 8 (d), Fig. 8 (e), Fig. 8 (f).

Liftingbody figure is encrypted by the method proposed by the present invention, then by encryption figure shearing 20%, 30%, 40%, obtain the cutting figure after the encryption as shown in Fig. 8 (g), Fig. 8 (h), Fig. 8 (i)；Again the image after cutting is decrypted, Obtain the deciphering figure of use the inventive method as shown in Fig. 8 (j), Fig. 8 (k), Fig. 8 (l).

Comparison diagram 8 (d), Fig. 8 (e), Fig. 8 (f) and Fig. 8 (j), Fig. 8 (k), Fig. 8 (l), it is possible to find after the encryption of hyperchaos method Image be decrypted after cutting, some part of the image after deciphering cannot be restored by after cutting, and along with cutting It is increasingly severe that degree increases impact, and still it can be seen that original image in the image after the encryption method deciphering used by the present invention In most information.Indicate the inventive method there is certain opposing to cut out attacking ability.

To sum up, the present invention not only has the key that sensitivity is the strongest, also has good robustness, so having the highest simultaneously Safety.

Claims (6)

1. a score field image encryption method based on three-dimensional cat face conversion with hyperchaotic system, including:

(1) the gray level image F of a width M × N is inputted, it is thus achieved that and the two-dimensional matrix f of this gray level image (s, t), and to this two-dimensional matrix Decompose, obtain the three-dimensional matrice set omega of gray level image_n={ A₁,A₂,...,A_n, wherein A_nRepresent three-dimensional matrice set Ω_nIn the n-th three-dimensional matrice, M >=N；

(2) transformation matrix parameter and the iterations m of three-dimensional cat face conversion are chosen, to three-dimensional matrice set omega_nIn each three-dimensional square Battle array makees m three-dimensional cat face conversion respectively, obtains the three-dimensional matrice set omega ' after scramble_n={ A '₁,A′₂,...,A′_n, then will put Three-dimensional matrice set omega ' after unrest_nReconstruct the image array f after two dimension scramble₁(s,t)；

(3) fractional fourier transform conversion exponent number p in x, y direction is chosen₁、p₂, to the image array f after two dimension scramble₁(s, T) two dimension fractional fourier transform, the image array after being converted are carried out

(4) x is chosen respectively₀、y₀、z₀As the initial value of Clifford hyperchaotic system, and it is super mixed that this initial value is substituted into Clifford Ignorant system equation is iterated, obtains three chaos sequence { x_i}、{y_i}、{z_i, i=0,1,2 ..., 9999+M；

(5) respectively by first chaos sequence { x_iAnd second chaos sequence { y_iFront 10000 numerical value remove, and to it Re-start numbering, obtain acting on the final chaos sequence in x directionWith the original chaotic sequence acting on y direction {y′_i′, j₁=0,1,2 ..., M-1, i '=0,1,2 ..., M-1；

(6) choose and act on the original chaotic sequence { y ' in y direction_i′Top n element and rename, obtain acting on y side To final chaos sequencej₂=0,1,2 ..., N-1；

(7) the final chaos sequence in x directionFinal chaos sequence with y directionCarry out by order from small to large Sequence, obtains two orderly new chaos sequencesWithAnd record the new chaos sequence in x direction respectivelyY direction New chaos sequenceIn each element final chaos sequence in x directionFinal chaos sequence with y direction In Position Number, obtain line shuffle address setWith row scramble address setWhereinRepresent the new chaos sequence in x directionIn r₁+ 1 element is in x direction Whole chaos sequenceIn Position Number,Represent the new chaos sequence in y directionIn r₂+ 1 element is in y direction Final chaos sequenceIn Position Number, r₁=0,1,2 ..., M-1, r₂=0,1,2 ..., N-1；

(8) image array after the conversion that will obtain in step (3)Row, column successively according to line shuffle address set Element in Q and row scramble address set P carries out scramble, and image array g after being encrypted (u, v).

2. according to the method described in claims 1, wherein this two-dimensional matrix is decomposed by step (1), by following step Suddenly carry out:

(1a) the three-dimensional matrice set omega after decomposition is determined_nNumber n of middle element:

(1a1) total number S of element of image is calculated₀=M × N, to S₀Open cube and result is rounded, obtaining the first cube Line number value a of the three-dimensional matrice of body shape₁, make n=1；

(1a2) the element number S of image after n-1 three-dimensional matrice before calculating is removed_n-1Deduct image after the n-th three-dimensional matrice Element number a_n ³Value, obtain removing the element number S of image after the n-th three-dimensional matrice_n；

(1a3) the element number S of image after the n-th three-dimensional matrice is removed in judgement_nWhether ＞ 100 sets up: if setting up, then to removal The element number S of image after n-th three-dimensional matrice_nOpen cube and result is rounded, making n=n+1, returning step (1a2)；If It is false, then makes remaining element number a₀For S now_n, end loop；

(1b) by two-dimensional matrix f, (s t) resolves into the three-dimensional matrice set omega of n three-dimensional matrice composition_n={ A₁,A₂,...,A_n}:

(1b1) by two-dimensional matrix f, (s t) reconstructs one-dimension array B [M × N], according to order from left to right by the element of each column Being placed in one-dimension array, the element in each column is placed from the top down, obtains a dimension containing M × N number of element Group B [M × N]；

(1b2) the n numerical value of basis carries out segmentation: if n=1, then need not carry out segmentation；If n >=2, then to one-dimension array B [M × N] In element carry out segmentation, this one-dimension array will intercept n fragment of Length discrepancy according to order from front to back, wherein n-th The number of the element contained in individual fragment is the element number that the n-th three-dimensional matrice contains

(1b3) element of the n-th fragment is placed in the n-th three-dimensional matrice of correspondence, will be in n-th sectionIndividual element according to Placing from the order of bottom-up layer, element is placed into each column by every layer from left to right, and the element in each column is from the top down Arranging, obtaining a size is a_n×a_n×a_nThree-dimensional matrice A_n；

(1b4) n fragment is carried out above-mentioned (1b3) operation, obtains three-dimensional matrice set omega_n={ A₁,A₂,...,A_n}。

3. according to the method described in claims 1, the wherein conversion of the three-dimensional cat face in step (2), carried out by following formula:

$\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\\ z^{\′}\end{array}\right]=A\left[\begin{array}{c}x\\ y\\ z\end{array}\right]\mathrm{mod}\left(N\right),$

WhereinIt is referred to as conversion Matrix, a_x、a_y、a_zIt is respectively two dimension cat face transformation matrix a expansion parameter in the x, y, z-directions, b_x、b_y、b_zFor two dimension cat face Transformation matrix b expansion parameter in the x, y, z-directions；X, y, z is respectively the abscissa before conversion, vertical coordinate, ordinate；x′、 Y ', z ' are the abscissa after three-dimensional cat face change action, vertical coordinate, ordinate；Mod represents modular arithmetic.

4. according to the method described in claims 1, wherein by the three-dimensional matrice set omega ' after scramble in step (1)_n= {A′₁,A′₂,...,A′_nReconstruct two dimension scramble after image array f₁(s, t), is carried out as follows:

(2a) by the n-th three-dimensional matrice A_nIn h₁The h of page₂Row h₃The element of row is placed on one-dimension array B_n?Individual position, obtains one-dimension array B_n；

(2b) n three-dimensional matrice is carried out above-mentioned (2a) operation, obtains n one-dimension arrayh₁=1,2,3 ..., a_n, h₂ =1,2,3 ..., a_n, h₃=1,2,3 ..., a_n；

(2c) by n one-dimension arrayIt is emitted on successively in new one-dimension array B ' [M × N] according to the size of array；If a₀ ≠ 0, then will decompose two-dimensional matrix f (s, remaining a time t)₀Individual element comes backmost, and obtain containing M × N number of element is new One-dimension array B ' [M × N]；

(2d) by the M × N number of element in new one-dimension array B ' [M × N] according to from left to right be subsequently placed at two dimension scramble After image array f₁(s, t) in each column, the element in each column places from the top down, obtains the image after two dimension scramble Matrix f₁(s,t)。

5., according to the method described in claims 1, wherein the initial value of Clifford hyperchaotic system is substituted into by step (4) Clifford hyperchaotic system equation is iterated, obtains three chaos sequence { x_i}、{y_i}、{z_i, obtain as follows :

4a) input initial value x₀、y₀、z₀, make k=0；

4b) calculate first chaos sequence { x_i+ 1 element x of kth_k+1, x_k+1=sin (ay_k)-z_kcos(bx_k), wherein a= 2.24, b=0.43；

4c) calculate second chaos sequence { y_i+ 1 element y of kth_k+1, y_k+1=z_ksin(cx_k)-cos(dy_k) wherein c=- 0.65, d=-2.43；

4d) calculate the 3rd chaos sequence { z_i+ 1 element { z of kth_i, z_k+1=ecos (bx_k), wherein e=1.0；

4e) numerical value of k is increased by 1, it is judged that the magnitude relationship of k Yu 9999+M, if k≤9999+M, return 4b)；Otherwise, jump out Circulation, terminates calculating, obtains three chaos sequence { x_i}、{y_i}、{z_i, wherein i=0,1,2 ..., 9999+M.

6. according to the method described in claims 1, wherein by the image array after conversion in step (8)'s Row, column carries out scramble according to the element in line shuffle address set Q and row scramble address set P successively, is first by image arrayR₁+ 1 line replacement is toOK, then by image arrayR₂+ 1 column permutation is toRow, r₁=0,1,2 ..., M-1, r₂=0,1,2 ..., N-1.