CN114915695A - Bit-level image encryption method based on 2D-Chebyshev chaotic mapping - Google Patents
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- H—ELECTRICITY
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
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- H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
- H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
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Abstract
The invention provides a bit-level image encryption method based on 2D-Chebyshev chaotic mapping, which comprises the steps of firstly coupling 1D-Chebyshev mapping and Fuch mapping, and then expanding one dimension to two dimensions to generate output to obtain the 2D-Chebyshev chaotic mapping. The complexity of the chaotic system is improved, the randomness of a key sequence is enhanced, the parameter range is greatly expanded, and the safety of the encryption system is effectively improved. By introducing a plurality of control parameters and expansion dimensions, the number of keys of the chaotic system is increased, and the key space is enlarged, so that the method can resist violent attack. By improving the binary conversion rule, the problem of digit limitation is solved, and the randomness during scrambling is improved. The chaos sequence is XOR with the adjacent pixels, the tiny change of the pixels is diffused to the whole image, and the capability of the encryption method for resisting differential attack is effectively improved.
Description
Technical Field
The invention belongs to the technical field of digital image encryption algorithms, and particularly relates to a bit-level image encryption method based on 2D-Chebyshev chaotic mapping.
Background
With the rapid development of digital technology and the popularization of the internet, more and more multimedia data are widely spread in the internet. However, due to the accessibility and the sharing of the network, a great deal of important information is revealed when multimedia data is transmitted. Among a plurality of multimedia information, a digital image containing a large amount of visual information is an important tool for transmitting multimedia data, so that a research hotspot is formed by designing an efficient image encryption method to ensure the safety of image information aiming at the special properties of high redundancy rate, large data volume, strong correlation of adjacent pixels and the like of the digital image. The chaotic system is widely applied to the field of image encryption because of the characteristics of initial value sensitivity, unpredictability, pseudo-randomness and the like.
The image encryption method based on the one-dimensional chaotic system is simple in chaotic behavior and can be cracked through brute force attack. Although the high-dimensional chaotic system has complex chaotic behaviors and chaotic tracks of the chaotic system are difficult to predict, the high-dimensional system has high calculation cost and high energy consumption. The chaotic image encryption method with high security also needs to have good capability of resisting typical attacks such as statistical attack, differential attack and the like.
Disclosure of Invention
Based on the problems, the invention provides a bit-level image encryption method based on 2D-Chebyshev chaotic mapping, which comprises the following steps:
step 1: acquiring an image to be encrypted, calculating by using an SHA-256 function to obtain an encryption key, and then taking the key as an initial value of a chaotic sequence;
step 2: substituting the initial value and the given control parameter into a 2D-Chebyshev chaotic map to obtain a chaotic sequence X 1 And Y 1 The 2D-Chebyshev chaotic map couples the 1D-Chebyshev map and the Fuch map, and then one dimension is expanded into two dimensions to generate output;
and step 3: converting the pixel value of the image to be encrypted into a twelve-bit binary pixel sequence according to a bitwise system conversion method, and then converting the pixel value into a decimal number to obtain an encryption matrix F;
and 4, step 4: using the chaotic sequence X 1 Integrally scrambling the matrix F to obtain an encryption matrix E;
and 5: converting each decimal value of the matrix E into a binary pixel sequence, and then converting the decimal value into a decimal number according to the bit-wise binary conversion method to obtain an encryption matrix R;
step 6: for the chaotic sequence X 1 And Y 1 Performing mod remainder to obtain chaotic sequences x 'and y';
and 7: and scanning the encryption matrix R into a one-dimensional matrix U according to the Zig-Zag sequence, then obtaining a one-dimensional matrix V through XOR operation, and reconstructing the matrix V into a two-dimensional matrix to obtain an encrypted image.
Further, the step 1 specifically comprises:
obtaining an image to be encrypted with the size of M multiplied by N, wherein M and N are positive integers, mapping the image to be encrypted by an SHA-256 hash function to generate an external secret key with 256 bits, representing the external secret key as an array H consisting of 64 2-bit hexadecimal numbers, and converting elements in the H into decimal numbers, namely d 1 ，d 2 ，…，d 64 It is divided into 8 groups, each group containing 8 values, i.e. h 1 ，h 2 ，…，h 8 Respectively carrying out XOR on the numerical values of the 1 st group, the 3 rd group, the 5 th group and the 7 th group to obtain a middle array h containing 8 numerical values 0 I.e. h 0 ＝h 1 ⊕h 3 ⊕h 5 ⊕h 7 Then h is added 0 Adding the sum of the rest 4 number groups as the initial value x of the chaotic system 0 Respectively carrying out XOR on the values of the 2 nd group, the 4 th group, the 6 th group and the 8 th group to obtain a middle array h containing 8 values 0 ', i.e. h 0 '＝h 2 ⊕h 4 ⊕h 6 ⊕h 8 Then h is added 0 ' adding the result of summing the remaining 4 number groups as the initial value y of the chaotic system 0 The iterative initial value x of 2D-Chebyshev is calculated according to the following formula 0 ，y 0 ：
Further, the step 2 specifically includes:
the mathematical model of the 2D-Chebyshev chaotic mapping is specifically as follows:
wherein a and k are control parameters, and k belongs to [0.2,100], when a is 8.98, the 2D-Chebyshev has chaotic behavior;
in the step 2, the initial value is substituted into a chaos mapping 2D-Chebyshev to obtain a chaos sequence X 1 And Y 1 The method specifically comprises the following steps: iterating an initial value x based on given parameters a and k of the chaotic map 0 And y 0 Iterating the 2D-Chebyshev chaotic mapping M multiplied by N +1000 times to obtain chaotic sequences X and y, then abandoning the first 1000 items of the sequences X and y, and modifying the chaotic sequences into chaotic sequences X with length of M multiplied by N 1 And Y 1 。
Further, the step 3 specifically includes:
carrying out binary conversion on each pixel value of an image I to be encrypted with the size of M multiplied by N according to bits: each digit of the decimal pixel value is converted into a four-digit binary number respectively, and after the four-digit binary numbers are combined into a twelve-digit binary number, the binary number is directly converted into a decimal number, and a matrix F is obtained.
Further, the step 5 specifically includes:
and converting each decimal value of the encryption matrix E into a twelve-bit binary sequence, converting each sequence from left to right, converting each four bits into a decimal number, and merging the decimal number into a new decimal number to obtain the encryption matrix R.
Further, the step 6 specifically includes:
the chaotic sequence X is divided according to the following formula 1 And Y 1 Respectively mapping to integers in the range of 0-255 to obtain chaotic sequences x 'and y':
further, the step 7 specifically includes:
scanning the encryption matrix R into a one-dimensional matrix U according to the sequence of the Zig-Zag, then carrying out XOR operation with chaotic sequences x 'and y' and adjacent pixels, and storing the result in a one-dimensional matrix V:
and reconstructing the one-dimensional matrix V into a two-dimensional matrix to obtain an encrypted image.
The invention has the beneficial effects that:
the invention provides a bit-level image encryption method based on 2D-Chebyshev chaotic mapping, which comprises the steps of firstly coupling 1D-Chebyshev mapping and Fuch mapping, and then expanding one dimension to two dimensions to generate output to obtain the 2D-Chebyshev chaotic mapping. Compared with a one-dimensional chaotic system, the 2D-Chebyshev chaotic mapping effectively improves the complexity of the chaotic system, enhances the randomness of a key sequence, greatly expands the parameter range of the chaotic system and effectively improves the safety of an encryption system. By introducing a plurality of control parameters and expansion dimensions, the number of keys of the chaotic system is increased, and the key space is enlarged, so that the algorithm can better resist violent attack. The small change of the pixels is expanded to the whole image through the XOR of the adjacent pixels, and the capability of the encryption system for resisting differential attack is effectively improved.
The above description is an overview of the technical solutions of the present invention, and in order to make the technical means, implementation procedures, objects, and advantages of the present invention more clear, the following description is given by way of example to illustrate specific embodiments of the present invention.
Drawings
FIG. 1 is a schematic flow diagram of a bit-level image encryption method based on 2D-Chebyshev chaotic mapping in the present invention.
Fig. 2 is a schematic flow chart of decrypting a ciphertext image in the present invention.
FIG. 3 is a plaintext diagram, a ciphertext diagram, and a ciphertext decryption diagram of an experimental image in accordance with the present invention; (a) the text is a plaintext image of an experimental image, (b) is a ciphertext image of the experimental image, and (c) is a ciphertext decryption image of the experimental image.
FIG. 4 is a pixel histogram of a ciphertext graph of an experimental image of the present invention.
FIG. 5 is a schematic diagram showing the correlation between ciphertext graphs of an experimental image in different directions; (a) the graph is a schematic diagram of the horizontal direction correlation of the ciphertext image of the experimental image, (b) is a schematic diagram of the vertical direction correlation of the ciphertext image of the experimental image, and (c) is a schematic diagram of the diagonal direction correlation of the ciphertext image of the experimental image.
Detailed Description
The invention is further described with reference to the following figures and specific examples. The invention aims to solve the problems of low sequence randomness, small key space and median limitation in the traditional bit encryption method generated by the traditional chaotic mapping. Firstly, coupling is carried out by utilizing a 1D-Chebyshev mapping and a Fuch mapping, and then one dimension is expanded into two dimensions to generate output, so that a 2D-Chebyshev chaotic mapping is obtained. The complexity of the chaotic system is improved, the randomness of a key sequence is enhanced, the parameter range is greatly expanded, and the safety of the encryption system is effectively improved. By introducing a plurality of control parameters and expansion dimensions, the number of keys of the chaotic system is increased, and the key space is enlarged, so that the method can resist violent attack. By improving the binary conversion rule, the problem of digit limitation is solved, and the randomness during scrambling is improved. The chaos sequence is XOR with the adjacent pixels, the tiny change of the pixels is diffused to the whole image, and the capability of the encryption method for resisting differential attack is effectively improved.
As shown in fig. 1, a bit-level image encryption method based on 2D-Chebyshev chaotic mapping, during encryption, transmits key information through a secret channel, transmits a ciphertext image through a public channel, and sets a pixel size of the plaintext image as mxn, includes:
step 1: acquiring an image to be encrypted, calculating by using an SHA-256 function to obtain an encryption key, and then taking the key as an initial value of a chaotic sequence;
step 2: substituting the initial value and the given control parameter into a 2D-Chebyshev chaotic map to obtain a chaotic sequence X 1 And Y 1 The 2D-Chebyshev chaotic map couples the 1D-Chebyshev map and the Fuch map, and then expands one dimension to two dimensions to generate output;
and step 3: converting the pixel value of the image to be encrypted into a twelve-bit binary pixel sequence according to a bitwise system conversion method, and then converting the pixel value into a decimal number to obtain an encryption matrix F;
and 4, step 4: using the chaotic sequence X 1 Integrally scrambling the matrix F to obtain an encryption matrix E;
and 5: converting each decimal value of the matrix E into a binary pixel sequence, and then converting the decimal value into a decimal number according to the bit-wise binary conversion method to obtain an encryption matrix R;
step 6: for the chaotic sequence X 1 And Y 1 Performing mod remainder to obtain chaotic sequences x 'and y';
and 7: and scanning the encryption matrix R into a one-dimensional matrix U according to the Zig-Zag sequence, then obtaining a one-dimensional matrix V through XOR operation, and reconstructing the matrix V into a two-dimensional matrix to obtain an encrypted image.
In a specific embodiment, the step 1 specifically includes:
obtaining an image to be encrypted with the size of M multiplied by N, wherein M and N are positive integers, mapping the image to be encrypted by an SHA-256 hash function to generate an external secret key with 256 bits, representing the external secret key as an array H consisting of 64 2-bit hexadecimal numbers, and converting elements in the H into decimal numbers, namely d 1 ，d 2 ，…，d 64 It is divided into 8 groups, each group containing 8 values, i.e. h 1 ，h 2 ，…，h 8 Respectively carrying out XOR on the values of the 1 st group, the 3 rd group, the 5 th group and the 7 th group to obtain an intermediate array h containing 8 values 0 I.e. h 0 ＝h 1 ⊕h 3 ⊕h 5 ⊕h 7 Then h is mixed 0 Adding the sum of the rest 4 number groups as the initial value x of the chaotic system 0 Respectively carrying out XOR on the values of the 2 nd group, the 4 th group, the 6 th group and the 8 th group to obtain a middle array h containing 8 values 0 ', i.e. h 0 '＝h 2 ⊕h 4 ⊕h 6 ⊕h 8 Then h is added 0 ' adding the result of summing the remaining 4 number groups as the initial value y of the chaotic system 0 The initial iteration of 2D-Chebyshev was calculated according to the following formulaStarting value x 0 ，y 0 ：
In an embodiment, in the step 2, the mathematical model of the 2D-Chebyshev chaotic map is specifically:
wherein a and k are control parameters, and k belongs to [0.2,100], when a is 8.98, the 2D-Chebyshev has chaotic behavior;
in the step 2, the initial value is substituted into a chaos mapping 2D-Chebyshev to obtain a chaos sequence X 1 And Y 1 The method specifically comprises the following steps: iterating an initial value x based on given parameters a and k of the chaotic map 0 And y 0 Iterating the 2D-Chebyshev chaotic mapping M multiplied by N +1000 times to obtain chaotic sequences X and y, then abandoning the first 1000 items of the sequences X and y, and modifying the chaotic sequences into chaotic sequences X with length of M multiplied by N 1 And Y 1 。
In a specific embodiment, the step 3 specifically includes:
carrying out binary conversion on each pixel value of an image I to be encrypted with the size of M multiplied by N according to bits: each digit of the decimal pixel value is converted into a four-digit binary number respectively, and after the four-digit binary numbers are combined into a twelve-digit binary number, the binary number is directly converted into a decimal number, and a matrix F is obtained.
In a specific embodiment, the step 5 specifically includes:
and converting each decimal value of the encryption matrix E into a twelve-bit binary sequence, converting each sequence from left to right, converting each four bits into a decimal number, and merging the decimal number into a new decimal number to obtain the encryption matrix R.
In a specific embodiment, the step 6 specifically includes:
the chaotic sequence X is expressed as 1 And Y 1 Respectively map toIntegers in the range of 0-255, obtaining chaotic sequences x 'and y':
in a specific embodiment, the step 7 specifically includes:
scanning the encryption matrix R into a one-dimensional matrix U according to the sequence of Zig-Zag, and then carrying out exclusive OR operation with the chaotic sequence x 'and y' and adjacent pixels, and storing the result in a one-dimensional matrix V:
and reconstructing the one-dimensional matrix V into a two-dimensional matrix to obtain an encrypted image.
The decryption process (i.e. the inverse process of encryption) of the ciphertext image obtained by encrypting by using the method of the invention is shown in fig. 2, and the specific process is as follows:
1) inputting a key: carrying out chaotic mapping according to the steps 2 and 6 in the encryption process to obtain a chaotic sequence for exclusive or diffusion;
2) and (3) carrying out inverse operation of exclusive or of the ciphertext image: converting the ciphertext image matrix into a one-dimensional matrix, performing exclusive or inverse operation on adjacent pixels and the chaotic sequence, and restoring pixel diffusion;
3) chaotic mapping: and generating a chaotic sequence according to the step 2 of the encryption process, and using the chaotic sequence for reducing and scrambling to obtain a plaintext image so as to realize image decryption.
The method is used for processing digital images with any size, the embodiment is a gray scale image of a 512 multiplied by 512 experimental image, the gray scale is 256, encryption/decryption and related safety test experiments are carried out, and the experimental result image is shown in figures 3-5.
The effectiveness of the method of the invention is further verified by measuring the index of the capability of resisting common attack means.
Histogram analysis: the method is adopted to carry out histogram analysis on the encrypted image; the uniform distribution of the histogram shows that the plaintext information can be better hidden, and an attacker can hardly recover the plaintext image through the histogram analysis attack.
Adjacent pixel correlation: the method of the invention is adopted to randomly select 1000 in the horizontal, vertical and diagonal directions of the plaintext and the ciphertext image respectively to analyze the adjacent pixel points; the value difference between adjacent pixels of the plaintext image is small, the pixel values between adjacent positions of the image have strong correlation, the correlation between adjacent pixels of the ciphertext image is close to 0, and the correlation between the pixel values between adjacent positions of the image is weak.
Claims (7)
1. A bit-level image encryption method based on 2D-Chebyshev chaotic mapping is characterized by comprising the following steps:
step 1: acquiring an image to be encrypted, calculating by using an SHA-256 function to obtain an encryption key, and then taking the key as an initial value of a chaotic sequence;
and 2, step: substituting the initial value and the given control parameter into a 2D-Chebyshev chaotic map to obtain a chaotic sequence X 1 And Y 1 The 2D-Chebyshev chaotic map couples the 1D-Chebyshev map and the Fuch map, and then expands one dimension to two dimensions to generate output;
and step 3: converting the pixel value of the image to be encrypted into a twelve-bit binary pixel sequence according to a bitwise system conversion method, and then converting the pixel value into a decimal number to obtain an encryption matrix F;
and 4, step 4: using the chaotic sequence X 1 Integrally scrambling the matrix F to obtain an encryption matrix E;
and 5: converting each decimal value of the matrix E into a binary pixel sequence, and then converting the decimal value into a decimal number according to the bit-wise binary conversion method to obtain an encryption matrix R;
step 6: for the chaotic sequence X 1 And Y 1 Performing mod remainder to obtain chaotic sequences x 'and y';
and 7: and scanning the encryption matrix R into a one-dimensional matrix U according to the Zig-Zag sequence, then obtaining a one-dimensional matrix V through XOR operation, and reconstructing the matrix V into a two-dimensional matrix to obtain an encrypted image.
2. The method of claim 1, wherein: the step 1 specifically comprises the following steps:
obtaining an image to be encrypted with the size of M multiplied by N, wherein M and N are positive integers, mapping the image to be encrypted by an SHA-256 hash function to generate an external secret key with 256 bits, representing the external secret key as an array H consisting of 64 2-bit hexadecimal numbers, and converting elements in the H into decimal numbers, namely d 1 ，d 2 ，...，d 64 It is divided into 8 groups, each group containing 8 values, i.e. h 1 ，h 2 ，...，h 8 Respectively carrying out XOR on the numerical values of the 1 st group, the 3 rd group, the 5 th group and the 7 th group to obtain a middle array h containing 8 numerical values 0 I.e. by
Then h is put 0 Adding the sum of the rest 4 number groups as the initial value x of the chaotic system 0 Respectively carrying out XOR on the values of the 2 nd group, the 4 th group, the 6 th group and the 8 th group to obtain a middle array h containing 8 values 0 ', i.e. that
Then h is put 0 ' adding the result of summing the remaining 4 number groups as the initial value y of the chaotic system 0 The iterative initial value x of 2D-Chebyshev is calculated according to the following formula 0 ，y 0 ：
3. The method of claim 1, wherein: the step 2 specifically comprises the following steps:
the mathematical model of the 2D-Chebyshev chaotic mapping is specifically as follows:
wherein a and k are control parameters, k belongs to [0.2,100], and when a is 8.98, 2D-Chebyshev has chaotic behavior;
in the step 2, the initial value is substituted into a chaos mapping 2D-Chebyshev to obtain a chaos sequence X 1 And Y 1 The method specifically comprises the following steps: iterating an initial value x based on given parameters a and k of the chaotic map 0 And y 0 Iterating the 2D-Chebyshev chaotic mapping M multiplied by N +1000 times to obtain chaotic sequences X and y, then abandoning the first 1000 items of the sequences X and y, and modifying the chaotic sequences into chaotic sequences X with length of M multiplied by N 1 And Y 1 。
4. The method of claim 1, wherein: the step 3 specifically comprises the following steps:
carrying out binary conversion on each pixel value of an image I to be encrypted with the size of M multiplied by N according to bits: each digit of the decimal pixel value is converted into a four-digit binary number respectively, and after the four-digit binary numbers are combined into a twelve-digit binary number, the binary number is directly converted into a decimal number, and a matrix F is obtained.
5. The method of claim 1, wherein: the step 5 specifically comprises the following steps:
and converting each decimal value of the encryption matrix E into a twelve-bit binary sequence, converting each sequence from left to right, converting each four bits into a decimal number, and merging the decimal number into a new decimal number to obtain the encryption matrix R.
6. The method of claim 1, wherein: the step 6 specifically comprises the following steps:
the chaotic sequence X is expressed as 1 And Y 1 Respectively mapping to integers in the range of 0-255 to obtain chaotic sequences x 'and y':
7. the method of claim 1, wherein: the step 7 specifically comprises the following steps:
scanning the encryption matrix R into a one-dimensional matrix U according to the sequence of Zig-Zag, and then carrying out exclusive OR operation with the chaotic sequence x 'and y' and adjacent pixels, and storing the result in a one-dimensional matrix V:
and reconstructing the one-dimensional matrix V into a two-dimensional matrix to obtain an encrypted image.
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