CN112765635B - Image encryption method based on coupling mapping grid model - Google Patents
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Abstract
The invention provides an image encryption method based on a coupled mapping grid model. The method comprises the steps of calculating by utilizing a hash value of a plaintext image P and an external key to obtain control parameters and an initial value of a coupled mapping lattice chaotic system; then, iterating the coupled mapping grid system to obtain f (x) chaotic sequences and coupled mapping grid chaotic sequences; scrambling the plaintext image P by using the index matrix; then, performing diffusion operation by using the chaotic matrix and the replacement image; and finally, performing reverse diffusion operation on the diffusion image to obtain a final ciphertext image. The method fully utilizes the intermediate chaotic sequence generated by the mapping of the coupled mapping grid system, simultaneously uses the chaotic sequence for multiple times, improves the utilization rate of the chaotic sequence, has enough key space and high key sensitivity, and has higher safety and applicability.
Description
Technical Field
The invention relates to the technical field of image encryption, in particular to an image encryption method based on a coupled mapping grid model.
Background
With the rapid development of computer technology and network technology, more and more images are transmitted through the network, but the openness and the shareability of the network pose a great threat to the security of image information. Therefore, it becomes especially important to secure image transmission, and image encryption is an important means for securing images. Because the image has the characteristics of large information amount, high redundancy and high adjacent pixel correlation, the efficiency of traditional encryption algorithms such as a Data Encryption Standard (DES), an International Data Encryption Algorithm (IDEA), an improved encryption standard (AES) and the like is low, and the requirement of people on real-time encryption of the image cannot be met. The chaotic system is a nonlinear system, has the characteristics of ergodicity, pseudo-randomness, unpredictability, high sensitivity to initial values and the like, and is more suitable for image encryption.
However, the f (x) function of many existing image encryption algorithms based on the Coupled Mapping Lattice (CML) model mostly adopts a one-dimensional Logistic function, but the Logistic chaotic system has the defects of short period, insufficient key space and the like, for example, Wang et al propose a CML-based block image encryption algorithm (XYWang, XMBao. A novel block encryption system based on the coordinated chromatic mapping. nonlinear Dynamics,2013,72(4):707-715), Wang et al also propose a color image encryption algorithm using CML and DNA operations (XY Wang, HL Zhang, XM Bao. color image encryption scheme using CML and DNA sequence operations, Biosystems (2016) 19-26), Wu et al propose a CML-based color image DNA encryption algorithm (XJ. Wu, KS-. In addition, in the process of generating the CML chaotic sequence X, f (X) chaotic system is required to be brought to generate intermediate sequences, the intermediate sequences are also chaotic sequences, and a certain time is also required for calculating f (X), but in the traditional encryption algorithm based on the CML chaotic system, only the X sequence is used, so that the chaotic sequence is lost, and the safety of the original encryption algorithm is not too high. Still other algorithms are only related to the key in the encryption process, so that the encryption algorithm is easily attacked by selecting plaintext and cannot meet the requirement of high security.
Disclosure of Invention
Aiming at the problems that the traditional encryption method is low in safety and easy to attack by selecting plaintext, the invention provides an image encryption method based on a coupled mapping lattice model.
The invention provides an image encryption method based on a coupled mapping grid model, which comprises the following steps:
step 1: calculating by utilizing the hash value of the plaintext image P and an external key to obtain a control parameter and an initial value of the coupled mapping lattice chaotic system; the size of the plaintext image P is M multiplied by N, M is the number of rows, and N is the number of columns;
step 2: iteratively coupling the mapping grid system according to the control parameters and the initial values to obtain F (x) chaotic sequences which are recorded as F ═ F 1 ,F 2 ,F 3 The chaos sequence of the coupled mapping grids is recorded as X ═ X 1 ,X 2 ,X 3 }；
And step 3: using sorting function to respectively align sequences F 1 And sequence X 1 Sequencing to respectively obtain corresponding index matrixes findex and xindex, and scrambling the plaintext image P by using the index matrixes findex and xindex to obtain a replacement image P';
and 4, step 4: will sequence F 2 And sequence X 2 Respectively converted into integer sequences F of 0 to 255 2 ' and X 2 ', then two sequences of integers F 2 ' and X 2 ' conversion into M × N matrices F, respectively 2 "and X 2 Using the two resulting M N matrices F 2 "and X 2 Performing diffusion operation with the replacement image P to obtain a diffusion image C';
and 5: will sequence F 3 And sequence X 3 Respectively converted into integer sequences F of 0 to 255 3 ' and X 3 ', then two integer sequences F 3 ' and X 3 ' convert into M × N matrix F respectively 3 "and X 3 Using the two resulting M N matrices F 3 "and X 3 And performing reverse diffusion operation with the diffusion image C' to obtain a final ciphertext image C.
Further, in step 1, the coupling mapping grid system is shown as formula (1):
wherein epsilon is a composite coupling parameter, n is a time series, j is a space index, L is the number of lattices, L is 3, and f (×) is a chaotic mapping function.
Further, in step 1, the hash value of the plaintext image and the external key are used to calculate the control parameters epsilon, tau and the initial value x of the coupled mapping lattice chaotic system according to the formula (3) 0 (1)、x 0 (2)、x 0 (3)：
Where hex2dec (×) indicates the conversion of the hexadecimal number into the corresponding decimal number, H is a 256-bit hash value for generating the plaintext image P using the hash function SHA-256, 32 groups are obtained in a group of 8 bits, and H is represented as H ═ H 1 ,h 2 ,...h 32 ]；ε 0 ,τ 0 And x 01 ,x 02 ,x 03 And the control parameters and the initial values of the external key of the coupled mapping grid chaotic system under the f (#) chaotic mapping function.
Further, the chaotic mapping function f (×) is mapped by a PWLCM.
Further, in step 3, the sequences F are respectively sorted according to the sorting function shown in formula (5) 1 And sequence X 1 And sorting to respectively obtain corresponding index matrixes findex and xindex:
wherein sort (#) denotes sorting the sequence in ascending order, SF 1 Represents sequence F 1 Sorting results in an ascending order; SX 1 Represents sequence X 1 And (5) sequencing the results in an ascending order.
Further, in step 3, the plaintext image P is scrambled by using the index matrices findex and xindex according to formula (6), so as to obtain a permuted image:
wherein, P' represents a replacement image obtained by replacing the plaintext image P by using an index matrix findex; p "represents a replacement image obtained by arranging the replacement image P' using the index matrix xindex.
Further, in step 4, the sequence F is expressed according to the formula (7) 2 And sequence X 2 Converting the integer sequence F into an integer sequence of 0 to 255 2 ' and X 2 ′：
Where floor (×) denotes a down-rounding function, mod denotes a modulo operation, and i is 1,2,3 …, MN.
Further, in step 4, the two resulting M × N matrices F are utilized according to equation (9) 2 "and X 2 "diffusion operation with the replacement image P" to obtain a diffusion image C':
wherein the content of the first and second substances,
indicating an exclusive or operation.
Further, in step 5, the sequence F is expressed according to the formula (10) 3 And sequence X 3 Respectively converted into integer sequences F of 0 to 255 3 ' and X 3 ′：
Where floor (×) denotes a down-rounding function, mod denotes a modulo operation, and i is 1,2,3 …, MN.
Further, in step 5, the two resulting M × N matrices F are utilized according to equation (12) 3 "and X 3 And performing reverse diffusion operation with the diffusion image to obtain a final ciphertext image C:
wherein the content of the first and second substances,
indicating an exclusive or operation.
The invention has the beneficial effects that:
(1) in the invention, the chaos sequence generated by the coupled mapping lattice model is utilized, and in the encryption process, not only the CML chaos sequence X is used, but also the intermediate chaos sequence generated by f (X) mapping in the model is used, so that the chaos sequence generated by the system is fully used for encrypting the image, and the security of the encryption method is effectively enhanced.
(2) The image encryption method of the invention designs two diffusion operations, one forward diffusion operation and one reverse diffusion operation, thereby effectively improving the security of the encryption method of the invention.
(3) In the encryption method, the initial value and the control parameter of the chaotic system are related to the plaintext image, so that the key is related to the plaintext image and the external key, and the capacity of resisting the attack of selecting the plaintext is enhanced.
(4) Experiments prove that the encryption method has enough key space, high key sensitivity and higher safety and applicability.
Drawings
Fig. 1 is a schematic flowchart of an image encryption method based on a coupled-map lattice model according to an embodiment of the present invention;
fig. 2 is a diagram of the encryption and decryption effects provided by the embodiment of the present invention and using the method of the present invention: (a) is a plaintext image; (b) is a ciphertext image; (c) to decrypt the image;
fig. 3 is a graph of the key sensitivity test results provided by the embodiment of the present invention: (a) is a plaintext image; (b) is a ciphertext image; (c) to use the decrypted image of the correct key; (d) to use the decrypted image of the wrong key;
fig. 4 is a graph illustrating a correlation distribution between adjacent pixels of a plaintext image and a ciphertext image according to an embodiment of the present invention: (a) is a plaintext image level correlation; (b) horizontal correlation for ciphertext images; (c) is the plaintext image vertical correlation; (d) is the vertical correlation of the ciphertext image; (e) is the plaintext image angular dependency; (f) is the ciphertext image angular dependency;
fig. 5 is a histogram of a plaintext image, a ciphertext image, and a decrypted image according to an embodiment of the present invention: (a) a clear text image histogram; (b) a histogram of the ciphertext image; (c) is a decrypted image histogram;
fig. 6 is a shear attack test result diagram provided by the embodiment of the present invention: (a) the image after 1/16 is cut in the upper left corner of the ciphertext image; (b) an image after being cut 1/8 in the lower left corner of the ciphertext image; (c) an image after being cut 1/4 in the lower right corner of the ciphertext image; (d) for (a) the corresponding decrypted image; (e) for (b) the corresponding decrypted image; (f) is (c) the corresponding decrypted image.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, an embodiment of the present invention provides an image encryption method based on a coupled shadow lattice model, including the following steps:
s101, calculating a control parameter and an initial value: firstly, calculating control parameters and initial values of a coupled mapping lattice chaotic system (hereinafter referred to as a CML system) by utilizing a hash value of a plaintext image and an external key; in order to avoid loss of generality, the size of the plaintext image P is defined as M × N, where M is the number of rows and N is the number of columns.
As an implementation manner, in the embodiment of the present invention, a coupled mapping grid system shown in formula (1) is adopted:
wherein epsilon is a composite coupling parameter, n is a time series, j is a space index, L is the number of lattices, L is 3, and f (×) is a chaotic mapping function. When f (#) is a chaotic system, the coupled mapping grid system displays the chaotic characteristics of the chaotic system, so the mapping function f (#) can be any chaotic mapping. For example, the embodiment of the present invention may adopt PWLCM mapping as a mapping function, where the mapping is:
wherein, the independent variable x belongs to [0,1], the control parameter tau belongs to (0, 0.5);
as an implementation manner, the hash value of the plaintext image and the external key are used to calculate the control parameters epsilon, tau and the initial value x of the coupled mapping lattice chaotic system according to formula (3) 0 (1)、x 0 (2)、x 0 (3)：
Where hex2dec (×) represents the conversion of hexadecimal numbers into corresponding decimal numbers, H is a 256-bit hash value of the plaintext image P generated by the hash function SHA-256, and 32 groups are obtained in a group of 8 bits, and H is represented as:
H＝[h 1 ,h 2 ,...h 32 ](4)
ε 0 ,τ 0 ,x 01 ,x 02 ,x 03 are control parameters and initial values of the external keys of the CML system based on PWLCM mapping.
S102, generating a chaos sequence: using the control parameters and the initial values obtained in step S101 to iterate the coupled mapping grid system, and obtaining F (x) chaotic sequences respectively, which are denoted as F ═ F 1 ,F 2 ,F 3 The chaos sequence of the coupled mapping grids is recorded as X ═ X 1 ,X 2 ,X 3 }；
Specifically, to eliminate transient effects, the first l is discarded during the iterative coupled-map trellis system 0 And continuously iterating the chaotic sequences M multiplied by N times to obtain F (X) chaotic sequences F and coupling mapping grid chaotic sequences X. In this embodiment, the chaotic sequence F 1 ,F 2 ,F 3 ,X 1 ,X 2 ,X 3 All of them are M.times.N in length. l 0 Is specified as required.
S103, replacement operation: taking the first sequence F in the F sequence 1 And the first sequence X of the X sequences 1 Separately aligning the sequences F using an ordering function 1 And sequence X 1 Sequencing to respectively obtain corresponding index matrixes findex and xindex, and scrambling the plaintext image P by using the index matrixes findex and xindex to obtain a replacement image P';
as an implementation, the sequences F are respectively sorted according to the sorting function shown in formula (5) 1 And sequence X 1 And sorting to obtain index matrixes findex and xindex respectively:
wherein sort (#) denotes sorting the sequence in ascending order, SF 1 Represents sequence F 1 Sorting results in an ascending order; SX 1 Represents sequence X 1 And (5) sequencing the results in an ascending order.
As an implementation, the plaintext image P is scrambled by using the index matrices findex and xindex according to formula (6), so as to obtain a permuted image:
wherein, P' represents a replacement image obtained by replacing the plaintext image P by using an index matrix findex; p "represents a replacement image obtained by arranging the replacement image P' using the index matrix xindex.
S104, diffusion operation: taking the second sequence F in the F sequence 2 And the second sequence X of the X sequences 2 The sequence F 2 And sequence X 2 Respectively converted into integer sequences F of 0 to 255 2 ' and X 2 ', then two integer sequences F 2 ' and X 2 ' conversion into M × N matrices F, respectively 2 "and X 2 Using the two resulting M N matrices F 2 "and X 2 Performing diffusion operation with the replacement image P to obtain a diffusion image C';
as an implementation, the sequence F is expressed according to equation (7) 2 And sequence X 2 Converting the integer sequence F into an integer sequence of 0 to 255 2 ' and X 2 ′：
Where floor (×) denotes a down-rounding function, mod denotes a modulo operation, and i is 1,2,3 …, MN.
As an implementation, the one-dimensional sequence F is expressed by equation (8) 2 ' and X 2 ' conversion into M rows and N columns of matrix F 2 "and X 2 ″：
Where reshape (×) denotes the transformation of the specified matrix into a particular dimension matrix function.
As an implementation, the two resulting M N matrices F are utilized according to equation (9) 2 "and X 2 "diffusion operation with the replacement image P" to obtain a diffusion image C':
wherein, the first and the second end of the pipe are connected with each other,
indicating an exclusive or operation.
S105, reverse diffusion operation: taking the third sequence F in the F sequence 3 And the third sequence X of the X sequences 3 The sequence F 3 And sequence X 3 Respectively converted into integer sequences F of 0 to 255 3 ' and X 3 ', then two integer sequences F 3 ' and X 3 ' conversion into M × N matrices F, respectively 3 "and X 3 Using the two resulting M N matrices F 3 "and X 3 And performing reverse diffusion operation with the diffusion image C' to obtain a final ciphertext image C.
As an implementable way, the sequence F is expressed according to the formula (10) 3 And sequence X 3 Respectively converted into integer sequences F of 0 to 255 3 ' and X 3 ′：
Where floor denotes a down-rounding function, mod denotes a modulo operation, and i is 1,2,3 …, MN.
As an implementable way, the one-dimensional sequence F is expressed by equation (11) 3 ' and X 3 ' conversion into M rows and N columns of matrix F 3 "and X 3 ″：
Where reshape (×) denotes the transformation of the specified matrix into a particular dimension matrix function.
As an implementation manner, the two M × N matrices obtained are used to perform inverse diffusion operation with the diffusion image according to equation (12), so as to obtain the final ciphertext image C:
wherein the content of the first and second substances,
indicating an exclusive or operation.
The decryption method is the inverse operation of the encryption method, and is not described herein again.
In order to verify the effectiveness of the image encryption method provided by the invention, the invention also provides the following experimental data.
The hardware environment of this validation experiment is shown in table 1:
TABLE 1 software and hardware Environment
The parameter values set in this verification experiment are shown in table 2:
TABLE 2 Algorithm input parameters
| Type (B) | Value of |
| CML control parameters | ε 0 ＝0.133 |
| PWLCM control parameters | τ 0 ＝0.155 |
| Initial values of CML mapping and PWLCM mapping | x 01 ＝0.133，x 02 ＝0.333，x 03 ＝0.533 |
| Number of discarded chaotic sequences | l 0 ＝200 |
FIG. 2 is a diagram showing the effects of encryption and decryption by the method of the present invention, and it can be seen from FIG. 2(b) that the resulting ciphertext image is similar to noise and is unable to obtain any information of the original image from the encrypted image; as can be seen from fig. 2(c), the decrypted image is identical to the original image.
Fig. 3 is a diagram of key sensitivity analysis, in which fig. 3(a) is a plaintext image, fig. 3(b) is a ciphertext image, and fig. 3(c) is an image decrypted by using a correct key. Mapping the coupling to the control parameter epsilon of the lattice model 0 Modified as epsilon 0 +10 -14 And other parameters are unchanged, the original ciphertext image is decrypted, and the decryption effect is shown in fig. 3(d), so that when the key value is slightly changed, the decrypted image is in a completely disordered state, which shows that the method has strong key sensitivity.
And randomly selecting 1000 pairs of adjacent pixel points to test in the horizontal direction, the vertical direction and the diagonal direction of the Lena plaintext image and the ciphertext image. The correlation relationship between the plaintext and the ciphertext image in three directions is shown in fig. 4, and it can be seen from the figure that the correlation between the adjacent pixels of the original text of the Lena image in three directions is stronger, and there is almost no relationship between the adjacent points of the ciphertext image.
FIG. 5 is a statistical histogram of a Lena plaintext image, a ciphertext image and a decrypted image, which can be visually seen through the histogram, and the histogram of the decrypted image is identical to the histogram of the plaintext image, which shows that the decryption effect is good; meanwhile, the pixel values of the ciphertext image are almost uniformly distributed, which shows that the method can effectively resist statistical attack.
The Lena ciphertext image is cut at different positions in different proportions, and then is decrypted to test the shearing resistance of the method, and the test result is shown in fig. 6. Where fig. 6(a), (b), and (c) are images corresponding to the ciphertext image upper left corner, lower left corner, and lower right corner clips 1/16, 1/8, and 1/4, respectively, and fig. 6(d), (e), and (f) are corresponding decrypted images. As can be seen from FIG. 6, the method of the present invention can effectively resist shear attack.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (3)
1. The image encryption method based on the coupling mapping grid model is characterized by comprising the following steps:
step 1: calculating by utilizing the hash value of the plaintext image P and an external key to obtain a control parameter and an initial value of the coupled mapping lattice chaotic system; the size of the plaintext image P is M multiplied by N, M is the number of rows, and N is the number of columns; calculating control parameters epsilon and tau and an initial value x of the coupled mapping lattice chaotic system by using the Hash value of the plaintext image and the external key according to the formula (3) 0 (1)、x 0 (2)、x 0 (3)：
Where hex2dec (×) indicates the conversion of the hexadecimal number into the corresponding decimal number, H is a 256-bit hash value for generating the plaintext image P using the hash function SHA-256, 32 groups are obtained in a group of 8 bits, and H is represented as H ═ H 1 ,h 2 ,...h 32 ]；ε 0 ,τ 0 And x 01 ,x 02 ,x 03 Is a coupled mapping grid chaotic system under f (#) chaotic mapping functionControl parameters and initial values of the external key;
step 2: iteratively coupling the mapping grid system according to the control parameters and the initial values to obtain F (x) chaotic sequences which are recorded as F ═ F 1 ,F 2 ,F 3 The chaos sequence of the coupled mapping grids is recorded as X ═ X 1 ,X 2 ,X 3 }；
And step 3: using sorting function to respectively pair sequences F 1 And sequence X 1 Sequencing to respectively obtain corresponding index matrixes findex and xindex, and scrambling the plaintext image P by using the index matrixes findex and xindex to obtain a replacement image P'; the sequences F are respectively aligned according to the sorting function shown in the formula (5) 1 And sequence X 1 And sorting to respectively obtain corresponding index matrixes findex and xindex:
wherein sort (#) denotes an ascending sort function performed on the sequence, SF 1 Represents sequence F 1 Sorting results in an ascending order; SX 1 Represents sequence X 1 Sorting results in an ascending order;
and (3) scrambling the plaintext image P by using the index matrixes findex and xindex according to the formula (6) to obtain a replacement image:
wherein, P' represents a replacement image obtained by replacing the plaintext image P by using an index matrix findex; p 'represents a replacement image obtained by arranging the replacement image P' by using an index matrix xindex;
and 4, step 4: will sequence F 2 And sequence X 2 Respectively converted into integer sequences F 'of 0 to 255' 2 And X' 2 Then the sequence of two integers F' 2 And X' 2 Respectively converted into M × N matrix F ″) 2 And X ″) 2 Using the obtained two M valuesN matrix F ″) 2 And X ″) 2 Carrying out diffusion operation with the replacement image P 'to obtain a diffusion image C'; sequence F according to equation (7) 2 And sequence X 2 Converted into an integer sequence F 'of 0 to 255' 2 And X' 2 ：
Wherein floor (—) represents a downward rounding function, mod represents a modulo operation, i ═ 1,2,3 …, MN;
the two resulting M N matrices F ″, are utilized according to equation (9) 2 And X ″) 2 And performing diffusion operation with the replacement image P 'to obtain a diffusion image C':
wherein the content of the first and second substances,
represents an exclusive or operation;
and 5: will sequence F 3 And sequence X 3 Respectively converted into integer sequences F 'of 0 to 255' 3 And X' 3 Then the sequence of two integers F' 3 And X' 3 Respectively converted into M × N matrix F ″) 3 And X ″) 3 Using the two resulting M N matrices F ″ 3 And X ″) 3 Performing reverse diffusion operation with the diffusion image C' to obtain a final ciphertext image C; sequence F according to equation (10) 3 And sequence X 3 Respectively converted into integer sequences F 'of 0 to 255' 3 And X' 3 ：
Wherein floor (—) represents a downward rounding function, mod represents a modulo operation, i ═ 1,2,3 …, MN;
the two resulting M N matrices F ″, are utilized according to equation (12) 3 And X ″) 3 And performing reverse diffusion operation with the diffusion image to obtain a final ciphertext image C:
wherein the content of the first and second substances,
indicating an exclusive or operation.
2. The method of claim 1, wherein in step 1, the coupled shadow trellis system is represented by equation (1):
wherein epsilon is a composite coupling parameter, n is a time series, j is a space index, L is the number of lattices, L is 3, and f (×) is a chaotic mapping function.
3. The method according to claim 1 or 2, characterized in that the chaotic mapping function f (×) employs PWLCM mapping.
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