CN110602346A - Lossless color image encryption method based on hyperchaotic system - Google Patents
Lossless color image encryption method based on hyperchaotic system Download PDFInfo
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Abstract
The invention discloses a lossless color image encryption method based on a hyperchaotic system, which comprises the following steps: separating a color image to be encrypted into three primary color component matrixes; obtaining an original chaotic sequence by the three-primary-color component matrix through a hyperchaotic system; training the original chaotic sequence by using a BP neural network, and outputting a new chaotic sequence; eliminating the transient effect by combining the new chaotic sequence and encrypting; converting the image encrypted in the step (4) into a frequency domain space through two-dimensional discrete wavelet transform to obtain a corresponding sub-band; scrambling and encrypting the sub-bands of the frequency domain space; performing two-dimensional discrete wavelet inverse transformation on the scrambled and encrypted sub-band to convert the scrambled and encrypted sub-band into a space domain to obtain a three-primary-color ciphertext image; and combining the three-primary-color ciphertext images to obtain the encrypted color image. The method effectively improves the safety of the image encryption algorithm, and can effectively resist the attack means which is difficult to resist at present, such as plaintext attack.
Description
Technical Field
The invention relates to a color image encryption technology, in particular to a lossless color image encryption method based on a novel hyper-chaotic system.
Background
To solve the security problem in digital image transmission, many scholars are continuously improving on encryption algorithms. Because digital images are stored in a two-dimensional array form, the traditional DES, AES and RSA cannot meet the current encryption requirements. Based on the Edward Lorenz, the chaos theory is applied to a computer system for the first time in 1963 and is widely applied, the method for obtaining the encrypted image based on Shannon scrambling and diffusion rules is increasingly applied to systems such as secret communication and image encryption, but with the continuous improvement of computer capacity, the previously proposed low-dimensional chaos system cannot meet the requirement of the current cryptography and the safety of the low-dimensional chaos system is reduced continuously. Therefore, the learners propose two-dimensional and even higher-dimensional chaotic systems, but the effect on resisting chosen plaintext attack is still not ideal, so that more and more novel encryption algorithms combining various encryption algorithms are proposed successively at present.
The space domain encryption and the frequency domain encryption are used as two current main image encryption modes and have the characteristics respectively. The spatial domain encryption is based on the traditional idea of changing pixel positions to perform scrambling and diffusion. To break the correlation between the pixels of the image, spatial encryption algorithms usually act directly on the pixels of the image, but the resulting encrypted image is not compressible and at the same time very sensitive to errors. Based on this, the researchers at home and abroad are moving the research direction to the frequency domain encryption method. The main method of frequency domain encryption comprises the steps of converting an image into a frequency domain by utilizing discrete Cosine transform (DWT), Fourier Transform (FT), Discrete Wavelet Transform (DWT), discrete Wavelet transform (transform) and the like, scrambling and encrypting the obtained frequency domain sub-bands by utilizing a generated chaotic random sequence to obtain a final ciphertext image. By combining the two types of encryption algorithms, the security of the whole algorithm is effectively improved, and simultaneously, lossless decrypted images can be obtained, so that the method has higher value in the fields with real-time performance such as medical treatment, military affairs and the like.
Disclosure of Invention
The invention provides a novel hyper-chaotic system aiming at the defects of small phase space and easy cracking of the traditional Qi chaotic system, and provides a lossless color image encryption method on the basis of the novel hyper-chaotic system so as to further improve the safety of a color image encryption algorithm.
In order to realize the task, the invention adopts the following technical scheme:
a lossless color image encryption method based on a hyperchaotic system comprises the following steps:
step 1, separating a color image to be encrypted into three primary color component matrixes;
step 2, obtaining an original chaotic sequence by the three-primary-color component matrix through a hyperchaotic system;
step 3, training the original chaotic sequence by using a BP neural network, and outputting a new chaotic sequence;
step 4, eliminating the transient effect by combining the new chaotic sequence and encrypting;
step 5, converting the image encrypted in the step 4 into a frequency domain space through two-dimensional discrete wavelet transform to obtain a corresponding sub-band;
step 6, scrambling and encrypting the sub-bands of the frequency domain space;
step 7, performing two-dimensional discrete wavelet inverse transformation on the scrambled and encrypted sub-band to convert the scrambled and encrypted sub-band into a space domain to obtain a three-primary-color ciphertext image; and combining the three-primary-color ciphertext images to obtain the encrypted color image.
Further, the separating the color image to be encrypted into three primary color component matrices includes:
setting a plaintext color image I to be encrypted0Size M × N, I0R, G, B, three primary colors are separated to obtain three component matrixes PR, PG and PB with the size of M multiplied by N.
Further, the obtaining of the original chaotic sequence by the three-primary-color component matrix through the hyperchaotic system includes:
the hyperchaotic system is expressed as follows:
in the above formula, x1,x2x3,x4Each of which represents an initial value of the signal,each represents x1,x2x3,x4The result of the iteration of (1), parameter a 50,b＝10，c＝13，d＝5，e＝12；
set the initial value x of the system1,x2x3,x4All 1, the cycle number len, the four-order Runge Kutta formula is utilized to solve the hyperchaotic system, and the obtained iteration result isSubstituting the obtained iteration result into the following formula to calculate the variable r:
after the variable r is obtained by calculation, the variable at the next iteration is selected according to the following rule:
when r is equal to 0, willAs variable x at the next iteration1,x2x3,x4；
When r is 1, willAs variable x at the next iteration1,x2x3,x4；
When r is 2, willAs variable x at the next iteration1,x2x3,x4；
When r is 3, willAs variable x at the next iteration1,x2x3,x4。
Substituting the determined variables into the system for the next iteration, iterating len times according to the same method, and recording the last iteration result as a sequence D0I.e. the original chaotic sequence.
Further, the loss function of the BP neural network is:
wherein the content of the first and second substances,representing the correlation, p, of the actual output sequenceYIndicating the correlation of the desired output sequence.
Further, the eliminating the transient effect by combining the new chaotic sequence and encrypting comprises:
step 4.1, calculating control parameters t of the three component matrixes PR, PG and PB, and respectively recording the control parameters t as t1,t2,t3(ii) a In sequence from t1,t2,t3Beginning to intercept chaotic sequence D1To obtain a new 256-bit sequence Dr,Dg,Db(ii) a The calculation method of the control parameter t comprises the following steps:
for an image with a pixel size of M × N, assuming that S is the sum of pixel values and avg is the average value of pixels, the method for calculating the control parameter t is as follows:
t＝M×N+mod(avg×1012,8×(M+N))
step 4.2, respectively using Dr,Dg,DbDesigning a corresponding S box, and encrypting each primary color image by using the S box to obtain an encrypted image R1,G1,B1。
Further, the technical design method of the S-box comprises the following steps:
creating a 256-length empty array Seq, circularly reading the numerical value of the new sequence and simultaneously inserting the numerical value into the Seq corresponding to the index value; if the inserting position is empty, inserting operation is carried out; if the inserted position has elements, the empty position of the Seq is inquired backwards, and the insertion operation is carried out after the empty position is inquired;
after each value of the new sequence is inserted into Seq, the inserted index values are combined into a new sequence, and the new sequence is then converted into a 16 x 16S-box.
Further, the encrypting each primary color image by using the S-box includes:
firstly, carrying out XOR operation on the component matrix and the target key to obtain a state matrix, and then carrying out two rounds of circular encryption, wherein each round of encryption process is as follows:
(1) byte substitution: mapping the element value in the state matrix into a new byte, wherein the specific mapping rule is as follows: the high 4 bits of each element byte are used as row coordinates, and the low 4 bits are used as column coordinates, so that the value corresponding to the S box is inquired for replacement;
(2) line shifting: performing left cyclic shift operation on the state matrix;
(3) mixing: matrix multiplication is carried out on a group of fixed matrixes and a state matrix;
(4) carrying out round dense phase addition: and carrying out bitwise exclusive-or operation of the matrix on the state matrix and the target key.
On the basis of providing a novel hyper-chaotic system, the invention simultaneously combines a BP neural network, designs a loss function suitable for the algorithm to carry out secondary scrambling on the chaotic sequence obtained by the hyper-chaotic system, and carries out first round encryption on a plaintext image by combining the chaotic sequence obtained based on the secondary scrambling with an encryption algorithm redesigned from an S box. Meanwhile, aiming at the problem that the current ciphertext image can not be compressed, the image is converted into a frequency domain for encryption by combining two-dimensional discrete wavelet transform, and the final encrypted image is obtained through inverse transformation, so that the safety of an image encryption algorithm is effectively improved, and the attack means which is difficult to resist at present, such as plaintext attack selection, can be effectively resisted.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a three-dimensional phase diagram of the novel hyper-chaotic system provided by the invention;
FIG. 3 is a Lyapunov index graph of a hyper-chaotic system along with time t;
FIG. 4 is a diagram of a BP neural network architecture;
FIG. 5 is a schematic flow chart of the encryption of each primary color image;
fig. 6 (a) shows a color image to be encrypted, (b) shows an encrypted image, and (c) shows a decrypted image.
Detailed Description
The invention provides a lossless color image encryption method based on a hyperchaotic system, which comprises the steps of firstly separating a color image into R, G, B three layers, further randomizing the chaotic sequence generated by the novel hyperchaotic system through a neural network, and then scrambling and diffusing the image; then, converting a round of encrypted images into a frequency domain through DWT, and scrambling each sub-band by combining with a chaos sequence generated before; and finally, the IDWT is utilized to reversely convert the sub-band data into a space domain to obtain a ciphertext image. The method comprises the following specific steps:
step 1, separating a color image to be encrypted into three primary color component matrixes
Setting a plaintext color image I to be encrypted0Size M × N, I0R, G, B, three primary colors are separated to obtain three component matrixes PR, PG and PB with the size of M multiplied by N.
Step 2, obtaining an original chaotic sequence by the three-primary-color component matrix through a hyperchaotic system
The scheme provides a novel hyperchaotic system which specifically comprises the following steps:
compared with the traditional chaotic system, the four-wing hyper-chaotic system has larger phase space and can provide larger encryption space, the scheme is improved on the traditional Qi chaotic system, and the improved hyper-chaotic system has the following expression:
in the above formula, x1,x2x3,x4Respectively represents the initial values of the four-wing chaotic attractor in four directions,respectively representx1,x2x3,x4The iteration result of (2). When the parameters a is 50, b is 10, c is 13, d is 5, e is 12, and f is 30, the Lyapunov indexes of the system are respectively: l is1＝3.82，L2＝1.62，L3＝-15.21，L4-48.23, the system satisfies L1＞L2＞0＞L3＞L4Having hyperchaotic characteristics, as shown in fig. 2; meanwhile, the system can generate a real four-wing chaotic attractor as shown in figure 3.
In this embodiment, when the system parameter a is 50, b is 10, c is 13, d is 5, e is 12, and f is 30, the initial value x of the system is set1,x2x3,x4All 1, the cycle number len is 8 multiplied by 256, the four-order Runge Kutta formula is utilized to solve the hyperchaotic system, and the iteration result is obtainedSubstituting the obtained iteration result into the following formula to calculate the variable r:
in the above equation, mod () represents the remainder and floor represents the rounding down.
After the variable r is obtained by calculation, the variable at the next iteration is selected according to the following rule:
when r is equal to 0, willAs variable x at the next iteration1,x2x3,x4；
When r is 1, willAs variable x at the next iteration1,x2x3,x4；
When r is 2, willAs variable x at the next iteration1,x2x3,x4；
When r is 3, willAs variable x at the next iteration1,x2x3,x4。
Substituting the determined variables into the system for the next iteration, iterating len times according to the same method, and recording the last iteration result as a sequence D0I.e. the original chaotic sequence.
Step 3, training the original chaotic sequence by using the BP neural network
The BP neural network is the simplest neural network architecture and is composed of at least three connection layers, and feedforward full connection is realized through a plurality of neurons in each layer. The basic model of BP neural network mainly includes three parts of input layer, hidden layer and output layer, and through nonlinear mapping change between a large number of inputs and outputs, and according to forward and backward propagation through comparison loss function, the weight is continuously and automatically adjusted to minimize output error and output final result. The structure of the three-layer BP neural network is shown in figure 4.
Wherein the input layer is a sequence X ═ X1,x2,x3...xn) The output layer is likewise a sequence Y ═ Y (Y)1,y2,y3...ym) Each connection between layers has a weight W ═ W (W)1,w2,w3...wn) The excitation function herein employs a sigmoid function, which is defined as:
g(x)＝1/(1+e-x)
the standard training mode of the BP neural network is:
in the formula, WkRepresents the weight of the kth neuron, W0＝W0Expressed as initial weight assignment, h > 0 as learning step, E (W)k) Representing the error under the weight of the kth neuron,is E (W)k) At point WkOf the gradient of (c).
According to the scheme, a new loss function is designed according to the correlation of the generated chaotic sequence to train a neural network, and since the sequence is considered to be weakly correlated when the correlation of a group of sequences is between 0.2 and 0.4, the new loss function is designed:
wherein the content of the first and second substances,representing the correlation, p, of the actual output sequenceYExpressing the correlation of the expected output sequence, the calculation formula is as follows:
wherein, XiRepresenting the input of the ith neuron, YiRepresents the output of the ith neuron,which represents the average of all the inputs and,represents the average of all outputs, and n represents the number of neurons. Can be calculated by the above formulaAnd ρY。
In this step, the correlation ρ of the desired output sequence in the loss function is setYThe weights of the network are all initialized randomly 0.3. Will be originalChaotic sequence D0As the input of the neural network, a new chaotic sequence D is output after 10000 rounds of neural network iteration1。
Step 4, eliminating the transient effect by combining the new chaotic sequence and encrypting
For an image of pixel size M × N, let S be the sum of its pixel values and avg be its pixel average, then t is a control parameter closely related to the plaintext pixels, where:
t＝M×N+mod(avg×1012,8×(M+N))
step 4.1, in the step, calculating the control parameter t of the three component matrixes PR, PG and PB obtained in the step 1 according to the above two formulas, and respectively recording the control parameter t as t1,t2,t3(ii) a In sequence from t1,t2,t3Beginning to intercept chaotic sequence D1In order to eliminate the adverse effect caused by transient effect, 256-bit new sequence D is obtainedr,Dg,Db. E.g. t1500, then represents D1256 bits are selected as a sequence D from the 501 th bitr。
Step 4.2, respectively using Dr,Dg,DbDesigning a corresponding S box, and encrypting each primary color image by using the S box to obtain an encrypted image R1,G1,B1。
In the scheme, in order to remove the elements which are repeated in the sequence for generating the S box and keep the randomness of the sequence, a novel S box design method is provided, and the method specifically comprises the following steps:
creating a null array Seq of length 256, reading cyclically said new sequence (D)rOr DgOr Db) The numerical value of (2) is simultaneously inserted into the Seq of the corresponding index value; if the inserting position is empty, inserting operation is carried out; if the inserted position has elements, the empty position of the Seq is inquired backwards, and the insertion operation is carried out after the empty position is inquired;
after each value of the new sequence is inserted into Seq, the inserted index values are combined into a new sequence, and the new sequence is then converted into a 16 x 16S-box.
After the S-boxes are designed, the encryption of each primary image is performed using the following algorithm, as shown in fig. 5:
firstly, carrying out XOR operation on a component matrix (PR or PG or PB) and a target key to obtain a state matrix, and then carrying out two rounds of cyclic encryption, wherein each round of encryption process is as follows:
(1) byte substitution: mapping the element value in the state matrix into a new byte, wherein the specific mapping rule is as follows: and the high 4 bits of each element byte are used as row coordinates, and the low 4 bits are used as column coordinates, so that the value corresponding to the S box is inquired for replacement.
(2) Line shifting: the state matrix is left cyclically shifted.
(3) Mixing: matrix multiplication is performed by using a set of fixed matrices and a state matrix, wherein the matrix multiplication is defined in binary operation based on GF (2^ 8).
(4) Carrying out round dense phase addition: and carrying out bitwise exclusive-or operation of the matrix on the state matrix and the target key.
Respectively carrying out the encryption process on the component matrixes PR, PG and PB of the primary colors to obtain an encrypted image R1,G1,B1。
Step 5, the image R encrypted in the step 4 is transformed by two-dimensional discrete wavelet1,G1,B1Converting to a frequency domain space to obtain a corresponding sub-band;
two-dimensional discrete wavelet transform is a frequency domain processing technology for decomposing and compressing signals, and has characteristics of multi-resolution, local time-frequency and frequency compression, so that the two-dimensional discrete wavelet transform is widely favored in the fields of picture coding, image processing, image compression and the like. The core working principle is as follows: firstly, for the input signal source LL0And performing wavelet decomposition on the obtained intermediate data according to rows and columns. To the input signal source LL0After one-level discrete wavelet transform, the signal source is divided into four sub-bands: low frequency sub-band (LL)1) And high frequency sub-bands(HL1、LH1、HH1). Such as: for the low frequency sub-band LL1The discrete wavelet transform is continuously executed to obtain four sub-bands LL2、HL2、LH2、HH2The result of n-level transformation can be obtained by continuously performing n times of similar operations on the low-frequency sub-band, and the reconstruction of the image can be realized by performing IDWT (inverse discrete wavelet transform) on the decomposed sub-band, so as to obtain the original image.
In this step, the first round encrypted image R is processed by the following formula1,G1,B1And performing two-dimensional discrete wavelet transform to respectively obtain four corresponding wavelet sub-bands.
In the above formula, dwt2(X, 'Haar') denotes performing a two-dimensional discrete wavelet transform on X; r, G, B are images R after the first round of encryption1,G1,B1，LL1、HL1、LH1、HH1Is R1And performing wavelet transformation on the corresponding four wavelet sub-bands.
Step 6, scrambling and encrypting the sub-band of the frequency domain space
Step 6.1, the chaos sequence D obtained in the step 4 is processedr,Dg,DbThe sequence T is converted into (0, M.times.N) by using the following formular,Tg,Tb：
In the above formula:
max(x)＝max(x(k)|k＝1,2,...ml×nl)
min(x)＝min(x(k)|k＝1,2,...,ml×nl)
x (k) (1, 2,3.. ml.. nl), representing the kth number of sequences; k represents the sequence position, 1 being the first of the sequence; m, N represents the image length and width; ml × nl indicates the mth of the sequence; round means rounded and randomly rounded, possibly rounded up and possibly rounded down; mod represents the remainder.
Step 6.2, respectively sequencing the sequences Tr,Tg,TbSequence T in order of arrival from childhoodr′,Tg′,Tb', will sequence Tr′,Tg′,Tb' adding the two sub-bands respectively with corresponding positions of the sub-bands to obtain scrambled and encrypted sub-bands:
step 7, performing two-dimensional discrete wavelet inverse transformation on the scrambled and encrypted sub-band to convert the scrambled and encrypted sub-band into a space domain to obtain a three-primary-color ciphertext image; and combining the three-primary-color ciphertext images to obtain the encrypted color image.
In the above equation, idwt2(Y, 'Haar') denotes that the two-dimensional inverse discrete wavelet transform is performed on the sub-band Y, and C1, C2, and C3 are three primary-color ciphertext images. As shown in fig. 6, the image after color image encryption and an example of restoration are shown.
Claims (7)
1. A lossless color image encryption method based on a hyperchaotic system is characterized by comprising the following steps:
step 1, separating a color image to be encrypted into three primary color component matrixes;
step 2, obtaining an original chaotic sequence by the three-primary-color component matrix through a hyperchaotic system;
step 3, training the original chaotic sequence by using a BP neural network, and outputting a new chaotic sequence;
step 4, eliminating the transient effect by combining the new chaotic sequence and encrypting;
step 5, converting the image encrypted in the step 4 into a frequency domain space through two-dimensional discrete wavelet transform to obtain a corresponding sub-band;
step 6, scrambling and encrypting the sub-bands of the frequency domain space;
step 7, performing two-dimensional discrete wavelet inverse transformation on the scrambled and encrypted sub-band to convert the scrambled and encrypted sub-band into a space domain to obtain a three-primary-color ciphertext image; and combining the three-primary-color ciphertext images to obtain the encrypted color image.
2. The lossless color image encryption method based on the hyperchaotic system as claimed in claim 1, wherein the separating the color image to be encrypted into three primary color component matrices comprises:
setting a plaintext color image I to be encrypted0Size M × N, I0R, G, B, three primary colors are separated to obtain three component matrixes PR, PG and PB with the size of M multiplied by N.
3. The lossless color image encryption method based on the hyperchaotic system as claimed in claim 1, wherein the obtaining of the original chaotic sequence by the three primary color component matrix through the hyperchaotic system comprises:
the hyperchaotic system is expressed as follows:
in the above formula, x1,x2 x3,x4Each of which represents an initial value of the signal,each represents x1,x2 x3,x4The iteration result of (1) is that the parameters a is 50, b is 10, c is 13, d is 5, and e is 12;
set the initial value x of the system1,x2 x3,x4All 1, the cycle number len, the four-order Runge Kutta formula is utilized to solve the hyperchaotic system, and the obtained iteration result isGenerating the obtained iteration resultThe variable r is calculated by the following formula:
after the variable r is obtained by calculation, the variable at the next iteration is selected according to the following rule:
when r is equal to 0, willAs variable x at the next iteration1,x2x3,x4；
When r is 1, willAs variable x at the next iteration1,x2x3,x4；
When r is 2, willAs variable x at the next iteration1,x2x3,x4；
When r is 3, willAs variable x at the next iteration1,x2x3,x4。
Substituting the determined variables into the system for the next iteration, iterating len times according to the same method, and recording the last iteration result as a sequence D0I.e. the original chaotic sequence.
4. The lossless color image encryption method based on the hyperchaotic system as claimed in claim 1, wherein the loss function of the BP neural network is:
wherein the content of the first and second substances,representing the correlation, p, of the actual output sequenceYIndicating the correlation of the desired output sequence.
5. The lossless color image encryption method based on the hyperchaotic system as claimed in claim 1, wherein said eliminating the transient effect and encrypting by combining the new chaotic sequence comprises:
step 4.1, calculating control parameters t of the three component matrixes PR, PG and PB, and respectively recording the control parameters t as t1,t2,t3(ii) a In sequence from t1,t2,t3Beginning to intercept chaotic sequence D1To obtain a new 256-bit sequence Dr,Dg,Db(ii) a The calculation method of the control parameter t comprises the following steps:
for an image with a pixel size of M × N, assuming that S is the sum of pixel values and avg is the average value of pixels, the method for calculating the control parameter t is as follows:
t＝M×N+mod(avg×1012,8×(M+N))
step 4.2, respectively using Dr,Dg,DbDesigning a corresponding S box, and encrypting each primary color image by using the S box to obtain an encrypted image R1,G1,B1。
6. The lossless color image encryption method based on the hyperchaotic system as claimed in claim 5, wherein the technical design method of the S-box is as follows:
creating a 256-length empty array Seq, circularly reading the numerical value of the new sequence and simultaneously inserting the numerical value into the Seq corresponding to the index value; if the inserting position is empty, inserting operation is carried out; if the inserted position has elements, the empty position of the Seq is inquired backwards, and the insertion operation is carried out after the empty position is inquired;
after each value of the new sequence is inserted into Seq, the inserted index values are combined into a new sequence, and the new sequence is then converted into a 16 x 16S-box.
7. The lossless color image encryption method based on the hyperchaotic system as claimed in claim 5, wherein the encrypting each primary color image by using S-box comprises:
firstly, carrying out XOR operation on the component matrix and the target key to obtain a state matrix, and then carrying out two rounds of circular encryption, wherein each round of encryption process is as follows:
(1) byte substitution: mapping the element value in the state matrix into a new byte, wherein the specific mapping rule is as follows: the high 4 bits of each element byte are used as row coordinates, and the low 4 bits are used as column coordinates, so that the value corresponding to the S box is inquired for replacement;
(2) line shifting: performing left cyclic shift operation on the state matrix;
(3) mixing: matrix multiplication is carried out on a group of fixed matrixes and a state matrix;
(4) carrying out round dense phase addition: and carrying out bitwise exclusive-or operation of the matrix on the state matrix and the target key.
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