CN116192362A - Lyapunov exponent adjustable chaotic system and image encryption and decryption method - Google Patents
Lyapunov exponent adjustable chaotic system and image encryption and decryption method Download PDFInfo
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Abstract
The invention belongs to the field of digital image encryption, and particularly relates to a Lyapunov exponent adjustable chaotic system, an image encryption and decryption method realized by using the chaotic system, and an image encryption transmission system. The chaotic system belongs to a two-dimensional chaotic system, and a group of control parameters for visually adjusting the Lyapunov exponent of the system are arranged in the system. In the image encryption process, output generated under the input condition of a primary key by parabolic expansion mapping in a chaotic system is mainly used as input of hyperbolic tangent expansion mapping, two chaotic sequences are generated, and finally the two chaotic sequences are used for carrying out matrix processing on a plaintext image to realize image encryption. The image decryption process utilizes the primary key and the secondary key to generate corresponding chaotic sequences, and then the chaotic sequences are used for carrying out inverse processing on the ciphertext images. The invention solves the problems of poor complexity controllability, and insufficient confidentiality and robustness of an image encryption scheme of the traditional chaotic system.
Description
Technical Field
The invention belongs to the field of digital image encryption, and particularly relates to a Lyapunov exponent adjustable chaotic system, an image encryption and decryption method realized by using the chaotic system as a tool, and an image encryption transmission system.
Background
Digital images are one of the most widely spread forms of data on networks; in social networks, people send images of individuals or families to each other, doctors need to rely on medical images to perform disease auxiliary diagnosis in hospitals, and images are needed to realize certain works in various industries such as agriculture and industry. The images contain a large amount of important information related to individuals or groups, and are usually transmitted among specific objects, and once the images are accessed by illegal attackers, immeasurable losses can be caused. How to encrypt an image to prevent information from being illegally cracked has become a research hotspot.
The chaos-based image encryption method overcomes the limitation of the traditional encryption method. The random sequence generated by the chaotic map along with the parameter change can be applied to interference to cover pixel points in the image. The chaotic sequences themselves and their combination with image pixels determine the security and efficiency of the encryption scheme, and how to combine them better is considered a very promising research direction. The security of the encryption scheme depends largely on the performance of the chaotic map. In addition to the high performance of chaotic systems, a method of disturbing pixels that is efficient and safe is also indispensable.
The one-dimensional chaotic mapping structure is simple, the chaotic range is discontinuous, the control parameters are few, and the chaos behavior is lacked, so that the security of an encryption algorithm based on the chaotic system is weaker. The multi-chaotic system has a more complex structure and rich dynamic characteristics, the complexity of the multi-chaotic system can be reflected by positive Lyapunov indexes, however, the existing multi-dimensional chaotic system cannot accurately determine the value of the Lyapunov indexes. The application of a plurality of innovative and effective methods in chaotic image encryption promotes the development of the image encryption field.
However, many chaotic system-based image encryption schemes have keys independent of the plaintext image, which results in encryption algorithms that are not resistant to selective plaintext attacks or known plaintext attacks. Second, many conventional high-confidentiality image encryption schemes have extremely high requirements on the stability of the communication transmission process, which can affect the correct restoration of an image once an information frame is lost or an interference signal occurs. Therefore, how to develop an image encryption method with high complexity, effective attack resistance and strong anti-interference property is a technical problem to be solved by those skilled in the art.
Disclosure of Invention
In order to solve the problem that the conventional image encryption algorithm cannot achieve balance in multiple performances such as complexity, image attack resistance and signal interference resistance, the invention provides a Lyapunov exponent adjustable chaotic system, an image encryption and decryption method realized by using the chaotic system as a tool, and an image encryption transmission system.
The invention is realized by adopting the following technical scheme:
a Lyapunov exponent adjustable chaotic system belongs to a two-dimensional chaotic system, and a group of control parameters for visually adjusting the Lyapunov exponent of the system are arranged in the chaotic system, so that the free customization of the complexity of the system is realized, and the obtained value is obtained.
The chaotic system is used for generating two required sets of chaotic sequences X= { X 1 ，x 2 ，…x n }，Y＝{y 1 ，y 2 ，…y n }. The chaotic system comprises two forms, namely parabolic expansion mapping and hyperbolic tangent expansion mapping. The mapping relation of the parabolic expansion mapping is as follows:
the mapping relation of the hyperbolic tangent expansion map is as follows:
in the above formula, i is the iteration number, x, y is the iteration output value, x i ，y i The value obtained for the ith iteration; mod is a modulo operation; a, a 1 、a 2 And u are system control parameters in the parabolic expansion map, and a 1 、a 2 Lyapunov exponent useful for quantitative adjustment systems; a' 1 、a′ 2 And u 'are both system control parameters in the hyperbolic tangent expansion map, and a' 1 and a′2 Can be used for quantitatively adjusting the Lyapunov exponent of a system.
As a further development of the invention, in the parabolic expansion map, the control parameter a 1 ，a 2 The value of (2) is the value of two Lyapunov indexes of the system; when controlling parameter a 1 ，a 2 When any one of the chaotic systems is larger than zero, the chaotic system is in a chaotic state; when controlling parameter a 1 ，a 2 All are larger than zero, and the chaotic system is in a hyperchaotic state.
In hyperbolic tangent expansion mapping, the control parameter a' 1 and a′2 The value of (2) is the value of two Lyapunov indexes of the system; when controlling parameter a' 1 and a′2 When any one of the chaotic systems is larger than zero, the chaotic system is in a chaotic state; when controlling parameter a' 1 and a′2 All are larger than zero, and the chaotic system is in a hyperchaotic state.
As a further improvement of the invention, the design method of the chaotic system is as follows:
(1) The following classical one-dimensional Logistic map is obtained:
x i+1 ＝ux i (1-x i )
wherein u is a control parameter; i is the iteration number; x is an iteration output value; x is x i The value obtained for the ith iteration; when u is E [3.57,4 ]]And mapping to a chaotic state.
(2) And carrying out dimension lifting, logic transformation, coefficient adjustment and modulo operation on the one-dimensional Logistic mapping to obtain the following two-dimensional parabolic expansion mapping:
in the above formula, i is the iteration number, x, y is the iteration output value, x i ，y i The value obtained for the ith iteration; mod is a modulo operation; a, a 1 ，a 2 And u are each a set of adjustable system control parameters.
(3) 1-y in the above step i Replaced by 1-tan i The following two-dimensional hyperbolic tangent expansion map is obtained:
in the above, a' 1 、a′ 2 And u' are each a set of adjustable system control parameters.
The invention also comprises an image encryption method, which adopts the Lyapunov exponent adjustable chaotic system as an encryption tool to generate a ciphertext image E with the same size as the original plaintext image A. The image encryption method comprises the following steps:
s1: the parabolic expansion mapping is transformed into a plaintext hash function as follows and is used as a required primary chaotic system:
s2: respectively calculating the pixel average value o of the clear text image A with the size of M multiplied by N to be encrypted 1 Information entropy o 2 Total pixel value o 3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein M and N are the number of rows and columns of the plaintext image A, respectively.
S3: for three image feature values o of the previous step 1 、o 2 、o 3 Normalization processing is carried out to obtain a normalized value x 1 (1)，y 1 (2)，y 1 (3) Presetting a in first-order chaotic system 1 ，a 2 And u, will x 1 (1)，y 1 (2)，y 1 (3)，a 1 ，a 2 And u together as the required primary key.
S4: according to the known primary key, performing iterative generation on an X-group hash sequence and a Y-group hash sequence through a primary chaotic system, and respectively performing random sampling and modulus taking on the output chaotic sequences X and Y to obtain two values, and marking the two values as X 0 ，y 0 。
S5: the hyperbolic tangent expansion mapping is used as a required secondary chaotic system, and a control parameter a 'in the secondary chaotic system is manually set' 1 、a′ 2 And u' and takes it as a secondary key; in x 0 ，y 0 As initial values of the two-stage chaotic system, two chaotic sequences X and Y of length mxn are generated.
S6: and performing modular processing on the chaotic sequences X and Y respectively to obtain a required scrambling sequence S and a diffusion sequence Q.
S7: the scrambling sequence S is used for scrambling the plaintext image A, and the process is as follows:
s71: the original image a of mxn to be encrypted is converted into a one-dimensional image matrix P of 1×mn.
S72: and (5) carrying out ascending arrangement on the disorder sequence S to obtain an ascending arranged matrix F and a corresponding index matrix G.
S73: and scrambling the one-dimensional image matrix P by using the index matrix G to obtain a scrambled image matrix B.
S8: and performing diffusion and dimension changing operation on the disordered image matrix B by using a diffusion sequence Q to obtain a ciphertext image E, wherein the process is as follows:
S81: and performing exclusive OR processing on the diffusion sequence Q and the scrambled image matrix B to obtain a diffusion image matrix C.
S82: and performing matrix-column number transformation on the diffusion image matrix C to obtain an M-row and N-column ciphertext image E.
In the present invention, the normalization function of the image feature values in step S3 is as follows:
in the above formula, α is a preset characteristic magnification, and in the present invention, α=2 15 ；β 1 、β 2 、β 3 Respectively preset offsets of all characteristic values, wherein the values of the offset, the offset and the offset are positive numbers smaller than 1, and in the invention, beta 1 、β 2 、β 3 The values are 0.1, 0.2 and 0.3 respectively.
In step S4 of the present invention, x is an initial value of the two-stage chaotic system 0 ，y 0 The following sampling formula is adopted for generation:
in the above, lambda 1 and λ2 Respectively control x 0 and y0 Hash sequence x in corresponding original sample 1 Is used for the adjustment coefficient of the iteration round of (a).
In step S6 of the present invention, the chaotic sequences X and Y are subjected to modulo processing using the following formula:
in the above, S i and Qi Each round of iteration values of S and Q respectively; x is x i and yi Each round of iteration values of X and Y respectively;floor represents a round down function.
The resulting scrambling sequence S is an integer sequence mapped to a range of 1-MN and the resulting spreading sequence Q is an integer sequence mapped to a range of 0-255.
In the present invention, step S71 uses a sort function to perform ascending order arrangement on the disorder sequence S, so as to obtain an index matrix G, and the mathematical expression is as follows:
[F,G]＝sort(S)
wherein F is a matrix obtained by arranging the disordered sequences S in an ascending order.
In step S73, the generation formula of the scrambling matrix B is as follows:
B(i)＝P(G(i))，i∈[1，MN]。
in the present invention, the generation formula of the diffusion image matrix C of step S81 is as follows:
E(i)＝B(i)⊕Q(i)，i∈[1，MN]
where # -is an exclusive-or operator.
In step S82, the matrix row number and column number conversion formula of the encrypted image E is as follows:
E＝reshape(C,M,N)
wherein reshape is a matrix row-column transform function, and M and N are the row number and column number of the ciphertext image E, respectively.
The invention also comprises an image decryption method, which adopts the Lyapunov exponent adjustable chaotic system as the decryption tool, and restores the generated ciphertext image E which adopts the image encryption method as the original plaintext image A according to the known primary key and the secondary key.
The image decryption method provided by the invention comprises the following steps:
s01: the required scrambling sequence S and spreading sequence Q are generated from the known primary and secondary keys using the same procedure as in steps S1-S6 in the image encryption method.
S02: the ciphertext image E is converted into a corresponding one-dimensional matrix E ', and is exclusive-or' ed with a diffusion sequence Q, so that a scrambled image matrix B is restored, and the mathematical expression is as follows:
B(i)＝E′(i)⊕Q(i)。
S03: the relative disorder sequence S is arranged in ascending order by utilizing the sort function to obtain an index matrix G, and the mathematical expression is as follows:
[F,G]＝sort(S)
f is a matrix obtained by ascending arrangement of scrambling sequences S; g is the ordered index matrix.
S04: and (3) carrying out ascending arrangement on the index matrix G by utilizing the sort function again to obtain an index matrix H, wherein the mathematical expression is as follows:
[T,H]＝sort(G)
wherein T is a matrix obtained by ascending the matrix G, and H is an index matrix corresponding to the ordered matrix T.
S05: the index matrix H is utilized to restore the scrambled image matrix B into a one-dimensional plaintext image matrix P, and the expression of the operation process is as follows:
P(i)＝B(H(i))。
s06: the one-dimensional plaintext image matrix P is restored to the plaintext image A with the original size of M multiplied by N by utilizing a matrix row-column number transformation function reshape, and the expression is as follows:
A＝reshape(P,M,N)。
the invention also comprises an image encryption transmission system which is used for realizing the encryption transmission of the image information between the data transmitting end and the data receiving end. The image encryption transmission system provided by the invention carries out encryption processing on the plaintext image A to be transmitted by adopting the image encryption method at the data sending end, and restores the received ciphertext image E into the original plaintext image A by adopting the image decryption method at the data receiving end.
Specifically, the image encryption transmission system provided by the invention comprises: the system comprises a channel, a synchronous sequence generating module, an information encrypting module, an information transmitting module, an information receiving module and an information decrypting module.
The channel is used as a data channel for encrypted data transmission between the data transmitting end and the data receiving end.
The synchronous sequence generating module comprises two synchronous data transmitting terminals and dataAnd a chaotic sequence generating unit at the receiving end. The chaotic sequence generation unit comprises a first-level chaotic system and a second-level chaotic system; the chaotic sequence generating unit is used for executing the following operations at the data transmitting end and the data receiving end respectively in the encryption transmission process: (1) Generating and outputting a group of sequence values x by using a first-order chaotic system according to a known first-order secret key 0 and y0 And takes the initial value as an iteration initial value of the two-stage chaotic system. (2) According to the known secondary secret key, two chaotic sequences with the same length as the multiplication product of the pixel row and column values of the plaintext image are generated by using a secondary chaotic system and are used as a scrambling sequence S and a diffusion sequence Q.
The information encryption module is positioned at the signal transmitting end and is used for generating a ciphertext image E to be transmitted according to the plaintext image A. The information encryption module comprises a scrambling unit and a diffusion unit. The scrambling unit is used for converting an M multiplied by N original image A to be encrypted into a one-dimensional image matrix P of 1 multiplied by MN; then, the disordered sequences S are arranged in an ascending order to obtain a matrix F after the ascending order and a corresponding index matrix G; and finally, the index matrix G is utilized to scramble the one-dimensional image matrix P, and a scrambled image matrix B is obtained. The diffusion unit is used for performing exclusive or processing on the diffusion sequence Q and the scrambled image matrix B to obtain a diffusion image matrix C; and then, performing matrix-column number transformation on the diffusion image matrix C to obtain an M-row and N-column ciphertext image E.
The information sending module is used for packaging the primary key, the secondary key and the ciphertext image E according to a preset data format and then sending the packaged primary key, the packaged secondary key and the ciphertext image E to the data receiving end through a channel.
The information receiving module is used for receiving the data packet sent by the signal sending module and unpacking the data packet to obtain a corresponding primary key, a corresponding secondary key and a corresponding ciphertext image. The primary key and the secondary key are used as input of a synchronous sequence generating module at a data receiving end and generate a corresponding scrambling sequence S and a corresponding spreading sequence Q.
The information decryption module is positioned at the signal receiving end and is used for restoring the original plaintext image A according to the received ciphertext image E, the scrambling sequence S and the diffusion sequence Q. The information decryption module comprises a scrambled image restoration unit, an index matrix generation unit, a one-dimensional image restoration unit and an image size restoration unit; the scrambled image restoring unit is used for converting the ciphertext image E into a corresponding one-dimensional matrix E ', and performing exclusive OR on the E' and the diffusion sequence Q, so as to restore a scrambled image matrix B. The index matrix generating unit is used for firstly carrying out ascending arrangement on the disordered sequence S by utilizing the sort function to obtain an index matrix G, and then carrying out ascending arrangement on the index matrix G by utilizing the sort function to obtain an index matrix H. The one-dimensional image restoration unit is used for restoring the scrambled image matrix B into a one-dimensional plaintext image matrix P by utilizing the index matrix H. The image size reduction unit uses a matrix row-column number transformation function reshape to reduce the one-dimensional plaintext image matrix P into a plaintext image A with the original size of MxN.
The technical scheme provided by the invention has the following beneficial effects:
the chaotic system provided by the invention can customize the Lyapunov exponent of the chaotic system by setting the value of the control parameter, and the chaotic mapping with controllable dynamic characteristics is obtained, so that the system has high complexity and high cracking difficulty, and can generate a chaotic sequence with higher randomness. When the chaotic system is used for encrypting data, the security is high. Meanwhile, the number of the keys of the encryption system is increased due to the increase of the control parameters, so that the key space is greatly enlarged.
The image encryption method provided by the invention applies the newly designed chaotic system, so that the complexity of the encryption system is further improved, and the security is higher. Meanwhile, the statistical characteristics of the plaintext image are generated into the initial value of the chaotic sequence through the plaintext hash function, the pseudo-random sequence related to the plaintext is generated, and even if the plaintext is subjected to any small change, the generated ciphertext is completely different, so that the encryption algorithm can effectively resist the attack of the selected plaintext or the attack of the known plaintext.
In addition, the encryption party generates an encryption map with larger information redundancy of each area, has high tolerance to loss and noise in the communication process, and can realize higher-definition image restoration in the image decryption process even if a larger degree of pixel loss or more noise is included.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
fig. 1 is a flowchart of steps of an image encryption method provided in embodiment 2 of the present invention.
Fig. 2 is a signal flow diagram of the image encryption method of fig. 1.
Fig. 3 is a flowchart illustrating steps of an image decryption method according to embodiment 3 of the present invention.
Fig. 4 is a signal flow diagram of the image decryption method in fig. 3.
Fig. 5 is a network architecture diagram of an image encryption transmission system provided in embodiment 4 of the present invention.
Fig. 6 is a conventional sample image and its histogram used in the performance test procedure.
Fig. 7 is a ciphertext image corresponding to a sample image and a histogram thereof during performance testing.
Fig. 8 is a correlation distribution diagram of adjacent pixels of a sampling pixel in a plain image in three directions of horizontal, vertical and diagonal in the performance test process.
Fig. 9 is a correlation distribution diagram of adjacent pixels in three directions of horizontal, vertical and diagonal of a sampling pixel in a ciphertext image during a performance test.
FIG. 10 is a graph showing the result of decrypting a sample image with a pixel loss ratio of 1/16 of the original ciphertext image during performance testing.
FIG. 11 is a graph showing the result of decrypting a sample image with a pixel loss ratio of 1/4 of the original ciphertext image during performance testing.
FIG. 12 is a graph showing the result of decrypting a sample image with a pixel loss ratio of 1/2 of the original ciphertext image during performance testing.
Fig. 13 is a decryption result of a ciphertext image after adding 1% salt-pepper noise in the performance test process.
Fig. 14 shows the decryption result of the ciphertext image after adding 5% salt and pepper noise in the performance test process.
Fig. 15 shows the decryption result of the ciphertext image after adding 10% salt and pepper noise in the performance test process.
Fig. 16 is an encryption result of a full black image during performance test.
Fig. 17 is an encryption result of a full white image during performance testing.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Example 1
The embodiment provides a Lyapunov exponent adjustable chaotic system, which belongs to a two-dimensional chaotic mapping. Most particularly: in the embodiment, a group of control parameters for visually adjusting the Lyapunov exponent of the chaotic system are arranged in the chaotic system. A user can customize the lyapunov exponent of the chaotic system by setting the value of the parameter to obtain the chaotic map with the desired dynamic characteristic, which is not possessed by other many chaotic systems.
The embodiment also designs two-dimensional chaotic maps with two different forms for the chaotic system, namely parabolic expansion map and hyperbolic tangent expansion map.
The mapping relation of the parabolic expansion mapping is as follows:
the mapping relation of the hyperbolic tangent expansion map is as follows:
in the above formula, i is the iteration number, x, y is the iteration output value, x i ，y i The value obtained for the ith iteration; mod is a modulo operation; a, a 1 、a 2 And u is a parabolic shapeSystem control parameters in line spread map, and a 1 、a 2 Can be used for quantitatively adjusting the Lyapunov exponent of a system. a' 1 、a′ 2 And u 'are both system control parameters in the hyperbolic tangent expansion map, and a' 1 and a′2 Can be used for quantitatively adjusting the Lyapunov exponent of a system.
As can be seen by combining the expression, with the increasing number of iterations, the parabolic expansion map and the hyperbolic tangent expansion map can generate two chaotic sequences X and Y with increasing lengths, wherein X= { X 1 ，x 2 ，…x n }，Y＝{y 1 ，y 2 ，…y n }. The values of the elements in the sequence are subject to an initial value and three controllable parameters a 1 and a2 And u (or a' 1 、a′ 2 And u'). One typical application of the chaotic system provided in the present embodiment is in generating a chaotic sequence with strong randomness in an encryption process. Because the lyapunov exponent of the chaotic map can be artificially controlled, a user can obtain the chaotic system meeting the expected dynamic complexity, and the chaotic system of the embodiment can generate the chaotic sequence with high complexity and high randomness. Meanwhile, the chaotic mapping of the embodiment is a two-dimensional chaotic mapping obtained by expanding the dimension of the one-dimensional chaotic mapping, and the number of keys of the encryption system is increased due to the increase of initial values and system parameters, so that the key space is greatly expanded.
Further, the analysis is performed taking the hyperbolic tangent expansion map as an example, with the controllable parameter a' 1 、a′ 2 And u' is adjusted, and Lyapunov exponent LE corresponding to chaotic mapping of two dimensions in hyperbolic tangent expansion mapping 1 、LE 2 The arrangement of (2) is exemplified by the following table:
table 1: relation between two lyapunov indices and control parameters of a system in hyperbolic tangent expansion mapping
Analysis of the above TableIt can be found that: in the designed hyperbolic tangent expansion mapping, the Lyapunov exponent of the system is directly determined by the parameter a 1 and a2 (or a' 1 、a′ 2 ) And determining and manually setting a system control parameter value to be exactly equal to the Lyapunov exponent corresponding to the chaotic map. Considering that the complexity of the chaotic system can be intuitively evaluated through the Lyapunov exponent, the chaotic system provided by the embodiment can meet the 'customization' requirement of a user on the complexity of the chaotic system. The user only needs to set corresponding control parameters according to the required complexity, and the Lyapunov index of the system can be determined intuitively as long as the parameters are set.
Further, analysis of the foregoing expression shows that: in the parabolic expansion map provided in the present embodiment, when the control parameter a 1 ，a 2 When any one of the chaotic systems is larger than zero, the chaotic system is in a chaotic state; when controlling parameter a 1 ，a 2 All are larger than zero, and the chaotic system is in a hyperchaotic state. Accordingly, in the hyperbolic tangent expansion map of the present embodiment, when the parameter a 'is controlled' 1 and a′2 When any one of the chaotic systems is larger than zero, the chaotic system is in a chaotic state; when controlling parameter a' 1 and a′2 All are larger than zero, and the chaotic system is in a hyperchaotic state.
That is, in the designed chaotic system, when two lyapunov indexes manually set in the parabolic expansion map and the hyperbolic tangent expansion map are positive numbers, it is indicated that the chaotic system can realize the hyperchaotic behavior.
The two-dimensional chaotic system provided by the embodiment is designed based on classical one-dimensional Logistic mapping, and the design method of the Lyapunov exponent-adjustable chaotic system comprises the following steps:
(1) The following classical one-dimensional Logistic map is obtained:
x i+1 ＝ux i (1-x i )
wherein u is a control parameter; i is the iteration number; x is an iteration output value; x is x i The value obtained for the ith iteration; when u is E [3.57,4 ]]When mapped asChaotic state.
(2) And carrying out dimension lifting, logic transformation, coefficient adjustment and modulo operation on the one-dimensional Logistic mapping to obtain the following two-dimensional parabolic expansion mapping:
In the above formula, i is the iteration number, x, y is the iteration output value, x i ，y i The value obtained for the ith iteration; mod is a modulo operation; a, a 1 ，a 2 And u are each a set of adjustable system control parameters.
(3) 1-y in the above step i Replaced by 1-tan i The following two-dimensional hyperbolic tangent expansion map is obtained:
in the above, a' 1 、a′ 2 And u' are each a set of adjustable system control parameters.
Example 2
On the basis of the chaotic system designed in embodiment 1, the embodiment further provides an image encryption method. The image encryption method adopts the Lyapunov exponent adjustable chaotic system in the embodiment 1 as an encryption tool, and can generate a ciphertext image E with the same size as the original plaintext image A in the encryption process.
Specifically, as shown in fig. 1 and fig. 2, the image encryption method provided in this embodiment includes the following steps:
s1: the parabolic expansion mapping is transformed into a plaintext hash function as follows and is used as a required primary chaotic system:
s2: respectively calculating plaintext image A with size of MxN to be encryptedPixel average o of (2) 1 Information entropy o 2 Total pixel value o 3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein M and N are the number of rows and columns of the plaintext image A, respectively.
S3: for three image feature values o of the previous step 1 、o 2 、o 3 Normalization processing is carried out to obtain a normalized value x 1 (1)，y 1 (2)，y 1 (3). Then, presetting a in the first-order chaotic system 1 ，a 2 And u, will x 1 (1)，y 1 (2)，y 1 (3)，a 1 ，a 2 And u together as the required primary key.
The standard form of the normalization function of the image feature values in this embodiment is as follows:
in the above formula, alpha is a preset characteristic magnification factor, beta 1 、β 2 、β 3 Respectively the preset offset of each characteristic value, the values of the three are positive numbers smaller than 1,
in the present embodiment, α=2 15 ；β 1 、β 2 、β 3 The values are respectively 0.1, 0.2 and 0.3; i.e. the normalization function is:
s4: according to the known primary key, performing iterative generation on an X-group hash sequence and a Y-group hash sequence through a primary chaotic system, and respectively performing random sampling and modulus taking on the output chaotic sequences X and Y to obtain two values, and marking the two values as X 0 ，y 0 。
In the present embodiment, x is an initial value of the two-stage chaotic system 0 ，y 0 The following sampling formula is adopted for generation:
in the above, lambda 1 and λ2 Respectively control x 0 and y0 Hash sequence x in corresponding original sample 1 Is used for the adjustment coefficient of the iteration round of (a).
For example: in a specific example of this embodiment, lambda 1 Set to 2 lambda 2 Let 1 be the value. That is to say: x is x 0 Is generated by using the result of iteration of the first-order chaotic system for MN/2 times, and y is 0 The result is generated after the first-level chaotic system iterates MN times. In addition, α in the sampling formula still takes a value of 2 15 The method comprises the steps of carrying out a first treatment on the surface of the Namely:
s5: the hyperbolic tangent expansion mapping is used as a required secondary chaotic system, and a control parameter a 'in the secondary chaotic system is manually set' 1 、a′ 2 And u' and takes it as a secondary key; in x 0 ，y 0 As initial values of the two-stage chaotic system, two chaotic sequences X and Y of length mxn are generated.
S6: and performing modular processing on the chaotic sequences X and Y respectively to obtain a required scrambling sequence S and a diffusion sequence Q.
The chaos sequences X and Y are subjected to modulo processing by adopting the following formula:
in the above, S i and Qi Each round of iteration values of S and Q respectively; x is x i and yi Each round of iteration values of X and Y respectively; floor represents a round down function.
After the above formula, the obtained scrambling sequence S is an integer sequence mapped to the range of 1-MN, and the obtained spreading sequence Q is an integer sequence mapped to the range of 0-255.
S7: the scrambling sequence S is used for scrambling the plaintext image A, and the process is as follows:
s71: the original image a of mxn to be encrypted is converted into a one-dimensional image matrix P of 1×mn.
S72: the disordered sequences S are arranged in an ascending order to obtain a matrix F after the ascending order and a corresponding index matrix thereof
G. Specifically, the relative disorder sequence S is arranged in ascending order by utilizing the sort function to obtain an index matrix G, and mathematics is that
The expression is as follows:
[F,G]＝sort(S)
wherein F is a matrix obtained by arranging the disordered sequences S in an ascending order.
S73: and scrambling the one-dimensional image matrix P by using the index matrix G to obtain a scrambled image matrix B. The generation formula of the scrambling matrix B is as follows:
s8: and performing diffusion and dimension changing operation on the disordered image matrix B by using a diffusion sequence Q to obtain a ciphertext image E, wherein the process is as follows:
s81: and performing exclusive OR processing on the diffusion sequence Q and the scrambled image matrix B to obtain a diffusion image matrix C. The generation formula of the diffusion image matrix C is as follows:
E(i)＝B(i)⊕Q(i)，i∈[1，MN]
where # -is an exclusive-or operator.
S82: and performing matrix-column number transformation on the diffusion image matrix C to obtain an M-row and N-column ciphertext image E. The matrix row number conversion formula of the encrypted image E is as follows:
E＝reshape(C,M,N)
wherein reshape is a matrix row-column transform function, and M and N are the row number and column number of the ciphertext image E, respectively.
The new image encryption method provided by the embodiment is realized by utilizing a newly designed chaotic system, firstly utilizing parabolic expansion mapping in the chaotic system to obtain a plaintext hash function, then generating a specific output according to the statistical characteristics of the plaintext image and related parameters in a preset primary secret key, and taking the output as an iteration initial value of hyperbolic tangent expansion mapping. Then, the hyperbolic tangent expansion mapping takes a preset secondary key as a control parameter, and iterates continuously, and outputs a chaotic sequence which has high complexity and is related to the image characteristics of the plaintext image to be encrypted. And finally, taking the obtained two-dimensional chaotic sequence as a scrambling sequence S and a diffusion sequence Q respectively, and performing a series of matrix operations on the original plaintext image to obtain a new encrypted image which has the same size as the original image and completely conceals the pixel characteristics in the original image.
The image confidentiality method provided by the embodiment has at least the following advantages:
(1) According to the method, two different chaotic mappings (or hyperchaotic mappings) are adopted, so that a chaotic sequence with extremely high complexity is generated in two-stage data processing, and after an original image is encrypted, the image is extremely difficult to crack, so that the scheme of the embodiment improves the confidentiality attribute of an encryption method.
(2) In the image encryption method, the statistical characteristics of the plaintext image are utilized to generate the initial value of the chaotic sequence, so that the pseudo-random sequence related to the plaintext image can be obtained. Even if the plaintext changes slightly, the generated ciphertext is completely different, so that the image encryption scheme provided by the embodiment can effectively enhance the resisting effect on the selected plaintext attack or the known plaintext attack.
Example 3
On the basis of embodiment 2, this embodiment further provides an image decryption method, which uses the lyapunov exponent adjustable chaotic system in embodiment 1 as a decryption tool, and restores the ciphertext image E generated by the image encryption method in embodiment 2 to the original plaintext image a according to the known primary key and secondary key.
Specifically, as shown in fig. 3, the image decryption method provided in this embodiment includes the following steps:
s01: the required scrambling sequence S and spreading sequence Q are generated from the known primary and secondary keys using the same procedure as in steps S1-S6 in the image encryption method.
S02: the ciphertext image E is converted into a corresponding one-dimensional matrix E ', and is exclusive-or' ed with a diffusion sequence Q, so that a scrambled image matrix B is restored, and the mathematical expression is as follows:
B(i)＝E′(i)⊕Q(i)。
s03: the relative disorder sequence S is arranged in ascending order by utilizing the sort function to obtain an index matrix G, and the mathematical expression is as follows:
[F,G]＝sort(S)
f is a matrix obtained by ascending arrangement of scrambling sequences S; g is the ordered index matrix.
S04: and (3) carrying out ascending arrangement on the index matrix G by utilizing the sort function again to obtain an index matrix H, wherein the mathematical expression is as follows:
[T,H]＝sort(G)
wherein T is a matrix obtained by ascending the matrix G, and H is an index matrix corresponding to the ordered matrix T.
S05: the index matrix H is utilized to restore the scrambled image matrix B into a one-dimensional plaintext image matrix P, and the expression of the operation process is as follows:
P(i)＝B(H(i))。
s06: the one-dimensional plaintext image matrix P is restored to the plaintext image A with the original size of M multiplied by N by utilizing a matrix row-column number transformation function reshape, and the expression is as follows:
A＝reshape(P,M,N)。
Furthermore, special emphasis is required: as shown in fig. 4, in the image decryption method provided in this embodiment, for the decrypted plaintext image a, the image features of the plaintext image may be further analyzed, that is: pixel average o 1 Information entropy o 2 And a total pixel value o 3 The method comprises the steps of carrying out a first treatment on the surface of the And normalizing the characteristic parameters of the image. The result x is then normalized 1 (1)，y 1 (2)，y 1 (3) Comparing the obtained image with the same parameters in the primary key to verify whether the decrypted image is completely consistent with the original plaintext image before encryption; or evaluate data during the transmission phaseLoss or noise.
Example 4
In combination with the foregoing aspects of the embodiments, the present embodiment further provides an image encryption transmission system for implementing encrypted transmission of image information between a data transmitting end and a data receiving end. The image encryption transmission system provided in this embodiment encrypts the plaintext image a to be transmitted by using the image encryption method as in embodiment 2 at the data transmitting end, and restores the received ciphertext image E to the original plaintext image a by using the image decryption method as in embodiment 3 at the data receiving end.
Specifically, as shown in fig. 5, the image encryption transmission system provided in this embodiment includes: the system comprises a channel, a synchronous sequence generating module, an information encrypting module, an information transmitting module, an information receiving module and an information decrypting module.
The channel is used as a data channel for encrypted data transmission between the data transmitting end and the data receiving end.
The synchronous sequence generating module comprises two chaotic sequence generating units which are completely synchronous and are respectively positioned at the data transmitting end and the data receiving end. The chaotic sequence generation unit comprises a first-level chaotic system and a second-level chaotic system; the chaotic sequence generating unit is used for executing the following operations at the data transmitting end and the data receiving end respectively in the encryption transmission process: (1) Generating and outputting a group of sequence values x by using a first-order chaotic system according to a known first-order secret key 0 and y0 And takes the initial value as an iteration initial value of the two-stage chaotic system. (2) According to the known secondary secret key, two chaotic sequences with the same length as the multiplication product of the pixel row and column values of the plaintext image are generated by using a secondary chaotic system and are used as a scrambling sequence S and a diffusion sequence Q.
The information encryption module is positioned at the signal transmitting end and is used for generating a ciphertext image E to be transmitted according to the plaintext image A. The information encryption module comprises a scrambling unit and a diffusion unit. The scrambling unit is used for converting an M multiplied by N original image A to be encrypted into a one-dimensional image matrix P of 1 multiplied by MN; then, the disordered sequences S are arranged in an ascending order to obtain a matrix F after the ascending order and a corresponding index matrix G; and finally, the index matrix G is utilized to scramble the one-dimensional image matrix P, and a scrambled image matrix B is obtained. The diffusion unit is used for performing exclusive or processing on the diffusion sequence Q and the scrambled image matrix B to obtain a diffusion image matrix C; and then, performing matrix-column number transformation on the diffusion image matrix C to obtain an M-row and N-column ciphertext image E.
The information sending module is used for packaging the primary key, the secondary key and the ciphertext image E according to a preset data format and then sending the packaged primary key, the packaged secondary key and the ciphertext image E to the data receiving end through a channel.
The information receiving module is used for receiving the data packet sent by the signal sending module and unpacking the data packet to obtain a corresponding primary key, a corresponding secondary key and a corresponding ciphertext image. The primary key and the secondary key are used as input of a synchronous sequence generating module at a data receiving end and generate a corresponding scrambling sequence S and a corresponding spreading sequence Q.
The information decryption module is positioned at the signal receiving end and is used for restoring the original plaintext image A according to the received ciphertext image E, the scrambling sequence S and the diffusion sequence Q. The information decryption module comprises a scrambled image restoration unit, an index matrix generation unit, a one-dimensional image restoration unit and an image size restoration unit; the scrambled image restoring unit is used for converting the ciphertext image E into a corresponding one-dimensional matrix E ', and performing exclusive OR on the E' and the diffusion sequence Q, so as to restore a scrambled image matrix B. The index matrix generating unit is used for firstly carrying out ascending arrangement on the disordered sequence S by utilizing the sort function to obtain an index matrix G, and then carrying out ascending arrangement on the index matrix G by utilizing the sort function to obtain an index matrix H. The one-dimensional image restoration unit is used for restoring the scrambled image matrix B into a one-dimensional plaintext image matrix P by utilizing the index matrix H. The image size reduction unit uses a matrix row-column number transformation function reshape to reduce the one-dimensional plaintext image matrix P into a plaintext image A with the original size of MxN.
Performance testing
In order to verify the performance of the image encryption/decryption method provided by the invention, a corresponding performance test is designed as follows, and the performance advantage of the image encryption/decryption method provided by the invention is analyzed according to the test result.
1. Pixel feature analysis
In the performance test process, the embodiment adopts two modes of histogram analysis and adjacent pixel correlation analysis to analyze the pixel characteristic distribution before and after image encryption
(1) Histogram
In the experiment, a female figure portrait with a sun hat is randomly downloaded from a network as an original plaintext image, and the plaintext image is encrypted by the method in the embodiment 2 to obtain a ciphertext image. Next, a histogram of the plaintext image and the ciphertext image is generated using image analysis software. In the histogram analysis process, the original plaintext image and its histogram are shown in fig. 6, and the encrypted ciphertext image and its histogram are shown in fig. 7. As is apparent from a comparison of fig. 6 and 7:
each pixel characteristic of the plaintext image is vividly distributed; this results in that an attacker can easily derive the rough information of the image from the characteristics of the pixel distribution. The histogram of the encrypted image is in a uniform distribution state, the characteristic information of the original image is covered, the occurrence frequency of each pixel is nearly consistent, and the method has good safety and can resist partial attacks.
(2) Adjacent pixel correlation
In the experiment, 4000 adjacent pixels are randomly selected in the horizontal, vertical and diagonal directions of the plaintext image and the ciphertext image respectively to perform correlation analysis between the adjacent pixels. Wherein, the correlation distribution diagrams of adjacent pixels in the three directions of horizontal, vertical and diagonal in the plaintext image are shown in fig. 8, and the correlation distribution diagrams of adjacent pixels in the three directions of horizontal, vertical and diagonal in the ciphertext image are shown in fig. 9. As can be seen by comparing fig. 8 and 9:
the adjacent pixels of the plaintext image have strong correlation in the horizontal, vertical and diagonal directions, can be fitted into a straight line, and are in linear regular distribution close to the diagonal on the image, and the correlation between the adjacent pixels of the ciphertext image is close to 0. This illustrates that the image encryption method provided in this embodiment can effectively mask the features between adjacent pixels in the image. This has a good effect on resisting conventional image cracking.
2. Robustness analysis
In the transmission process of the ciphertext, signal interference or information loss with different degrees exists, and even the attacker is faced with intentional disturbance attack. The image encryption and decryption scheme provided should therefore require some tamper resistance in decrypting the ciphertext image, i.e., decryption may still be successful in the event that the ciphertext information is partially lost or altered. In contrast, in this embodiment, the ciphertext image was decrypted using the scheme of embodiment 3, and the following pixel loss simulation test and noise disturbance test were designed.
(1) Pixel loss simulation
The experiment randomly selects 1/16, 1/4 and 1/2 areas in the generated ciphertext image as the information losing part of the sample image, and "blackens" the pixel value of the part, and then decrypts the sample image. Finally, the comparison of the ciphertext images and their decrypted images for three different pixel loss ratios is shown in fig. 10, 11 and 12. Analysis of the three images indicated above revealed that:
in the present embodiment, which provides an image encryption and decryption scheme, the less the proportion of pixel loss in the encrypted image, the sharper the decrypted image. And it can be seen from fig. 12 that even if the effective pixels in the encrypted image are lost to the extent that they contain only 1/2 of the original information, the decrypted image can still be visually recognized. That is to say, the image encryption and decryption method provided by the embodiment has good performance of resisting communication loss, and has strong robustness.
(2) Noise interference
In the experiment, 1%, 5% and 10% of salt and pepper noise are added to the encrypted ciphertext image respectively, and then decryption processing is carried out on the ciphertext image added with the salt and pepper noise. Finally, three comparison graphs of ciphertext images with different proportions of noise added and decrypted images thereof are shown in fig. 13, 14 and 15. Analysis of the three pictures indicated above showed that:
In the image encryption and decryption scheme provided in this embodiment, the less noise is contained in the image, the clearer the decrypted original image is. And as can be seen from fig. 15, even when the added noise information has reached 10%, the decrypted plain text image can still reach a visually recognizable level. That is to say, the image encryption and decryption method provided by the embodiment has good performance of resisting communication interference, and has strong robustness.
3. Analysis of attack resistance
In the process of cracking an encrypted image, an attacker typically uses a full black or full white image as a "special" plaintext image to attack the encryption algorithm, thereby cracking the data processing logic of the encryption algorithm. In fact, a particular image may disable the scrambling process in the encryption algorithm, thereby exposing more algorithm encryption details, rendering the algorithm unsafe.
In order to test the encryption effect of the encryption method of the present embodiment on the special image, two full black and full white images of 512×512 sizes were selected for encryption processing in this experiment. The full black image and the encryption result thereof are shown in fig. 16, and the full white image and the encryption result thereof are shown in fig. 17. As can be seen by comparing fig. 16 and 17: the encryption result of the image encryption method provided by the embodiment on special images such as full black or full white is the same as the encryption effect of the common image; this further demonstrates that the image encryption method proposed in this embodiment can resist selective plaintext attack.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (10)
1. The Lyapunov exponent adjustable chaotic system is characterized by being a two-dimensional chaotic system and comprising a group of control parameters for visually adjusting the Lyapunov exponent of the system, wherein the chaotic system is used for generating two groups of required chaotic sequences X= { X 1 ，x 2 ，…x n }，Y＝{y 1 ，y 2 ，…y n -a }; the chaotic system comprises two forms, namely parabolic expansion mapping and hyperbolic tangent expansion mapping; wherein the parabola isThe mapping relation of the extension mapping is as follows:
the mapping relation of the hyperbolic tangent expansion mapping is as follows:
in the above formula, i is the iteration number, x, y is the iteration output value, x i ，y i The value obtained for the ith iteration; mod is a modulo operation; a, a 1 、a 2 And u are system control parameters in the parabolic expansion map, and a 1 、a 2 Lyapunov exponent useful for quantitative adjustment systems; a, a 1 ′、a 2 'and u' are both system control parameters in the hyperbolic tangent expansion map, and a 1′ and a2 ' Lyapunov exponent that can be used to quantitatively adjust the system.
2. The lyapunov exponent adjustable chaotic system according to claim 1, wherein: in the parabolic expansion map, the control parameter a 1 ，a 2 The value of (a) is the value of two Lyapunov indexes of the system, when the control parameter a 1 ，a 2 When any one of the chaotic systems is larger than zero, the chaotic system is in a chaotic state; when controlling parameter a 1 ，a 2 All are larger than zero, and the chaotic system is in a hyperchaotic state;
in the hyperbolic tangent expansion map, the control parameter a 1′ and a2 The' value is the value of the two lyapunov indices of the system; when controlling parameter a 1′ and a2 When any one of the' is larger than zero, the chaotic system is in a chaotic state; when controlling parameter a 1′ and a2 ' all are larger than zero, and the chaotic system is in a hyperchaotic state.
3. The chaotic system with adjustable Lyapunov exponent according to claim 1, wherein the design method of the chaotic system is as follows:
(1) The following classical one-dimensional Logistic map is obtained:
x i+1 ＝ux i (1-x i )
wherein u is a control parameter; i is the iteration number; x is an iteration output value; x is x i The value obtained for the ith iteration; when u is E [3.57,4 ]]Mapping to a chaotic state;
(2) And performing dimension lifting, logic transformation, coefficient adjustment and modulo operation on the one-dimensional Logistic mapping to obtain the following two-dimensional parabolic expansion mapping:
In the above formula, i is the iteration number, x, y is the iteration output value, x i ，y i The value obtained for the ith iteration; mod is a modulo operation; a, a 1 ，a 2 And u is a set of adjustable system control parameters, respectively;
(3) 1-y in the above step i Replaced by 1-tan i The following two-dimensional hyperbolic tangent expansion map is obtained:
in the above, a 1 ′、a 2 'and u' are each a set of adjustable system control parameters.
4. An image encryption method, characterized in that the method adopts the Lyapunov exponent adjustable chaotic system as defined in any one of claims 1 to 3 as an encryption tool to generate a ciphertext image E with the same size as an original plaintext image A; the image encryption method comprises the following steps:
s1: the parabolic expansion mapping is transformed into a plaintext hash function as follows and is used as a required primary chaotic system:
s2: respectively calculating the pixel average value o of the clear text image A with the size of M multiplied by N to be encrypted 1 Information entropy o 2 Total pixel value o 3 The method comprises the steps of carrying out a first treatment on the surface of the Wherein M and N are the number of rows and columns of the plaintext image A respectively;
s3: for three image feature values o of the previous step 1 、o 2 、o 3 Normalization processing is carried out to obtain a normalized value x 1 (1)，y 1 (2)，y 1 (3) Presetting a in first-order chaotic system 1 ，a 2 And u, will x 1 (1)，y 1 (2)，y 1 (3)，a 1 ，a 2 And u together as the required primary key;
S4: according to the known primary key, performing iterative generation on an X-group hash sequence and a Y-group hash sequence through a primary chaotic system, and respectively performing random sampling and modulus taking on the output chaotic sequences X and Y to obtain two values, and marking the two values as X 0 ，y 0 ；
S5: taking hyperbolic tangent expansion mapping as a required secondary chaotic system, and manually setting a control parameter a in the secondary chaotic system 1 ′、a 2 The values of 'and u' and are used as secondary keys; in x 0 ，y 0 As the initial value of the secondary chaotic system, two chaotic sequences X and Y with the length of MxN are generated;
s6: respectively performing modulo processing on the chaotic sequence X and the chaotic sequence Y to obtain a required scrambling sequence S and a diffusion sequence Q;
s7: the scrambling sequence S is used for scrambling the plaintext image A, and the process is as follows:
s71: converting an M×N original image A to be encrypted into a 1×MN one-dimensional image matrix P;
s72: ascending arrangement is carried out on the disorder sequence S to obtain an ascending arranged matrix F and a corresponding index matrix G;
s73: the index matrix G is utilized to scramble the one-dimensional image matrix P, and a scrambled image matrix B is obtained;
s8: and performing diffusion and dimension changing operation on the disordered image matrix B by using a diffusion sequence Q to obtain a ciphertext image E, wherein the process is as follows:
s81: performing exclusive OR processing on the diffusion sequence Q and the scrambled image matrix B to obtain a diffusion image matrix C;
S82: and performing matrix-column number transformation on the diffusion image matrix C to obtain an M-row and N-column ciphertext image E.
5. The image encryption method according to claim 4, wherein: in step S3, the normalization function of the image feature values is as follows:
in the above formula, alpha is a preset characteristic magnification; beta 1 、β 2 、β 3 Respectively preset offset of each characteristic value, wherein the values of the offset, the offset and the characteristic value are positive numbers smaller than 1;
in step S4, x is an initial value of the secondary chaotic system 0 ，y 0 The following sampling formula is adopted for generation:
in the above, lambda 1 and λ2 Respectively control x 0 and y0 Hash sequence x in corresponding original sample 1 Is used for the adjustment coefficient of the iteration round of (a).
6. The image encryption method according to claim 5, wherein: in step S6, the chaotic sequences X and Y are subjected to modulo processing using the following formula:
in the above, S i and Qi Each round of iteration values of S and Q respectively; x is x i and yi Each round of iteration values of X and Y respectively; floor represents a downward rounding function;
the resulting scrambling sequence S is an integer sequence mapped to a range of 1-MN and the resulting spreading sequence Q is an integer sequence mapped to a range of 0-255.
7. The image encryption method according to claim 6, wherein: in step S71, the scrambling sequence S is arranged in ascending order by using a sort function, so as to obtain an index matrix G, where the mathematical expression is as follows:
[F,G]＝sort(S)
Wherein F is a matrix obtained by ascending and arranging the disordered sequence S;
in step S73, the generation formula of the scrambling matrix B is as follows:
B(i)＝P(G(i))，i∈[1，MN]。
8. the image encryption method according to claim 7, wherein: in step S81, the generation formula of the diffusion image matrix C is as follows:
wherein ,
is an exclusive or operator;
in step S82, the matrix row number and column number conversion formula of the encrypted image E is as follows:
E＝reshape(C,M,N)
wherein reshape is a matrix row-column transform function, and M and N are the row number and column number of the ciphertext image E, respectively.
9. An image decryption method, characterized in that: the method comprises the steps of adopting the Lyapunov exponent-adjustable chaotic system as defined in any one of claims 1 to 3 as a decryption tool, and restoring a ciphertext image E generated by adopting the image encryption method as defined in any one of claims 4 to 8 into an original plaintext image A according to a known primary key and a known secondary key;
the image decryption method comprises the following steps:
s01: generating a required scrambling sequence S and a spreading sequence Q by adopting the same process as steps S1-S6 in the image encryption method according to the known primary key and the secondary key;
s02: the ciphertext image E is converted into a corresponding one-dimensional matrix E ', and is exclusive-or' ed with a diffusion sequence Q, so that a scrambled image matrix B is restored, and the mathematical expression is as follows:
S03: and (3) carrying out ascending order arrangement on the scrambling sequence S by utilizing a sort function to obtain an index matrix G, wherein the mathematical expression is as follows:
[F,G]＝sort(S)
f is a matrix obtained by ascending arrangement of scrambling sequences S; g is the index matrix after sequencing;
s04: and (3) carrying out ascending order arrangement on the index matrix G by utilizing the sort function again to obtain an index matrix H, wherein the mathematical expression is as follows:
[T,H]＝sort(G)
wherein T is a matrix obtained by ascending order of the matrix G, and H is an index matrix corresponding to the ordered matrix T;
s05: the index matrix H is utilized to restore the scrambled image matrix B into a one-dimensional plaintext image matrix P, and the expression of the operation process is as follows:
P(i)＝B(H(i))；
s06: the one-dimensional plaintext image matrix P is restored to the plaintext image A with the original size of M multiplied by N by utilizing a matrix row-column number transformation function reshape, and the expression is as follows:
A＝reshape(P,M,N)。
10. an image encryption transmission system, characterized in that: the method is used for realizing the encryption transmission of the image information between the data transmitting end and the data receiving end; the image encryption transmission system encrypts a plaintext image A to be transmitted by adopting the image encryption method according to any one of claims 4-8 at a data transmitting end, and restores a received ciphertext image E to an original plaintext image A by adopting the image decryption method according to claim 9 at a data receiving end;
The image encryption transmission system includes:
the channel is used as a data channel for encrypted data transmission between the data transmitting end and the data receiving end;
the synchronous sequence generating module comprises two chaotic sequence generating units which are completely synchronous and are respectively positioned at a data transmitting end and a data receiving end; the chaotic sequence generation unit comprises a first-level chaotic system and a second-level chaotic system; the chaotic sequence generating unit is used for executing the following operations at the data transmitting end and the data receiving end respectively in the encryption transmission process: (1) Generating and outputting a group of sequence values x by using a first-order chaotic system according to a known first-order secret key 0 and y0 And taking the initial value as an iteration initial value of the secondary chaotic system; (2) Generating two chaotic sequences with the same length as the multiplication product of the pixel row value of the plaintext image by using a two-level chaotic system according to a known two-level secret key, and taking the two chaotic sequences as a scrambling sequence S and a diffusion sequence Q;
the information encryption module is positioned at the signal transmitting end and is used for generating a ciphertext image E to be transmitted according to the plaintext image A; the information encryption module comprises a scrambling unit and a diffusion unit; the scrambling unit is used for converting an M multiplied by N original image A to be encrypted into a 1 multiplied by MN one-dimensional image matrix P; then, the disordered sequences S are arranged in an ascending order to obtain a matrix F after the ascending order and a corresponding index matrix G; finally, the index matrix G is utilized to scramble the one-dimensional image matrix P, and a scrambled image matrix B is obtained; the diffusion unit is used for performing exclusive or processing on the diffusion sequence Q and the scrambled image matrix B to obtain a diffusion image matrix C; then, performing matrix-column number transformation on the diffusion image matrix C to obtain M rows and N columns of ciphertext images E;
The information sending module is used for packaging the primary key, the secondary key and the ciphertext image E according to a preset data format and then sending the packaged primary key, the packaged secondary key and the ciphertext image E to a data receiving end through a channel;
the information receiving module is used for receiving the data packet sent by the signal sending module and unpacking the data packet to obtain a corresponding primary key, a corresponding secondary key and a corresponding ciphertext image; the primary key and the secondary key are used as input of a synchronous sequence generating module at a data receiving end and generate a corresponding scrambling sequence S and a corresponding diffusion sequence Q; and
the information decryption module is positioned at the signal receiving end and is used for restoring an original plaintext image A according to the received ciphertext image E, the scrambling sequence S and the diffusion sequence Q; the information decryption module comprises a scrambled image restoration unit, an index matrix generation unit, a one-dimensional image restoration unit and an image size restoration unit; the scrambled image restoring unit is used for converting the ciphertext image E into a corresponding one-dimensional matrix E ', and performing exclusive OR on the E' and the diffusion sequence Q so as to restore a scrambled image matrix B; the index matrix generation unit is used for firstly carrying out ascending arrangement on the disorder sequence S by utilizing the sort function to obtain an index matrix G, and then carrying out ascending arrangement on the index matrix G by utilizing the sort function to obtain an index matrix H; the one-dimensional image restoration unit is used for restoring the scrambled image matrix B into a one-dimensional plaintext image matrix P by utilizing the index matrix H; the image size reduction unit uses a matrix row-column conversion function reshape to reduce a one-dimensional plaintext image matrix P into a plaintext image A with the original size of MXN.
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| CN116886270B (en) * | 2023-09-05 | 2023-11-21 | 山东科技大学 | Three-band encryption method based on national encryption algorithm and double-chaotic system |
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