CN109977686B - Image encryption method and image processing equipment based on composite chaotic system - Google Patents
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Abstract
The invention is applicable to the field of image encryption and provides an image encryption method and image processing equipment based on a composite chaotic system. The method comprises the following steps: using the Sine mapping, the Tent mapping and the Logistic mapping as seed mapping, and expanding the chaotic range by utilizing cascade operation and nonlinear combination to generate a composite chaotic system; the method comprises the steps of utilizing a composite chaotic system to generate a chaotic sequence to pre-encrypt a plaintext image to generate a pre-encrypted image; and acquiring a reference image, combining the pre-encrypted image and the reference image, and generating a visually meaningful ciphertext image by using a Discrete Wavelet Transform (DWT) algorithm. The method has wider chaos range and more complex chaos behaviors, and improves the encryption performance; and because the ciphertext image which is meaningful visually is generated, the attack probability is reduced, the chosen plaintext attack and the exhaustive attack can be resisted, and the encryption performance is better.
Description
Technical Field
The invention belongs to the field of image encryption, and particularly relates to an image encryption method and image processing equipment based on a composite chaotic system.
Background
The chaos-based image encryption technology is a technology for designing an encryption algorithm by using the basic characteristics of a chaos sequence and the characteristics of a digital image so as to improve the encryption safety and the operation efficiency. Because the digital images contain core confidential and sensitive information, such as military images, medical images and the like, reliable, fast and robust encryption algorithms are needed to ensure the safety and effectiveness in the transmission process. Chaos is a phenomenon that random-like behavior can occur without adding any random factors, namely, inherent randomness exists and extremely sensitive dependence on initial values exists.
The Chinese patent application with the application publication number of CN103971317A and the invention name of 'an image encryption method based on fractional order chaotic mapping' discloses an image encryption method based on fractional order chaotic mapping, wherein a mathematical model of the method is established on the basis of fractional order discrete Logistic mapping, and image information is scrambled by utilizing a fractional order discrete chaotic signal to achieve the effect of image encryption. However, the chaos range of the scheme is narrow, and the chaos behavior is not good. As shown in fig. 3 of the specification of the chinese patent application, only the plaintext image is encrypted, and the formed ciphertext image is an image having a pattern, which is very easy to be found by an attacker and has a high possibility of being attacked.
Disclosure of Invention
The invention aims to provide an image encryption method based on a composite chaotic system, a computer readable storage medium and an image processing device, and aims to solve the problems that the chaotic range of the image encryption method based on fractional order chaotic mapping is narrow, the chaotic behavior is poor, and a formed ciphertext image is an image with a pattern, is easy to be found by an attacker and has high possibility of being attacked.
In a first aspect, the present invention provides an image encryption method based on a composite chaotic system, the method comprising:
using the Sine mapping, the Tent mapping and the Logistic mapping as seed mapping, and expanding the chaotic range by utilizing cascade operation and nonlinear combination to generate a composite chaotic system;
the method comprises the steps of utilizing a composite chaotic system to generate a chaotic sequence to pre-encrypt a plaintext image to generate a pre-encrypted image;
and acquiring a reference image, combining the pre-encrypted image and the reference image, and generating a visually meaningful ciphertext image by using a Discrete Wavelet Transform (DWT) algorithm.
In a second aspect, the present invention provides a computer-readable storage medium storing a computer program which, when executed by a processor, implements the steps of the composite chaotic system-based image encryption method as described above.
In a third aspect, the present invention provides an image processing apparatus comprising:
one or more processors;
a memory; and
one or more computer programs, the processor and the memory being connected by a bus, wherein the one or more computer programs are stored in the memory and configured to be executed by the one or more processors, the processor implementing the steps of the composite chaotic system based image encryption method as described above when executing the computer programs.
In the invention, sine mapping, tent mapping and Logistic mapping are used as seed mapping, and a chaotic range is expanded by utilizing cascade operation and nonlinear combination to generate a composite chaotic system; the method comprises the steps of utilizing a composite chaotic system to generate a chaotic sequence to pre-encrypt a plaintext image to generate a pre-encrypted image; and a visually meaningful ciphertext image is generated by utilizing a Discrete Wavelet Transform (DWT) algorithm. Therefore, the method has wider chaos range and more complex chaos behaviors, and improves the encryption performance; and because the ciphertext image which is meaningful visually is generated, the attack probability is reduced, chosen plaintext attack and exhaustive attack can be resisted, and the encryption performance is better. In addition, because the discrete wavelet transform DWT algorithm is utilized, the following advantages are provided: (1) Ensuring that the watermark cannot be eliminated under JPEG2000 lossy compression; (2) In order to improve the robustness of the watermark, the human visual system is not very sensitive to the changes of the image edge and texture part, but is very sensitive to the changes of the image smooth area. Meanwhile, since the discrete wavelet transform can well limit the edge and texture parts to its detail descendants (such as HL, LH, HH, the coefficients of the detail sub-bands often represent the edge parts of the image), embedding the watermark therein can achieve good visual effect; (3) the watermark may be embedded directly in the compressed domain; (4) The discrete wavelet transform can greatly reduce or remove the correlation among different extracted features by selecting a proper filter, and can be quickly realized.
Drawings
Fig. 1 is a flowchart of an image encryption method based on a composite chaotic system according to an embodiment of the present invention.
Fig. 2 is a structural diagram of a composite chaotic system according to a first embodiment of the present invention.
FIG. 3 is an LE index and bifurcation diagram of the SL-T composite chaotic system.
Fig. 4 is a schematic diagram of the different types of DCT coefficients in an 8 x 8 sized DCT block.
Fig. 5 is a block diagram of the structure of an image encryption algorithm.
Fig. 6 is a block diagram of the structure of discrete wavelet transform.
Fig. 7 is a schematic diagram of an encryption process.
Fig. 8 is a block diagram of a specific structure of an image processing apparatus according to a third embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clearly apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order to illustrate the technical means of the present invention, the following description is given by way of specific examples.
The first embodiment is as follows:
referring to fig. 1, an image encryption method based on a composite chaotic system according to an embodiment of the present invention includes the following steps:
s101, using the Sine mapping, the Tent mapping and the Logistic mapping as seed mapping, and expanding the chaos range by utilizing cascade operation and nonlinear combination to generate a composite chaos system.
In the first embodiment of the present invention, the nonlinear combination specifically includes addition and modulo operation.
The structure of the composite chaotic system is shown in figure 2. The definition formula of the composite chaotic system is as follows:
x n+1 =F(G(x n )+H(x n ))mod1 (1)
where F (x), G (x), and H (x) are three seed maps. In the first embodiment of the present invention, a Sine map, a Tent map, and a Logistic map are selected as seed maps, and x is n Is the iteration value, x n+1 Is the output of a complex chaotic system, and mod operation is to ensure that the output is limited to 0,1]. The complex chaotic system enhances the complexity of the structure, can be more random and is beneficial to cascade combination and nonlinear operation.
The composite chaotic system interacts three seed mappings through two operations simultaneously, and a plurality of new chaotic mappings can be generated. S, T and L are used for representing Sine mapping, tent mapping and Logistic mapping respectively, and due to the fact that multiple composite chaotic systems are generated by seed mapping, chaotic ranges and chaotic behaviors of all the composite chaotic systems are verified one by one, and the composite chaotic system with the widest chaotic range is obtained and is an LS-T composite chaotic system. The LE value and the bifurcation graph of the LS-T composite chaotic system are shown in figure 3, and it can be seen from the graph that the LE value of the LS-T system is positive in the ranges of u e (0.08, 0.23), u e (0.33, 0.49) and u e (0.51, 1), and the LS-T composite chaotic system has a wider chaotic range and better chaotic behavior.
The LS-T composite chaotic system has the definition formula as follows:
x n+1 =4usin(πx n )((1-usin(πx n ))+(1-u)sin(πx n ))mod1 (2)
the LS-T composite chaotic system has better chaotic behavior and wider chaotic range and is better applied to an image encryption algorithm.
S102, the compound chaotic system is used for generating a chaotic sequence to pre-encrypt the plaintext image to generate a pre-encrypted image.
In the first embodiment of the present invention, S102 may specifically include the following steps:
s1021, extracting a significant area in the plaintext image by using a selective encryption algorithm;
s1022, the composite chaotic system is used for generating chaotic sequences to pre-encrypt the salient regions of the plaintext images, and pre-encrypted images are generated.
The S1021 specifically may include the following steps:
s10211, detecting a significant region of the plaintext image.
The method specifically comprises the following steps:
extracting color features and brightness features, namely calculating the difference between each block and all other blocks, and directly taking corresponding brightness feature values or color feature values C of the two blocks;
extracting texture features, and solving the distance between the texture vectors by using the norm, namely the difference T.
Fig. 4 shows different types of DCT coefficients in an 8 × 8 DCT (Discrete Cosine Transform) block, where the DCT coefficients in a block include DC coefficients and AC coefficients, and the black squares are DC coefficients. Among the DCT coefficients, the DC coefficient reflects the average value of each 8 × 8 pixel block.
Assuming that the three color components of red, green and blue of the DC coefficient are r, g and b, respectively, the calculation of the luminance characteristic can be calculated using equation (3):
l=(r+g+b)/3 (3)
a new red component R, a new green component G, a new blue component B and a new yellow component Y are generated from R, G and B, and the calculation formulas are shown in formulas (4) to (7):
R=r-(g+b)/2 (4)
G=g-(r+b)/2 (5)
B=b-(r+g)/2 (6)
Y=(r+g)/2-|r-b|/2-b (7)
according to the obtained new red component R, new green component G, new blue component B and new yellow component Y, the red-green confrontation component and the yellow-blue confrontation component obtained by adopting a color dual-confrontation system are the two color characteristics which are obtained:
C rg =R-G (8)
C by =B-Y (9)
the texture information of the image block is represented by AC coefficients. All points of each component of the luminance feature are added separately to obtain the total coefficient values of the three components, i.e. the texture feature T of each DCT block:
T={t LF ,t MF ,t HF } (10)
wherein, t LF 、t MF And t HF Representing the sum of all points of the respective portions of low, intermediate and high frequencies, respectively.
S10212, selecting a Gaussian algorithm based on position coordinate Euclidean distance between pixel blocks to define weight coefficients of block differences, and combining a brightness feature difference matrix, a color feature difference matrix and a texture feature difference matrix to obtain a significant region graph S k (k =1,2,3,4) and incorporates the salient region map S using a fusion rule based on normalization k (k =1,2,3,4) results in a final saliency map S of the plaintext image based on the compressed domain.
The formula for calculating the euclidean distance is shown in formula (11), and the euclidean distance d is the position coordinate between the block i and the block j ij :
The formula for calculating the weight coefficient is shown in formula (12), and the weight coefficient ω based on the euclidean distance between the block i and the block j is shown in formula (12) ij :
Where σ is a parameter of the gaussian model, σ =20 may be set.
The formula for calculating the feature saliency map is shown in formula (13), and the kth feature saliency value of block i
Wherein k ∈ { I, C rg ,C by ,T};The feature difference between DCT block i and block j for each feature.
Obtaining a salient region map S of brightness, color and texture features according to the formulas (11), (12) and (13) k (k=1,2,3,4)。
Combining saliency map S using normalization-based fusion rules k (k =1,2,3,4) the final saliency map S of the plaintext image based on the compressed domain is obtained:
S=∑γN(S k )+βΠN(S k ) (14)
wherein N is a normalization operation; γ and β are weight coefficients of corresponding portions in the formula, and γ = β =0.2 is set in the first embodiment of the present invention.
The S1022 specifically may include the following steps:
s10221, obtaining encryption key k e Initializing a control parameter f for a significant region of a plaintext image of size M × N 0 ,h 0 ,x 0 And u.
S10222, starting from L =1 to L, a loop is performed: the selected composite chaotic system is utilized to generate a chaotic sequence X, the replacement operation and the arrangement operation are executed, and the pixels of the salient region of the plaintext image are rearranged at the spatial position, so that the salient region of the plaintext image is changed into a meaningless chaotic image, the robustness is better, and a pre-encrypted image and a decryption password are generated.
Encryption key k e From f to f 0 ,h 0 ,x 0 And u is composed of f 0 ,h 0 And x 0 Is f n ,h n And x n Of (4) is calculated. Furthermore, the permutation process and the permutation process are repeated four times to improve the diffusion and aliasing characteristics of the pre-encrypted image. Thus, the initial value f 0 And h 0 Update L =4 times according to equation (15):
wherein p is in the range of [0,1]Random number of (c) 0 Denotes an initial value, x 0 Is the initial value of the chaotic sequence.
The image encryption algorithm contains two important steps: the permutation operation and the permutation operation are performed as shown in fig. 5. As can be seen from the figure, the image encryption algorithm has more control parameters, can ensure the key sensitivity of the encrypted image, and can resist various attacks, such as exhaustive attack and plaintext selection attack.
S103, acquiring a reference image, combining the pre-encrypted image and the reference image, and generating a visually meaningful ciphertext image by using a Discrete Wavelet Transform (DWT) algorithm.
Since the pre-encrypted image is an image with texture or obvious patterns, and the final objective of the first embodiment of the present invention is to generate a visually meaningful ciphertext image, the pre-encrypted image needs to be transformed by a digital watermarking algorithm. There are various digital watermarking algorithms, such as a spatial domain watermarking algorithm, a frequency domain watermarking algorithm, and the like. In the first embodiment of the present invention, a discrete wavelet transform algorithm in a frequency domain watermarking algorithm is mainly used. The discrete wavelet transform carries out multi-scale thinning on signals (functions) step by step through telescopic translation operation, finally achieves frequency subdivision at high frequency, can automatically adapt to the requirement of time-frequency signal analysis, and can focus on any details of the signals.
In the first embodiment of the present invention, S103 may specifically include the following steps:
acquiring a reference image, the reference image being a visually significant image;
the pre-encrypted image is converted into a visually meaningful ciphertext image having substantially the same size and pattern as the reference image using a Discrete-wavelet-Transform-based Content Transform (DWTCT). It is possible for the ciphertext image to be somewhat blurred compared to the reference image, but the degree of blurring can be reduced by adjusting the wavelet filter so that the ciphertext image and the reference image look identical.
The structure block diagram of the discrete wavelet transform is shown in fig. 6.
The DWTCT algorithm converts the pre-Encrypted Image P into a Visually Meaningful ciphertext Image, i.e., a visualized ciphertext Image (VMEI), having a size and pattern similar to the reference Image R. The image encryption method based on the composite chaotic system provided by the embodiment of the invention generates completely different VMEIs by using different reference images. This DWTCT is defined in equation (16). Ciphertext image E = T (P, R, K) of the same size as the reference image t )(16)
Wherein T represents DWTCT; k t Is a set of parameters for DWTCT that defines a set of wavelet filters for discrete wavelet transforms; r and E are reference and ciphertext images having the same size.
To sum up, on the premise that the size of the selected reference image is consistent with that of the plaintext image, the discrete wavelet transform can generate a better watermark effect on the pre-encrypted image, the generated ciphertext image is an image which is visually significant, that is, the ciphertext image is not different from a common image, and the purpose of protecting important information in the image is achieved, and a schematic diagram of the encryption process is shown in fig. 7. Where fig. 7 (a) is a plaintext image, fig. 7 (b) is a saliency image, fig. 7 (c) is a pre-encryption image, and fig. 7 (d) is a ciphertext image.
The second embodiment:
the second embodiment of the present invention provides a computer-readable storage medium, where a computer program is stored, and when the computer program is executed by a processor, the steps of the image encryption method based on the composite chaotic system provided in the first embodiment of the present invention are implemented.
Example three:
fig. 8 is a block diagram showing a specific structure of an image processing apparatus according to a third embodiment of the present invention, and an image processing apparatus 100 includes: one or more processors 101, a memory 102, and one or more computer programs, wherein the processors 101 and the memory 102 are connected by a bus, the one or more computer programs are stored in the memory 102 and configured to be executed by the one or more processors 101, and the processor 101 implements the steps of the image encryption method based on the composite chaotic system as provided in the first embodiment of the present invention when executing the computer programs.
In the invention, sine mapping, tent mapping and Logistic mapping are used as seed mapping, and a chaotic range is expanded by utilizing cascade operation and nonlinear combination to generate a composite chaotic system; the method comprises the steps of utilizing a composite chaotic system to generate a chaotic sequence to pre-encrypt a plaintext image to generate a pre-encrypted image; and a visually meaningful ciphertext image is generated by utilizing a Discrete Wavelet Transform (DWT) algorithm. Therefore, the method has wider chaotic range and more complex chaotic behaviors, and improves the encryption performance; and because the ciphertext image which is meaningful visually is generated, the attack probability is reduced, the chosen plaintext attack and the exhaustive attack can be resisted, and the encryption performance is better. In addition, because the discrete wavelet transform DWT algorithm is utilized, the following advantages are provided: (1) Ensuring watermark will not be eliminated under JPEG2000 lossy compression; (2) In order to improve the robustness of the watermark, the human visual system is not very sensitive to the changes of the image edge and texture part, but is very sensitive to the changes of the image smooth area. Meanwhile, since the discrete wavelet transform can well limit the edge and texture portions to its detail descendants (such as High-low, HL), low-High, LH, and High-frequency subbands (High-High, HH), the coefficients of the detail subbands often represent the edge portions of the image), good visual effects can be obtained by embedding the watermark therein; (3) the watermark may be embedded directly in the compressed domain; (4) The discrete wavelet transform can greatly reduce or remove the correlation among different extracted features by selecting a proper filter, and can be quickly realized.
Those skilled in the art will appreciate that all or part of the steps in the methods of the above embodiments may be implemented by associated hardware instructed by a program, which may be stored in a computer-readable storage medium, and the storage medium may include: read Only Memory (ROM), random Access Memory (RAM), magnetic or optical disks, and the like.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (6)
1. An image encryption method based on a composite chaotic system is characterized by comprising the following steps:
using Sine mapping, tent mapping and Logistic mapping as seed mapping, expanding chaos range by utilizing cascade operation and nonlinear combination, and generating a composite chaos system, wherein the composite chaos system has a definition formula as follows: x is the number of n+1 =F(G(x n )+H(x n ) Mod1, where F (x), G (x), and H (x) are three seed maps, sine, tent, and Logistic, respectively, x n Is the iteration value, x n+1 Is the output of the composite chaotic system;
extracting a significant region in a plaintext image by using a selective encryption algorithm;
generating a chaotic sequence by using a composite chaotic system to pre-encrypt a significant region of a plaintext image to generate a pre-encrypted image;
acquiring a reference image, combining the pre-encrypted image with the reference image, and generating a visually meaningful ciphertext image by using a Discrete Wavelet Transform (DWT) algorithm;
the extracting the significant region in the plaintext image by using the selective encryption algorithm specifically comprises the following steps:
detecting a salient region of a plaintext image;
selecting a Gaussian algorithm based on the Euclidean distance of position coordinates among pixel blocks to define weight coefficients of block differences, and combining a brightness characteristic, a color characteristic and a texture characteristic difference matrix to obtain a significant region graph S k (k =1,2,3,4) and incorporates the saliency region map S using a fusion rule based on normalization k (k =1,2,3,4) obtaining a final saliency map S of the plaintext image based on the compressed domain;
the pre-encrypting the significant region of the plaintext image by using the chaos sequence generated by the composite chaotic system to generate the pre-encrypted image specifically comprises the following steps:
obtaining an encryption key k e Initializing a control parameter f for a significant region of a plaintext image of size M × N 0 ,h 0 ,x 0 And u;
starting from L =1 to L, a loop is performed: and generating a chaotic sequence X by using the selected composite chaotic system, executing a replacement operation and an arrangement operation, rearranging the pixels of the significant region of the plaintext image at the spatial position, and generating a pre-encrypted image and a decryption password.
2. The method of claim 1, wherein S, T and L are used to represent a Sine map, a Tent map and a Logistic map, respectively, and the composite chaotic system is an LS-T composite chaotic system, and the LS-T composite chaotic system has a definition formula: x is the number of n+1 =4usin(πx n )((1-usin(πx n ))+(1-u)sin(πx n ))mod1。
3. The method according to claim 1, wherein said detecting a salient region of a plaintext image comprises the steps of:
extracting color features and brightness features, namely calculating the difference between each block and all other blocks, and directly taking corresponding brightness feature values or color feature values C of the two blocks;
extracting texture features, and solving the distance between the texture vectors by using a norm, namely the difference T;
the color feature extraction specifically comprises the following steps:
assuming that the three color components of red, green and blue of the DC coefficient are r, g and b, respectively, the calculation of the luminance characteristic is performed by using the formula l = (r + g + b)/3;
a new red component R, a new green component G, a new blue component B and a new yellow component Y are generated from R, G, B, and the calculation formula is as follows:
R=r-(g+b)/2;G=g-(r+b)/2;B=b-(r+g)/2;Y=(r+g)/2-|r-b|/2-b;
according to the obtained new red component R, new green component G, new blue component B and new yellow component Y, the red-green confrontation component and the yellow-blue confrontation component obtained by adopting the color dual confrontation system are the two color characteristics which are obtained: c rg =R-G;C by =B-Y;
The extraction of the textural features specifically comprises the following steps:
texture information of the image block is represented by AC coefficients; adding all the points of each component of the brightness characteristic respectively to obtain the total coefficient value of the three components, namely the texture characteristic T of each DCT block, T = { T = { (T) } LF ,t MF ,t HF }; wherein, t LF 、t MF And t HF Represents the sum of all points of the respective portions of low, intermediate and high frequencies, respectively;
the selection is based on the Gaussian algorithm of the Euclidean distance of the position coordinates between pixel blocks to define the weight coefficient of block difference, and the difference matrix of the brightness characteristic, the color characteristic and the texture characteristic is combined to obtain a significant region graph S k (k =1,2,3,4) and incorporates the saliency region map S using a fusion rule based on normalization k (k =1,2,3,4) the final saliency map S of the plaintext image based on the compressed domain is obtained by:
formula for calculating Euclidean distance asShown is the Euclidean distance d of the position coordinates between block i and block j ij ;
The formula for calculating the weight coefficient is as followsAs shown, the weight coefficient ω based on the euclidean distance between the block i and the block j ij (ii) a Wherein σ is a parameter of the gaussian model;
formula for calculating a saliency mapShown is the k-th characteristic significance value of block i->Wherein k ∈ { I, C rg ,C by ,T};/>Finally obtaining a significant area map S of brightness, color and texture characteristics for the characteristic difference between the DCT blocks i and j of each characteristic k (k=1,2,3,4);
Combining saliency map S using normalization-based fusion rules k (k =1,2,3,4) to obtain a final saliency map S of the plaintext image based on the compressed domain, S = ∑ γ N (S) k )+βΠN(S k ) (ii) a Wherein N is a normalization operation; γ and β are weight coefficients of corresponding parts in the formula, respectively;
the encryption key k e From f 0 ,h 0 ,x 0 And u is composed of f 0 ,h 0 And x 0 Is f n ,h n And x n The initial value of (1);
4. The method of any of claims 1 to 3, wherein the obtaining a reference image, combining the pre-encrypted image and the reference image, and generating the visually significant ciphertext image using the Discrete Wavelet Transform (DWT) algorithm specifically comprises:
acquiring a reference image, the reference image being a visually significant image;
the pre-encrypted image is converted to a visually meaningful ciphertext image having substantially the same size and pattern as the reference image using a discrete wavelet transform-based content transform.
5. A computer-readable storage medium storing a computer program, wherein the computer program when executed by a processor implements the steps of the composite chaotic system based image encryption method according to any one of claims 1 to 4.
6. An image processing apparatus comprising:
one or more processors;
a memory; and
one or more computer programs, the processor and the memory being connected by a bus, wherein the one or more computer programs are stored in the memory and configured to be executed by the one or more processors, characterized in that the processor, when executing the computer programs, implements the steps of the composite chaotic system based image encryption method according to any one of claims 1 to 4.
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