CN112153238B - Image encryption method based on Tent mapping and composite chaotic mapping - Google Patents

Abstract

The present invention provides an image encryption method based on Tent mapping and composite chaotic mapping in the technical field of image encryption, comprising the following steps: Step S10, acquiring an original image with a size of M×N, and creating a matrix with a size of M×N I: Store the matrix information of the original image in matrix I; Step S20, generate 6 initial keys based on the matrix information stored in the matrix I; Step S30, obtain Tent mapping and composite based on the initial key Three chaotic sequences of the chaotic map; step S40, performing two rounds of scrambling and diffusion operations on the original image based on the chaotic sequences to obtain an encrypted image. The advantages of the present invention lie in that the security of image encryption is greatly improved, and the execution cost is reduced.

Description

An Image Encryption Method Based on Tent Map and Compound Chaos Map

technical field

The invention relates to the technical field of image encryption, in particular to an image encryption method based on Tent mapping and compound chaotic mapping.

Background technique

With the rapid development of multimedia technology and the Internet, more and more images are transmitted, shared and stored on the Internet. The information security of images has always been a serious problem in the digital world. Although there are some traditional encryption algorithms with high security and mature verification capabilities, such as DES algorithm and RSA algorithm, due to the particularity of image data, traditional encryption algorithms The encryption algorithm is not suitable for the field of image encryption. The image is usually described by the pixel position and pixel value in the spatial domain, so the image encryption algorithm is mainly designed around scrambling and diffusion. The advantages of initial value sensitivity, etc., are very suitable for the field of image encryption.

Due to the disadvantage of uneven mapping distribution in one-dimensional chaotic map, the encryption effect of image encryption algorithm based on one-dimensional chaotic map is not good, and there is also the problem of small key space, which makes the algorithm unable to resist brute force attacks; although high-dimensional chaos Mapping has complex chaotic behavior and is difficult to predict, but it will lead to high execution cost of the algorithm, and requires relatively high computing power of the computer. At the same time, a good image encryption method also needs to have the ability to resist plaintext attacks.

Therefore, how to provide an image encryption method based on Tent mapping and composite chaotic mapping to improve the security of image encryption and reduce execution cost has become an urgent problem to be solved.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide an image encryption method based on Tent mapping and composite chaotic mapping, so as to improve the security of image encryption and reduce the execution cost.

The present invention is realized as follows: a kind of image encryption method based on Tent mapping and compound chaotic mapping, comprising the following steps:

Step S10, obtaining the original image with a size of M×N, and creating a matrix I with a size of M×N; the matrix information of the original image is stored in the matrix I;

Step S20, generate 6 initial keys based on the matrix information stored in the matrix 1;

Step S30, obtain 3 chaotic sequences of Tent mapping and composite chaotic mapping based on the initial key;

Step S40: Perform two rounds of scrambling diffusion operations on the original image based on the chaotic sequence to obtain an encrypted image.

Further, in the step S10, the matrix information includes pixel positions and pixel values.

Further, the step S20 specifically includes:

Step S21, creating a one-dimensional matrix X with a size of 1×4, randomly generating 3 random numbers with values ranging from 0 to 1 and storing them in the first three columns of the one-dimensional matrix X; obtaining the matrix information The sum of all pixel values in and stored in the 4th column of the one-dimensional matrix X;

Step S22: Calculate the complex chaotic mapping coefficients e ₁ , e ₂ , e ₃ and e ₄ based on the one-dimensional matrix X:

Step S23: Calculate initial keys x(1), y(1), a ₁ , μ ₁ , u and z(1) based on each of the composite chaotic mapping coefficients:

x(1)=e ₁ ;

y(1)=e ₂ ;

a ₁ =2+e ₃ ;

μ ₁ =0.99+e ₄ ;

u=1.999999+e ₄ ;

z(1)=0.000001+e ₄ .

Further, the step S30 is specifically:

The chaotic sequences s ₁ , s ₂ and s ₃ of the Tent map and the composite chaotic map are obtained based on each of the initial keys, and the three chaotic sequences are mapped to a pseudo-random sequence R _n in the range of 0 to 255:

_Rn =mod(ceil( _sn ×10∧3),256),n={1,2,3}.

Further, in the step S30, the mathematical model of the Tent mapping is:

Where u represents the control parameter, and the value range is [0, 2]; z _n is the iteration variable of the Tent map, and when the value range of the initial value z ₁ is (0, 1), the Tent map enters the chaotic region.

Further, in the step S30, the composite chaotic mapping adopts Sine mapping and Chebyshev mapping as the seed mapping, and utilizes the mapping generated by the perturbation bifurcation parameter, and the mathematical model of the composite chaotic mapping is:

The value range of μ is (0, 1]; x _n represents the output chaotic sequence, and the value range is (0, 1); when the absolute value of the initial key a ₁ is not less than 2, the composite chaotic map enters the chaotic area , generates an infinite-length aperiodic chaotic real-valued sequence under the condition of infinite precision; the value range of y _n is [-1, 1]; c represents the weighting parameter, which is 0.1; n represents the number of iterations; μ ₁ represents the control parameter Iterative initial value of μ; a ₁ represents the iterative initial value of the control parameter a; x _n+1 , y _n+1 represent the iterative variables of the composite chaotic map; μ _n+1 , a _n+1 represent the iterative variables of the control parameter.

Further, the step S40 specifically includes:

Step S41, utilize the circshift function to carry out the first round of scrambling to the matrix I to obtain the image I ₁ ;

Step S42, using the pseudo-random sequence R ₂ generated by the composite chaotic map to perform the first round of diffusion on the image I ₁ to obtain a matrix C:

where i represents the position information of the matrix; C(i) represents the i-th number in the matrix C; C(i+1) represents the i+1-th number in the matrix C;

Step S43, using the pseudo-random sequence _R3 generated by Tent mapping to perform a bit XOR operation on the matrix C to obtain the matrix CC generated by the second diffusion;

Step S44 , shuffling the matrix CC by using the pseudo-random sequence R ₁ generated by the composite chaotic map to obtain an encrypted image CCC generated by the second round of scrambling.

The advantages of the present invention are:

1. By using Sine map and Chebyshev map as seed map, and using perturbation bifurcation parameters to generate composite chaotic map, the complexity of composite chaotic map is improved, the key space is effectively expanded, and the security of image encryption is greatly improved sex.

2. By combining two one-dimensional chaotic maps into a new composite chaotic map, the execution cost of the image encryption algorithm is greatly reduced, and the dependence on the computing power of the computer is relieved.

3. By using the pixel values in the plaintext matrix information as the basis for generating the initial key, the ability of the image encryption algorithm to resist plaintext attacks is greatly improved.

Description of drawings

The present invention will be further described below with reference to the accompanying drawings and embodiments.

FIG. 1 is a flow chart of an image encryption method based on Tent mapping and composite chaotic mapping according to the present invention.

FIG. 2 is a schematic flowchart of an image encryption method based on Tent mapping and composite chaotic mapping according to the present invention.

FIG. 3 is a schematic diagram of the original image preprocessing of the present invention.

FIG. 4 is a schematic diagram of the second round of scrambling according to the present invention.

Figure 5 is a test image of the present invention.

Fig. 6 is the encryption effect diagram of the test image of the present invention.

Detailed ways

Please refer to FIG. 1 to FIG. 6 , one of the preferred embodiments of an image encryption method based on Tent mapping and composite chaotic mapping of the present invention includes the following steps:

Step S10, obtaining the original image with a size of M×N, and creating a matrix I with a size of M×N; the matrix information of the original image is stored in the matrix I;

Step S20, generate 6 initial keys based on the matrix information stored in the matrix 1;

Step S30, obtaining 3 chaotic sequences of Tent mapping and composite chaotic mapping based on the initial key; removing the first 1000 random numbers of each of the chaotic sequences to ensure the randomness of the chaotic sequences;

Step S40: Perform two rounds of scrambling diffusion operations on the original image based on the chaotic sequence to obtain an encrypted image.

In the step S10, the matrix information includes pixel positions and pixel values.

The step S20 specifically includes:

Step S21, creating a one-dimensional matrix X with a size of 1×4, randomly generating 3 random numbers with values ranging from 0 to 1 and storing them in the first three columns of the one-dimensional matrix X; obtaining the matrix information The sum of all pixel values in and stored in the 4th column of the one-dimensional matrix X;

Step S22: Calculate the complex chaotic mapping coefficients e ₁ , e ₂ , e ₃ and e ₄ based on the one-dimensional matrix X:

Step S23: Calculate initial keys x(1), y(1), a ₁ , μ ₁ , u and z(1) based on each of the composite chaotic mapping coefficients:

x(1)=e ₁ ;

y(1)=e ₂ ;

a ₁ =2+e ₃ ;

μ ₁ =0.99+e ₄ ;

u=1.999999+e ₄ ;

z(1)=0.000001+e ₄ ;

Among them, 2, 0.99, 1.999999, and 0.000001 are the preset initial values.

The step S30 is specifically:

The chaotic sequences s ₁ , s ₂ and s ₃ of the Tent map and the composite chaotic map are obtained based on each of the initial keys, and the three chaotic sequences are mapped to a pseudo-random sequence R _n in the range of 0 to 255:

R _n =mod(ceil(s _n ×10∧3),256),n={1,2,3};

The pseudo-random sequence R _n includes a pseudo-random sequence R ₁ generated by using a composite chaotic map, a pseudo-random sequence R ₂ generated by using a composite chaotic map, and a pseudo-random sequence R ₃ generated by using a Tent map.

In the step S30, the mathematical model of the Tent mapping is:

Where u represents the control parameter, and the value range is [0, 2]; z _n is the iteration variable of the Tent map, and when the value range of the initial value z ₁ is (0, 1), the Tent map enters the chaotic region.

In the step S30, the composite chaotic map is a map generated by using the Sine map and the Chebyshev map as the seed map, and the perturbation bifurcation parameter is used, and the mathematical model of the composite chaotic map is:

The value range of μ is (0, 1]; x _n represents the output chaotic sequence, and the value range is (0, 1); when the absolute value of the initial key a ₁ is not less than 2, the composite chaotic map enters the chaotic area , generates an infinite-length aperiodic chaotic real-valued sequence under the condition of infinite precision; the value range of y _n is [-1, 1]; c represents the weighting parameter, which is 0.1; n represents the number of iterations; μ ₁ represents the control parameter Iterative initial value of μ; a ₁ represents the iterative initial value of the control parameter a; x _n+1 , y _n+1 represent the iterative variables of the composite chaotic map; μ _n+1 , a _n+1 represent the iterative variables of the control parameter.

The step S40 specifically includes:

Step S41, utilize the circshift function to carry out the first round of scrambling to the matrix I to obtain the image I ₁ ;

Step S42, using the pseudo-random sequence R ₂ generated by the composite chaotic map to perform the first round of diffusion on the image I ₁ to obtain a matrix C:

where i represents the position information of the matrix; C(i) represents the i-th number in the matrix C; C(i+1) represents the i+1-th number in the matrix C;

Step S43, using the pseudo-random sequence _R3 generated by Tent mapping to perform a bit XOR operation on the matrix C to obtain the matrix CC generated by the second diffusion;

Step S44 , shuffling the matrix CC by using the pseudo-random sequence R ₁ generated by the composite chaotic map to obtain an encrypted image CCC generated by the second round of scrambling.

The decryption process of the encrypted image CCC is the inverse process of the image encryption algorithm, and the initial keys and chaotic sequences for decryption and encryption are the same.

The second preferred embodiment of an image encryption method based on Tent mapping and composite chaotic mapping of the present invention includes the following steps:

Step S10, acquiring a test image with a size of 512×512 (as shown in FIG. 3 ), and creating a matrix I with a size of 512×512; storing the matrix information of the original image in the matrix I; the matrix information Including pixel position and pixel value;

Step S20, generate 6 initial keys based on the matrix information stored in the matrix 1;

Step S30, iterate Tent map and composite chaotic map (1000+512×512) times respectively based on the initial key, generate 3 chaotic sequences, and remove the first 1000 random numbers of each described chaotic sequence;

Step S40 , performing two rounds of scrambling diffusion operations on the original image based on the chaotic sequence to obtain an encrypted test image (as shown in FIG. 4 ).

The step S20 specifically includes:

Step S21, creating a one-dimensional matrix X with a size of 1×4, randomly generating 3 random numbers with values ranging from 0 to 1 and storing them in the first three columns of the one-dimensional matrix X; obtaining the matrix information The sum of all pixel values in and stored in the 4th column of the one-dimensional matrix X;

Step S22: Calculate the complex chaotic mapping coefficients e ₁ , e ₂ , e ₃ and e ₄ based on the one-dimensional matrix X:

Step S23: Calculate initial keys x(1), y(1), a ₁ , μ ₁ , u and z(1) based on each of the composite chaotic mapping coefficients:

x(1)=e ₁ ;

y(1)=e ₂ ;

a ₁ =2+e ₃ ;

μ ₁ =0.99+e ₄ ;

u=1.999999+e ₄ ;

z(1)=0.000001+e ₄ ;

Among them, 2, 0.99, 1.999999, and 0.000001 are the preset initial values.

The step S40 specifically includes:

Step S41, utilize the circshift function to carry out the first round of scrambling to the matrix I, that is, to regard the matrix I as a one-dimensional matrix, and carry out a cyclic shift operation to each row and each column of the matrix I respectively, and then obtain an image. I ₁ ;

Step S42, using the pseudo-random sequence R ₂ generated by the composite chaotic map to perform the first round of diffusion on the image I ₁ , that is, converting the image I ₁ into a one-dimensional row vector, and the image I ₁ and the pseudo-random sequence R ₂ are equal in size. matrix, take out the values of the first positions of I ₁ and R ₂ respectively and add them together, perform a mod operation on 256, and perform an XOR operation on the calculation result of the mod operation and the previous calculation result, and so on, and then get the matrix C :

where i represents the position information of the matrix; C(i) represents the i-th number in the matrix C; C(i+1) represents the i+1-th number in the matrix C;

Step S43, using the pseudo-random sequence _R3 generated by Tent mapping to perform a bit XOR operation on the matrix C, that is, converting the matrix C and _R3 into a matrix with a size of 512×512, traversing the two matrices at the same time, and taking out The values in the same position of the two matrices are converted into a binary number represented by a string, and then the binary XOR operation is performed, and the result is converted into decimal, and so on, and the matrix CC generated by the second diffusion disorder is obtained;

Step S44, shuffling the matrix CC by using the pseudo _- random sequence R1 generated by the composite chaotic map, that is, performing _a sort operation _on the matrix R1, sorting the values in the matrix R1 in _ascending order, The position change data is stored in a new position matrix, and the matrix CC is scrambled according to the position matrix, thereby obtaining an encrypted test image generated by the second round of scrambling.

To sum up, the advantages of the present invention are:

1. By using Sine map and Chebyshev map as seed map, and using perturbation bifurcation parameters to generate composite chaotic map, the complexity of composite chaotic map is improved, the key space is effectively expanded, and the security of image encryption is greatly improved sex.

2. By combining two one-dimensional chaotic maps into a new composite chaotic map, the execution cost of the image encryption algorithm is greatly reduced, and the dependence on the computing power of the computer is relieved.

3. By using the pixel values in the plaintext matrix information as the basis for generating the initial key, the ability of the image encryption algorithm to resist plaintext attacks is greatly improved.

Although the specific embodiments of the present invention are described above, those skilled in the art should understand that the specific embodiments we describe are only illustrative, rather than used to limit the scope of the present invention. Equivalent modifications and changes made by a skilled person in accordance with the spirit of the present invention should be included within the scope of protection of the claims of the present invention.

Claims (6)

1. an image encryption method based on Tent mapping and composite chaotic mapping, is characterized in that: comprise the steps: Step S10, obtaining the original image with a size of M×N, and creating a matrix I with a size of M×N; the matrix information of the original image is stored in the matrix I; Step S20, generate 6 initial keys based on the matrix information stored in the matrix 1; Step S30, obtain 3 chaotic sequences of Tent mapping and composite chaotic mapping based on the initial key; Step S40, performing two rounds of scrambling and diffusion operations on the original image based on the chaotic sequence to obtain an encrypted image; The step S20 specifically includes: Step S21, creating a one-dimensional matrix X with a size of 1×4, randomly generating 3 random numbers with values ranging from 0 to 1 and storing them in the first three columns of the one-dimensional matrix X; obtaining the matrix information The sum of all pixel values in and stored in the 4th column of the one-dimensional matrix X; Step S22: Calculate the complex chaotic mapping coefficients e ₁ , e ₂ , e ₃ and e ₄ based on the one-dimensional matrix X:

Step S23: Calculate initial keys x(1), y(1), a ₁ , μ ₁ , u and z(1) based on each of the composite chaotic mapping coefficients: x(1)=e ₁ ; y(1)=e ₂ ; a ₁ =2+e ₃ ; μ ₁ =0.99+e ₄ ; u=1.999999+e ₄ ; z(1)=0.000001+e ₄ . 2 . The image encryption method based on Tent mapping and composite chaotic mapping according to claim 1 , wherein in the step S10 , the matrix information includes pixel positions and pixel values. 3 . 3. a kind of image encryption method based on Tent mapping and compound chaotic mapping as claimed in claim 1, is characterized in that: described step S30 is specifically: The chaotic sequences s ₁ , s ₂ and s ₃ of the Tent map and the composite chaotic map are obtained based on each of the initial keys, and the three chaotic sequences are mapped to a pseudo-random sequence R _n in the range of 0 to 255: _Rn =mod(ceil( _sn ×10^3),256),n={1,2,3}. 4. a kind of image encryption method based on Tent mapping and compound chaotic mapping as claimed in claim 1, is characterized in that: in described step S30, the mathematical model of described Tent mapping is:

Where u represents the control parameter, and the value range is [0, 2]; z _n is the iteration variable of the Tent map, and when the value range of the initial value z ₁ is (0, 1), the Tent map enters the chaotic region. 5. a kind of image encryption method based on Tent mapping and compound chaotic mapping as claimed in claim 1, is characterized in that: in described step S30, described compound chaotic mapping is to adopt Sine mapping and Chebyshev mapping as seed mapping, utilize The mapping generated by the perturbation bifurcation parameters, the mathematical model of the composite chaotic mapping is:

The value range of μ is (0, 1]; x _n represents the output chaotic sequence, and the value range is (0, 1); when the absolute value of the initial key a ₁ is not less than 2, the composite chaotic map enters the chaotic area , generates an infinite-length aperiodic chaotic real-valued sequence under the condition of infinite precision; the value range of y _n is [-1, 1]; c represents the weighting parameter, which is 0.1; n represents the number of iterations; μ ₁ represents the control parameter Iterative initial value of μ; a ₁ represents the iterative initial value of the control parameter a; x _n+1 , y _n+1 represent the iterative variables of the composite chaotic map; μ _n+1 , a _n+1 represent the iterative variables of the control parameter. 6. a kind of image encryption method based on Tent mapping and compound chaotic mapping as claimed in claim 3, is characterized in that: described step S40 specifically comprises: Step S41, utilize the circshift function to carry out the first round of scrambling to the matrix I to obtain the image I ₁ ; Step S42, using the pseudo-random sequence R ₂ generated by the composite chaotic map to perform the first round of diffusion on the image I ₁ to obtain a matrix C:

where i represents the position information of the matrix; C(i) represents the i-th number in the matrix C; C(i+1) represents the i+1-th number in the matrix C; Step S43, using the pseudo-random sequence _R3 generated by Tent mapping to perform bit XOR operation on the matrix C to obtain the matrix CC generated by the second round of diffusion; Step S44 , shuffling the matrix CC by using the pseudo-random sequence R ₁ generated by the composite chaotic map to obtain an encrypted image CCC generated by the second round of scrambling.

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