CN116684535A - Novel image encryption algorithm based on delayed chaotic synchronization update logic Boolean network - Google Patents
Novel image encryption algorithm based on delayed chaotic synchronization update logic Boolean network Download PDFInfo
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- 230000003111 delayed effect Effects 0.000 title claims abstract description 16
- 238000009792 diffusion process Methods 0.000 claims abstract description 36
- 238000013507 mapping Methods 0.000 claims abstract description 22
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- 230000010365 information processing Effects 0.000 abstract description 2
- 239000011159 matrix material Substances 0.000 description 11
- 230000002441 reversible effect Effects 0.000 description 7
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- 230000001360 synchronised effect Effects 0.000 description 4
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- 238000012163 sequencing technique Methods 0.000 description 2
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
- H04N1/44—Secrecy systems
- H04N1/448—Rendering the image unintelligible, e.g. scrambling
- H04N1/4486—Rendering the image unintelligible, e.g. scrambling using digital data encryption
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/50—Reducing energy consumption in communication networks in wire-line communication networks, e.g. low power modes or reduced link rate
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Abstract
The application relates to a novel image encryption algorithm based on a delayed chaotic synchronization update logic Boolean network, which belongs to the technical field of information processing and encryption and comprises the steps of constructing the delayed chaotic synchronization update logic Boolean network; generating a secret key; encrypting the image; the four steps of image decryption utilize scrambling two-dimensional cat mapping in an image scrambling stage, the scrambling cat mapping provided by the patent can eliminate the periodicity of the traditional cat mapping, and in an image diffusion stage, the patent constructs a novel positive and negative enhancement diffusion mode, compared with the traditional diffusion mode, the mode can furthest enhance the avalanche effect of an encryption algorithm, can obviously improve the capability of resisting differential attack of a ciphertext image, can effectively ensure the security of the ciphertext image, and can resist various attacks.
Description
Technical Field
The application relates to the field of information processing and encryption, in particular to a novel image encryption algorithm based on a delayed chaotic synchronization update logic Boolean network.
Background
The general chaotic image encryption algorithm comprises a replacement step and a diffusion step, wherein the replacement step can relocate pixels of a plaintext image, delete correlations of adjacent pixels and cannot change values of the pixels; the diffusion step can change pixel values, conceal useful information of a common image, and the two-dimensional Arnold-cat mapping (ACM) is a reversible chaotic mapping which is commonly used for scrambling the positions of pixels of a planar image, but has periodicity, so that the security of an encryption algorithm is reduced;
in the image diffusion stage, in order to improve the sensitivity of the encryption algorithm, a large number of encryption methods adopt a Hash function or an initial value of a chaotic system to generate a key, if one pixel of a plaintext image is changed, the value or initial value of the Hash function is changed, the key is completely changed, but decryption of different images needs different keys, which may bring trouble to a receiver of the encrypted image, while the sensitivity of the encryption algorithm can be improved by utilizing the high sensitivity of the chaotic system to the initial value, but the avalanche effect of the algorithm may be weakened by the dynamic degradation and calculation accuracy limitation of a pseudo-random number generator;
in view of the above, the present application provides a novel image encryption algorithm based on a delayed chaotic synchronization update logical boolean network.
Disclosure of Invention
Aiming at the situation, in order to overcome the defects of the prior art, the application provides a novel image encryption algorithm based on a delayed chaotic synchronous updating logic Boolean network, the application constructs a delayed chaotic synchronous updating logic Boolean network with 8 nodes as a pseudo-random number sequence generator, the generated chaotic sequence has very high information entropy, is quite suitable for the encryption algorithm, improves the original two-dimensional cat mapping, designs a scrambling type cat mapping, breaks the periodicity of the original cat mapping, can better ensure the security of the encryption algorithm, and designs a positive and negative enhancement diffusion method, when one pixel of a plaintext image is changed, all pixel values of the ciphertext image are changed in the forward diffusion and reverse diffusion processes, so that various selective attacks of the ciphertext image can be resisted.
The novel image encryption algorithm based on the delayed chaotic synchronization update logic Boolean network is characterized by comprising the following steps of:
s1: constructing a delayed chaotic synchronization update logic Boolean network: constructing a delay Boolean network with 8 nodes by using two-dimensional Henon mapping, wherein the dynamic behaviors of all nodes in the network are synchronously updated;
s2: key generation
S2-1: the key consists of 358 bits, wherein one part of the key is generated by randomly generating a string with 350 bits and the other part of the key (i.e. 8 bits) is generated by the last pixel after image diffusion;
s2-2: the string is truncated into 7 parts on average and 7 subkeys are generated: key1, key2, …, key 7 The first 4 subkeys are used for assigning values and parameters of the Hanon mapping;
s3: image encryption
S3-1: constructing a two-dimensional scrambling cat map;
s3-2: scrambling the original pixel point positions of the plaintext image by using scrambling cat mapping to obtain a scrambling image;
s3-3: by means of subkey keys 7 Generating a new pixel value, taking the pixel value as a starting point of diffusion to perform forward diffusion of the image, then performing backward diffusion, removing the initial and final pixel points, and taking the final pixel value as a complementary part of the secret key;
s4: image decryption
S4-1: a pixel value is generated using the last 8 bits of the key and the image diffusion effect is removed from the pixel value as a starting point.
S4-2: and resetting the positions of the pixel points by using the image with the diffusion effect removed and using the scrambling cat mapping to remove the scrambling effect of the encryption algorithm.
S4-3: and removing redundant pixel points, and performing image reconstruction to obtain a decrypted image.
The technical scheme has the beneficial effects that:
the application constructs a delay chaotic synchronous updating logic Boolean network with 8 nodes as a pseudo-random number sequence generator, the generated chaotic sequence has high information entropy, is quite suitable for an encryption algorithm, improves the original two-dimensional cat mapping, designs a scrambling type cat mapping, breaks the periodicity of the original cat mapping, and can better ensure the security of the encryption algorithm; in order to ensure the sensitivity of the algorithm, a positive and negative enhancement diffusion method is designed, and when one pixel of the plaintext image is changed, all pixel values of the ciphertext image are changed in the forward diffusion and backward diffusion processes, so that various selective attacks of the ciphertext image can be resisted.
Drawings
FIG. 1 is a schematic illustration of the forward diffusion and reverse diffusion process of the present application;
FIG. 2 is a schematic diagram of the principle of the forward and reverse enhanced diffusion resistance selective attack of the present application;
FIG. 3 is a flow chart of encryption in accordance with the present application;
FIG. 4 is a Lena (256×256) plain and encrypted image of the present application;
FIG. 5 is a fan histogram of the pixel value distribution of the present application;
FIG. 6 is a schematic diagram of the correlation between adjacent pixels of a plaintext image and a ciphertext image according to the present application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions in the embodiments of the present application will be clearly and completely described below, and it should be apparent that the described embodiments are some embodiments of the present application, but not all embodiments, and the present application is described in detail below with reference to the accompanying drawings, however, it should be understood that the accompanying drawings are provided only for better understanding of the present application, and they should not be construed as limiting the present application.
The detailed steps are as follows:
1. constructing a delayed chaotic synchronization updated logical Boolean network
As shown in formulas (1) and (2), a delayed chaotic synchronization update logic Boolean network is constructed
Wherein "," "V", V ""-" and>respectively represents AND, OR, XOR, implication and NOT operations, tau 1 、τ 2 、τ 3 And τ 4 Is a non-negative integer, τ represents the delay time and satisfies τ.gtoreq.max (τ 1 ，τ 2 ，τ 3 ，τ 4 )，U g (g=1, 2, …, 6) is generated from the henon map.
2. Generation of secret key and chaotic sequence
Step 1: the key is composed of a 358-bit character string, and the first 350 bits are randomly generated;
step 2: the first 350 bits of the key are truncated to 7 parts on average and 7 sub-keys are generated: key (Key) 1 ,Key 2 ,…,Key 7 Obviously, the length of the 7 subkeys is 50 bits, and the initial values and parameters of the hnon mapping by using the first four subkeys are assigned as follows:
step 3: through formulas (4) and (5), a chaotic sequence U can be obtained
U(t)＝dec2bin(u(t)) (5)
Wherein represents the maximum result of less than or equal to, function'dec2bin (U) "is used to obtain the equivalent binary string U of decimal number U, obviously U is an 8-bit binary number, we use U g To represent the g-th bit of U.
Step 4: will x 1 、x 2 、x 3 、x 4 、x 5 、x 6 、x 7 And x g Sequentially combining to construct a new chaotic sequence B, and scrambling the sequence B into
Wherein q is calculated by formula (7)
[H，Q]＝sort(u) (7)
Where "sort (·)" is an ordering index function, h= [ H ] 1 ，h 2 ，…，h L ]Is a sequence obtained by sequencing B in ascending order, and Q= [ Q ] 1 q 2 ，…，q L ]Is an index value of H, L representing the length of u.
3. Image encryption
The first stage: constructing two-dimensional scrambled cat maps
Step 1: a two-dimensional cat map is selected having the form:
wherein alpha and beta are control parameters, and a two-dimensional discrete cat map can be obtained by the above formula:
wherein N is a positive integer, x n ，y n ∈{0，1，N-1}。
Step 2: generating a chaotic sequence B with the length of L, and sequencing the sequence B according to the following form:
[v，η]＝sort(B) (10)
where v is the ordering vector and η is the corresponding index of each item of v in B.
Step 3: the vectors are shuffled as follows
And a second stage: image scrambling
Step 1: reconfiguring a plaintext image P with the size of MxN, if the shape of the plaintext image is square, the reconfiguration is not needed, and if the plaintext image is rectangular, namely M is not equal to N, M-N is equal to x min { M, N } pixel points with the pixel value of 255 are added on the basis of the plaintext image, so that a square matrix P with the size of L x L is obtained 1 Where l=max { M, N }.
Step 2: the two-dimensional cat mapping is applied to matrix P as follows 1 ：
Where n represents the nth iteration, (i) n ，j n ) Representing pixel at P 1 The values of alpha and beta are determined by the sub-Key Key 5 And Key 6 The following are given:
step 3: the vectors are shuffled as follows
Step 4: after n iterations, the device can be obtainedDisorder image P 3 Wherein the image P 3 The position (p 'of the pixel in (b)' n ，q′ n ) Can be obtained from equation (15):
P 3 (p′ n ，q′ n )＝P 2 (i n ，j n ) (15)
and a third stage: image diffusion
Step 1: generating a length L by delayed synchronous update of a logical boolean network 2 And ordering B into a chaotic sequence B of
[v′，η]＝sort(B) (16)
Step 2: for matrix P as follows 3 And (3) reconstruction:
P 3 ←reshape(P 3 ，L 2 ，1) (17)
step 3: in order to effectively achieve the avalanche effect, a forward and reverse enhanced diffusion is implemented, wherein the forward diffusion is implemented as:
wherein the method comprises the steps of
Step 4: the back diffusion is performed as follows:
wherein D (L) 2 +1)＝C(L 2 +1)。
Step 5: by means of Key keys 7 Generates a new pixel value D (1:L 2 +1) as the last 8 bits of the key, reconstructing the matrix D in the following manner, obtaining the ciphertext image P 4
P 4 ＝reshape(D(1:L 2 )，L，L) (20)
As shown in fig. 2, a 4×4 pixel image is shown in a diffusion process, where black circles in the image represent pixel points whose pixel values change, after forward diffusion, the colors of the pixel points behind the black circles change, which means that their pixel values also change, but the pixel values in front of the black circles do not change, so that the pixel values of the pixel points in front of the black circles do not change after reverse diffusion;
FIG. 2 shows that by adopting the forward and reverse diffusion modes, when a pixel point in an image is changed, completely different ciphertext images can be obtained, and the encryption method has strong capability of resisting differential attack;
as shown in fig. 5, the fan-shaped histogram is used to represent the distribution of pixel values, and it can be seen from fig. 5 (a) that the distribution of pixel values is uneven, which characterizes a certain feature of the pixel distribution of the plaintext image, while fig. 5 (b) shows that the distribution of pixel values of the ciphertext image is relatively uniform, which indicates that the ciphertext image well masks the pixel distribution characteristic of the plaintext image;
as shown in fig. 4, fig. 4 (a) is a plaintext image, and fig. 4 (b) is a ciphertext image, and it is obvious that the ciphertext image completely covers the information of the plaintext image;
as shown in fig. 6, fig. 6 (a) shows that the pixel values of the plain text image in the horizontal, vertical and diagonal directions are mainly distributed on the diagonal attachment, while fig. 6 (b) shows that the pixel value distribution of the plain text image is quite uniform, so that the relevance of the pixel points of the plain text image in the horizontal, vertical and diagonal directions is well eliminated;
if the common image is a color image, the R, G and B components of the common image are respectively used as gray images to carry out image confusion and diffusion operation, three encrypted images with the same size are obtained, and then the encrypted images are combined together to obtain a color encrypted image;
note that: r, G, B are three components of a color image, abbreviated as Red (Red), green (Green) and Blue (Blue) of the three primary colors, respectively.
4. Image decryption
Step 1: for matrix P as follows 4 ReconstructionObtaining matrix E
E＝reshape(P 4 ，L 2 ，1) (21)
Step 2: eliminating the back diffusion effect of the ciphertext image according to equation (22)
Wherein E (L) 2 +1)＝D(L 2 +1)。
Step 3: eliminating the forward diffusion effect of the ciphertext image according to equation (23)
Wherein F (L) 2 +1)＝D(L 2 +1)。
Step 4: the matrix F is reconstructed as follows
F＝reshape(F，L，L) (24)
The scrambling effect is eliminated for matrix F according to equation (25):
step 5: where n represents the nth iteration, p n ，q n ∈{1，2，…，L}，(p′ n ，q′ n ) Representing the position of the element in F.
Step 6: eliminating scrambling effects from cat mapping according to equation (26)
Step 7: combining steps 4-6 we can obtain matrix D 'after the nth iteration'
D’(I n ，j n )＝F(p′ n ，q′ n ) (27)
Step 8: and inverting the decimal matrix D 'into a binary matrix, and deleting M-N|xmin { M, N } pixels from the D', thereby obtaining the decrypted image.
The above embodiments are only for illustrating the technical solution of the present application, and not for limiting the same; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the application.
Claims (2)
1. The novel image encryption algorithm based on the delayed chaotic synchronization update logic Boolean network is characterized by comprising the following steps of:
s1: constructing a delayed chaotic synchronization update logic Boolean network: constructing a delay Boolean network with 8 nodes by using two-dimensional Henon mapping, wherein the dynamic behaviors of all nodes in the network are synchronously updated;
s2: key generation
S2-1: the key consists of 358 bits, wherein one part of the key is generated by randomly generating a character string with 350 bits, and the other part of the key is generated by the last pixel after the image diffusion;
s2-2: the string is truncated into 7 parts on average and 7 subkeys are generated: key (Key) 1 ,Key 2 ,…,Key 7 The first 4 subkeys are used for assigning values and parameters of the Hanon mapping;
s3: image encryption
S3-1: constructing a two-dimensional scrambling cat map;
s3-2: scrambling the original pixel point positions of the plaintext image by using scrambling cat mapping to obtain a scrambling image;
s3-3: by means of subkey keys 7 Generating a new pixel value, forward diffusing the image by taking the pixel value as a diffusion starting point, then backward diffusing, and removing the initial and final imagesA pixel point, and taking the ending pixel value as a complementary part of the secret key;
s4: image decryption
S4-1: a pixel value is generated using the last 8 bits of the key and the image diffusion effect is removed from the pixel value as a starting point.
S4-2: and resetting the positions of the pixel points by using the image with the diffusion effect removed and using the scrambling cat mapping to remove the scrambling effect of the encryption algorithm.
S4-3: and removing redundant pixel points, and performing image reconstruction to obtain a decrypted image.
2. The novel image encryption algorithm based on the delayed chaotic synchronization update logical boolean network according to claim 1, wherein if the plaintext image is square in S3, no reconstruction is needed, otherwise, pixels with values of 255 of |m-n|xmin { M, N } are added to construct the plaintext image into square, where mxn represents the size of the plaintext image.
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