CN112153238B - Image encryption method based on Tent mapping and composite chaotic mapping - Google Patents
Image encryption method based on Tent mapping and composite chaotic mapping Download PDFInfo
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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
- H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
- H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
- 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
- H04N1/32267—Methods relating to embedding, encoding, decoding, detection or retrieval operations combined with processing of the image
- H04N1/32272—Encryption or ciphering
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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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- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- 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
- H04L9/0863—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving passwords or one-time passwords
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- 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
- H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
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Abstract
The invention provides an image encryption method based on Tent mapping and composite chaotic mapping, which belongs to the technical field of image encryption and comprises the following steps: step S10, acquiring an original image with the size of M multiplied by N, and creating a matrix I with the size of M multiplied by N; storing the matrix information of the original image into a matrix I; step S20, generating 6 initial keys based on the matrix information stored in the matrix I; step S30, obtaining 3 chaotic sequences of Tent mapping and composite chaotic mapping based on the initial key; and step S40, performing two rounds of scrambling diffusion operation on the original image based on the chaotic sequence to obtain an encrypted image. The invention has the advantages that: the security of image encryption is greatly improved, and the execution cost is reduced.
Description
Technical Field
The invention relates to the technical field of image encryption, in particular to an image encryption method based on Tent mapping and composite chaotic mapping.
Background
With the rapid development of multimedia technology and the internet, more and more images are transmitted, shared, and stored on the internet. The information security of images is a serious problem in the digital world, and although some traditional encryption algorithms have higher security and mature authentication capability, such as the DES algorithm and the RSA algorithm, the traditional encryption algorithms are not suitable for the field of image encryption due to the particularity of image data. The image is usually described by two kinds of information, namely pixel position and pixel value, in a spatial domain, so that an image encryption algorithm is mainly designed around scrambling and diffusion, and a chaotic system has the advantages of no periodicity, unpredictability, pseudo-randomness, initial value sensitivity and the like, so that the image encryption algorithm is very suitable for the field of image encryption.
Due to the defect of uneven mapping distribution of the one-dimensional chaotic mapping, the encryption effect of an image encryption algorithm based on the one-dimensional chaotic mapping is poor, and the problem of small key space exists, so that the algorithm cannot resist violent attack; although the high-dimensional chaotic mapping has complex chaotic behaviors and is difficult to predict, the algorithm has high execution cost and high requirement on the computing power of a computer. Meanwhile, a good image encryption method also needs to have the capability of resisting plaintext attack.
Therefore, how to provide an image encryption method based on Tent mapping and composite chaotic mapping to improve the security of image encryption and reduce the execution cost becomes a problem to be solved urgently.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an image encryption method based on Tent mapping and composite chaotic mapping, so that the security of image encryption is improved, and the execution cost is reduced.
The invention is realized by the following steps: an image encryption method based on Tent mapping and composite chaotic mapping comprises the following steps:
step S10, acquiring an original image with the size of M multiplied by N, and creating a matrix I with the size of M multiplied by N; storing the matrix information of the original image into a matrix I;
step S20, generating 6 initial keys based on the matrix information stored in the matrix I;
step S30, obtaining 3 chaotic sequences of Tent mapping and composite chaotic mapping based on the initial key;
and step S40, performing two rounds of scrambling diffusion operation on the original image based on the chaotic sequence to obtain an encrypted image.
Further, in step S10, the matrix information includes pixel positions and pixel values.
Further, the step S20 specifically includes:
step S21, creating a one-dimensional matrix X with the size of 1 multiplied by 4, randomly generating 3 random numbers with the value range of 0 to 1 and storing the random numbers in the first 3 columns of the one-dimensional matrix X; the sum of all pixel values in the matrix information is obtained and stored in the 4 th column of a one-dimensional matrix X;
step S22, calculating a composite chaotic mapping coefficient e based on the one-dimensional matrix X1、e2、e3And e4：
Step S23, calculating initial keys x (1), y (1) and a based on each composite chaotic mapping coefficient1、μ1U and z (1):
x(1)＝e1；
y(1)＝e2；
a1＝2+e3；
μ1＝0.99+e4；
u＝1.999999+e4；
z(1)＝0.000001+e4。
further, the step S30 is specifically:
obtaining Tent mapping and chaos sequence s of composite chaos mapping based on each initial key1、s2And s3And mapping 3 of the chaotic sequences to a pseudo random sequence R ranging from 0 to 255n：
Rn＝mod(ceil(sn×10∧3),256),n＝{1,2,3}。
Further, in step S30, the mathematical model of the Tent map is:
wherein u represents a control parameter and has a value range of [0, 2 ]]；znIs an iterative variable mapped by Tent, and has an initial value of z1When the value range of (0, 1) is obtained, Tent mapping enters the chaotic region.
Further, in the step S30, the composite chaotic map is a map generated by using Sine map and Chebyshev map as seed maps and using perturbation bifurcation parameters, and a mathematical model of the composite chaotic map is as follows:
wherein the value range of mu is (0, 1)]；xnThe output chaotic sequence is represented, and the value range is (0, 1); initial key a1When the absolute value of the chaotic mapping is not less than 2, the compound chaotic mapping enters a chaotic region to generate an infinite-length non-periodic chaotic real value sequence under the infinite precision condition; y isnHas a value range of [ -1, 1](ii) a c represents a weighting parameter, and the value is 0.1; n represents the number of iterations; mu.s1An iteration initial value representing the control parameter mu; a is1Representing an iterative initial value of the control parameter a; x is the number ofn+1、yn+1An iterative variable representing a composite chaotic map; mu.sn+1、an+1An iteration variable representing a control parameter.
Further, the step S40 specifically includes:
step S41, performing first round scrambling on the matrix I by using a circshift function to obtain an image I1；
Step S42, pseudo-random sequence R generated by using composite chaotic mapping2For the image I1Performing a first round of diffusion to obtain a matrix C:
wherein i represents position information of the matrix; c (i) represents the ith number in the matrix C; c (i +1) represents the i +1 th number in the matrix C;
step S43, pseudo-random sequence R generated by Tent mapping3Carrying out bit XOR operation on the matrix C to obtain a matrix CC generated by a second diffusion disorder;
step S44, pseudo-random sequence R generated by using composite chaotic mapping1And shuffling and scrambling the matrix CC to obtain an encrypted image CCC generated by the second round of scrambling.
The invention has the advantages that:
1. by adopting Sine mapping and Chebyshev mapping as seed mapping and generating the composite chaotic mapping by using the disturbance bifurcation parameters, the complexity of the composite chaotic mapping is improved, the key space is effectively enlarged, and the security of image encryption is greatly improved.
2. The two one-dimensional chaotic maps form a new composite chaotic map, so that the execution cost of an image encryption algorithm is greatly reduced, and the dependence on the computing power of a computer is reduced.
3. The pixel value in the plaintext matrix information is used as the generation basis of the initial key, so that the capability of resisting plaintext attack of the image encryption algorithm is greatly improved.
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The invention will be further described with reference to the following examples with reference to the accompanying drawings.
FIG. 1 is a flow chart of an image encryption method based on Tent mapping and composite chaotic mapping according to the present invention.
FIG. 2 is a flow chart of an image encryption method based on Tent mapping and composite chaotic mapping according to the present invention.
FIG. 3 is a schematic diagram of the raw image pre-processing of the present invention.
Fig. 4 is a schematic diagram of a second round of scrambling according to the present invention.
Fig. 5 is a test image of the present invention.
FIG. 6 is a graph of the encryption effect of the test image of the present invention.
Detailed Description
Referring to fig. 1 to 6, one of the preferred embodiments of an image encryption method based on Tent mapping and composite chaotic mapping according to the present invention includes the following steps:
step S10, acquiring an original image with the size of M multiplied by N, and creating a matrix I with the size of M multiplied by N; storing the matrix information of the original image into a matrix I;
step S20, generating 6 initial keys based on the matrix information stored in the matrix I;
step S30, obtaining 3 chaotic sequences of Tent mapping and composite chaotic mapping based on the initial key; removing the first 1000 random numbers of each chaotic sequence to ensure the randomness of the chaotic sequences;
and step S40, performing two rounds of scrambling diffusion operation on the original image based on the chaotic sequence to obtain an encrypted image.
In step S10, the matrix information includes pixel positions and pixel values.
The step S20 specifically includes:
step S21, creating a one-dimensional matrix X with the size of 1 multiplied by 4, randomly generating 3 random numbers with the value range of 0 to 1 and storing the random numbers in the first 3 columns of the one-dimensional matrix X; the sum of all pixel values in the matrix information is obtained and stored in the 4 th column of a one-dimensional matrix X;
step S22, calculating a composite chaotic mapping coefficient e based on the one-dimensional matrix X1、e2、e3And e4：
Step S23, calculating initial keys x (1), y (1) and a based on each composite chaotic mapping coefficient1、μ1U and z (1):
x(1)＝e1；
y(1)＝e2；
a1＝2+e3；
μ1＝0.99+e4；
u＝1.999999+e4；
z(1)＝0.000001+e4；
wherein 2, 0.99, 1.999999, 0.000001 are preset initial values.
The step S30 specifically includes:
tent mapping and composite chaotic mapping are obtained based on each initial keyOf the chaotic sequence s1、s2And s3And mapping 3 of the chaotic sequences to a pseudo random sequence R ranging from 0 to 255n：
Rn＝mod(ceil(sn×10∧3),256),n＝{1,2,3}；
The pseudo-random sequence RnIncluding a pseudo-random sequence R generated using a composite chaotic map1Pseudo-random sequence R generated by using composite chaotic mapping2And a pseudo-random sequence R generated by Tent mapping3。
In step S30, the mathematical model of Tent mapping is:
wherein u represents a control parameter and has a value range of [0, 2 ]]；znAn iteration variable mapped for Tent, and an initial value z1When the value range of (0, 1) is obtained, Tent mapping enters the chaotic region.
In the step S30, the composite chaotic map is a map generated by using Sine map and Chebyshev map as seed maps and using perturbation bifurcation parameters, and a mathematical model of the composite chaotic map is as follows:
wherein the value range of mu is (0, 1)]；xnThe output chaotic sequence is represented, and the value range is (0, 1); initial key a1When the absolute value of the chaotic mapping is not less than 2, the compound chaotic mapping enters a chaotic region to generate an infinite-length non-periodic chaotic real value sequence under the infinite precision condition; y isnHas a value range of [ -1, 1](ii) a c represents a weighting parameter, and the value is 0.1; n represents the number of iterations; mu.s1An iteration initial value representing the control parameter mu; a is1Representing an iterative initial value of the control parameter a; x is the number ofn+1、yn+1An iterative variable representing a composite chaotic map; mu.sn+1、an+1An iteration variable representing a control parameter.
The step S40 specifically includes:
step S41, performing a first round of scrambling on the matrix I by using a circshift function to obtain an image I1；
Step S42, pseudo-random sequence R generated by using composite chaotic mapping2For the image I1Performing a first round of diffusion to obtain a matrix C:
wherein i represents position information of the matrix; c (i) represents the ith number in the matrix C; c (i +1) represents the i +1 th number in the matrix C;
step S43, pseudo-random sequence R generated by Tent mapping3Carrying out bit XOR operation on the matrix C to obtain a matrix CC generated by second diffusion disorder;
step S44, pseudo-random sequence R generated by using composite chaotic mapping1And shuffling and scrambling the matrix CC to obtain an encrypted image CCC generated by the second round of scrambling.
The decryption process of the encrypted image CCC is the inverse process of the image encryption algorithm, and the initial key and the chaotic sequence for decryption and encryption are the same.
The invention relates to a second preferred embodiment of an image encryption method based on Tent mapping and composite chaotic mapping, which comprises the following steps:
step S10, acquiring a test image (as shown in fig. 3) with a size of 512 × 512, and creating a matrix I with a size of 512 × 512; storing the matrix information of the original image into a matrix I; the matrix information comprises pixel positions and pixel values;
step S20, generating 6 initial keys based on the matrix information stored in the matrix I;
step S30, respectively iterating Tent mapping and composite chaotic mapping (1000+512 multiplied by 512) times based on the initial key to generate 3 chaotic sequences and removing the first 1000 random numbers of each chaotic sequence;
step S40, performing two rounds of scrambling and diffusing operations on the original image based on the chaotic sequence to obtain an encrypted test image (as shown in fig. 4).
The step S20 specifically includes:
step S21, creating a one-dimensional matrix X with the size of 1 × 4, randomly generating 3 random numbers with the value range of 0 to 1, and storing the random numbers in the first 3 rows of the one-dimensional matrix X; the sum of all pixel values in the matrix information is obtained and stored in the 4 th column of the one-dimensional matrix X;
step S22, calculating a composite chaotic mapping coefficient e based on the one-dimensional matrix X1、e2、e3And e4：
Step S23, calculating initial secret keys x (1), y (1), a based on each composite chaotic mapping coefficient1、μ1U and z (1):
x(1)＝e1；
y(1)＝e2；
a1＝2+e3；
μ1＝0.99+e4；
u＝1.999999+e4；
z(1)＝0.000001+e4；
wherein 2, 0.99, 1.999999, 0.000001 are preset initial values.
The step S40 specifically includes:
step S41, a first round of scrambling is carried out on the matrix I by using a circshift function, namely, the matrix I is regarded as a one-dimensional matrix, and cyclic displacement operation is respectively carried out on each row and each column of the matrix I, so that an image I is obtained1；
Step S42, pseudo-random sequence R generated by using composite chaotic mapping2For the image I1Performing a first round of diffusion, i.e. said image I1Conversion into one-dimensional linesVector, image I1And a pseudorandom sequence R2For equal-sized matrices, take out I respectively1And R2After the value of the first position is added, mod operation is performed on 256, and xor operation is performed on the calculation result of mod operation and the previous calculation result, and so on, so as to obtain a matrix C:
wherein i represents position information of the matrix; c (i) represents the ith number in the matrix C; c (i +1) represents the i +1 th number in the matrix C;
step S43, pseudo-random sequence R generated by Tent mapping3Performing a bit XOR operation on the matrix C, namely the matrices C and R3Converting the binary data into a matrix with the size of 512 multiplied by 512, traversing the two matrices simultaneously, respectively taking out the values at the same positions of the two matrices, converting the values into binary numbers represented in a character string form, then performing binary exclusive-or operation, converting the result into decimal, and so on to obtain a matrix CC generated by second diffusion disorder;
step S44, pseudo-random sequence R generated by using composite chaotic mapping1Shuffling said matrix CC, i.e. of matrix R1Performing sort operation to convert the matrix R1Sorting the values in ascending order, and sorting the matrix R1The position change data of the second round is stored in a new position matrix, and the matrix CC is scrambled according to the position matrix, so that an encrypted test image generated by the second round of scrambling is obtained.
In summary, the invention has the advantages that:
1. by adopting Sine mapping and Chebyshev mapping as seed mapping and generating the composite chaotic mapping by using the disturbance bifurcation parameters, the complexity of the composite chaotic mapping is improved, the key space is effectively enlarged, and the security of image encryption is greatly improved.
2. The two one-dimensional chaotic maps form a new composite chaotic map, so that the execution cost of an image encryption algorithm is greatly reduced, and the dependence on the computing power of a computer is reduced.
3. The pixel value in the plaintext matrix information is used as the generation basis of the initial key, so that the capability of resisting plaintext attack of the image encryption algorithm is greatly improved.
Although specific embodiments of the invention have been described above, it will be understood by those skilled in the art that the specific embodiments described are illustrative only and are not limiting upon the scope of the invention, and that equivalent modifications and variations can be made by those skilled in the art without departing from the spirit of the invention, which is to be limited only by the appended claims.
Claims (6)
1. An image encryption method based on Tent mapping and composite chaotic mapping is characterized in that: the method comprises the following steps:
step S10, acquiring an original image with the size of M multiplied by N, and creating a matrix I with the size of M multiplied by N; storing the matrix information of the original image into a matrix I;
step S20, generating 6 initial keys based on the matrix information stored in the matrix I;
step S30, obtaining 3 chaotic sequences of Tent mapping and composite chaotic mapping based on the initial key;
s40, performing two rounds of scrambling and diffusion operations on the original image based on the chaotic sequence to obtain an encrypted image;
the step S20 specifically includes:
step S21, creating a one-dimensional matrix X with the size of 1 × 4, randomly generating 3 random numbers with the value range of 0 to 1, and storing the random numbers in the first 3 rows of the one-dimensional matrix X; the sum of all pixel values in the matrix information is obtained and stored in the 4 th column of a one-dimensional matrix X;
step S22, calculating a composite chaotic mapping coefficient e based on the one-dimensional matrix X1、e2、e3And e4：
Step S23, calculating initial secret keys x (1), y (1), a based on each composite chaotic mapping coefficient1、μ1U and z (1):
x(1)＝e1；
y(1)＝e2；
a1＝2+e3；
μ1＝0.99+e4；
u＝1.999999+e4；
z(1)＝0.000001+e4。
2. the image encryption method based on Tent mapping and composite chaotic mapping as claimed in claim 1, wherein: in step S10, the matrix information includes pixel positions and pixel values.
3. The image encryption method based on Tent mapping and composite chaotic mapping as claimed in claim 1, wherein: the step S30 specifically includes:
obtaining Tent mapping and chaotic sequence s of composite chaotic mapping based on each initial key1、s2And s3And mapping 3 of the chaotic sequences to pseudo random sequences R ranging from 0 to 255n：
Rn＝mod(ceil(sn×10^3),256),n＝{1,2,3}。
4. The image encryption method based on Tent mapping and composite chaotic mapping as claimed in claim 1, wherein: in step S30, the mathematical model of the Tent map is:
wherein u represents a control parameter and has a value range of [0, 2 ]]；znAn iteration variable mapped for Tent, and an initial value z1When the value range of (0, 1) is obtained, Tent mapping enters the chaotic region.
5. The image encryption method based on Tent mapping and composite chaotic mapping as claimed in claim 1, wherein: in step S30, the composite chaotic map is a map generated by using Sine map and Chebyshev map as seed maps and using perturbation bifurcation parameters, and the mathematical model of the composite chaotic map is as follows:
wherein the value range of mu is (0, 1)]；xnThe output chaotic sequence is represented, and the value range is (0, 1); initial key a1When the absolute value of the chaotic mapping is not less than 2, the compound chaotic mapping enters a chaotic region to generate an infinite-length non-periodic chaotic real value sequence under the infinite precision condition; y isnHas a value range of [ -1, 1](ii) a c represents a weighting parameter, and the value is 0.1; n represents the number of iterations; mu.s1An iteration initial value representing the control parameter mu; a is1Representing an iteration initial value of the control parameter a; x is the number ofn+1、yn+1An iterative variable representing a composite chaotic map; mu.sn+1、an+1An iteration variable representing a control parameter.
6. The image encryption method based on Tent mapping and composite chaotic mapping as claimed in claim 3, wherein: the step S40 specifically includes:
step S41, performing first round scrambling on the matrix I by using a circshift function to obtain an image I1；
Step S42, pseudo-random sequence R generated by using composite chaotic mapping2For the image I1Performing a first round of diffusion to obtain a matrix C:
wherein i represents position information of the matrix; c (i) represents the ith number in the matrix C; c (i +1) represents the i +1 th number in the matrix C;
step S43, pseudo-random sequence R generated by Tent mapping3Carrying out bit XOR operation on the matrix C to obtain a matrix CC generated by the second round of diffusion;
step S44, pseudo-random sequence R generated by using composite chaotic mapping1And shuffling and scrambling the matrix CC to obtain an encrypted image CCC generated by the second round of scrambling.
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