CN113904765A - Airborne television guidance transmission image encryption method based on chaotic sequence - Google Patents

Airborne television guidance transmission image encryption method based on chaotic sequence Download PDF

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CN113904765A
CN113904765A CN202110716616.9A CN202110716616A CN113904765A CN 113904765 A CN113904765 A CN 113904765A CN 202110716616 A CN202110716616 A CN 202110716616A CN 113904765 A CN113904765 A CN 113904765A
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pixel
row
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CN113904765B (en
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潘勃
王栋
黄李龙
张欣
刘培欣
周向东
郗岳
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Air Force Engineering University of PLA
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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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • 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
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Abstract

The method for encrypting the airborne television guidance transmission image based on the chaos sequence comprises the following encryption steps: graying and pixel filling of an image, scrambling and encrypting in a row mode, blocking the image, extracting a central image, scrambling and encrypting the central image in a column mode, and performing cat mapping and encrypting on the central image; the decryption step comprises: the image is blocked and a central image is extracted, the generalized cat mapping pixel scrambling and decrypting of the central image, the column decrypting of the central image and the line decrypting of the image are carried out. The method realizes rapidity by adopting a mode of extracting the intermediate image for encryption, reduces the number of keys and reduces the memory occupation.

Description

Airborne television guidance transmission image encryption method based on chaotic sequence
Technical Field
The invention relates to the technical field of image processing, in particular to an encryption method for an airborne television guidance transmission image based on a chaos sequence.
Background
In the era of rapid development of the internet, digital images are widely applied and researched in various fields due to strong intuition and rich information quantity, and image information becomes one of the important modes for information transmission and communication of modern human beings. Meanwhile, the related security problem of image transmission is also attracting attention. Therefore, more and more scholars are dedicated to research on the subject, and in recent years, various new encryption algorithms and encryption modes are developed, which provides infinite possibility for the encryption mode of image transmission. Each encryption mode has the advantages or short boards of the encryption mode, the effect of making up for the deficiencies of the encryption modes can be achieved through reasonable combination and application of the encryption modes, and the safety performance of image transmission is greatly enhanced. Meanwhile, according to the actual situation, different encryption modes are designed to realize specific functions or endow ideal characteristics. In the military field, information security becomes increasingly important, and the information stealing and anti-stealing technology is mature from the perspective of information battlefields in all countries and military parties.
The air-to-air and air-to-ground missile is used as a main weapon for air-to-air combat and air-to-ground combat, and has irreplaceable effects on capturing air control right and striking ground targets. With the demand of air combat and the change of science and technology, the performance of air-ground missiles is gradually improved, and the air-ground missiles are developed into an air-ground missile family with multiple ranges, seriation, sea, land and air universalization and diversified guidance modes. A composite guidance system or a remote control guidance system used by an airborne television guidance missile needs to issue a control instruction to the missile according to target information of an image returned by a missile seeker at the present stage and control the missile to fly to a target. An enemy can intercept and capture image information returned by the missile through interception, defense and targeted interference are further implemented, an encryption method for the image of the television guidance system needs to be designed for preventing target information in the image from being decoded by the enemy, and particularly, protection for the central area of the image, namely target characteristics needs to be designed for attacking the target.
Missiles are increasingly becoming an important strategic deterrent and primary tactical means in modern warfare. The ground combat service receives the images transmitted back by the missiles in real time so as to ensure that the missiles can hit the target smoothly in the correct flight. The air-ground image transmission is an important ring, and the images must be encrypted in real time in the process so as to avoid missile interception and other conditions caused by interception of image information. Aiming at the characteristic of the transient change of the battlefield condition, the image encryption technology is required to have rapidity and safety.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a chaos sequence-based airborne television guidance transmission image encryption method, which specifically comprises the following steps:
first, encryption step
The first step is as follows: image graying and pixel filling
Acquiring the size M N of an original image to be encrypted, wherein M, N is a non-zero natural number which is greater than or equal to 16 and is a multiple of 16; representing pixel points of the image as P (0, 0), P (0, 1).. P (i, j).. P (M, N); i. j represents the horizontal and vertical coordinates of the pixel point, namely the pixel point is positioned in the ith row and the jth column; the original image is processed according to a weighted average formula
P(i，j)＝0.299*R(i，j)+0.578G(i，j)+0.114*B(i，j) ①
Carrying out image graying to obtain a grayscale image P0(ii) a Performing a boundary complement 0 operation, wherein 0 represents black, so that the length and the width of the image are equal; the method specifically comprises the following steps: if M is less than or equal to N, supplementing the image into a new image of N x N in a graph supplementing mode; if M is larger than N, supplementing the image into a new image of M by means of graph supplementing; suppose an image P obtained after supplementation1Size M x M, and pixel value matrix denoted A1；
The second step is that: line scrambling encryption
2.1 logical Logistic mapping
Nonlinear iterative equations of the mathematical model of the one-dimensional Logistic mapping:
Xk+1＝μXk(1-Xk) ②
wherein, mu belongs to [0, 4 ]]Referred to as Logistic parameter; k is an arbitrary natural number of 1 or more. When mu is not less than 3.57 and not more than 4, XkIs a random number, X, generated iteratively according to the formula-kEntering a chaotic state; and outside this range, the number series X is generated0、X1、X2…XkWill necessarily converge to a certain specific value;
2.2 definition of the region R
Defining the interval length as
Figure RE-GSB0000195688040000031
Interval(s)
Figure RE-GSB0000195688040000032
Corresponding to all pixels in the first line of the image, interval
Figure RE-GSB0000195688040000033
Corresponding to all pixels in the second row of the image
Figure RE-GSB0000195688040000034
All pixels (i is 1, 2 … M) in the ith row of the corresponding image;
2.3 line scrambling algorithm step
Giving Logistic mapping parameter mu and initial value X0(ii) a Mu and X0Corresponding to the time constant T, see table 2 for details.
TABLE 2 Logistic parameters Table
Figure RE-GSB0000195688040000035
According to the formula II, generating a chaotic value X through one iteration1Judgment of X1The range R, if X1∈RhReplacing the pixel point of the first row with the pixel point of the h row;
after M iterations, the operation is carried out on each row of pixel points, and then the row encryption of the image is completed; recording the encrypted image as P2The matrix of image pixels after line encryption is denoted A2；
The third step: image blocking and center image extraction
Will P2Is divided into blocks with the size of
Figure RE-GSB0000195688040000036
256 pixel blocks; denoted Q (0, 0), Q (0, 1) … … Q (15, 15);
the gray image pixel block matrix is represented as
Figure RE-GSB0000195688040000041
Extracting an intermediate partial image P3Constructing a new pixel matrix A3Picture P3A size of
Figure RE-GSB0000195688040000042
Figure RE-GSB0000195688040000043
Thereby completing the preprocessing of the image;
the fourth step: encrypting a center image by line scrambling
4.1 definition of the region R'
Defining the interval length as
Figure RE-GSB0000195688040000044
Interval(s)
Figure RE-GSB0000195688040000045
Corresponding to all pixels in the first column of the image, interval
Figure RE-GSB0000195688040000046
Corresponding to all pixels in the second row of the image
Figure RE-GSB0000195688040000047
Corresponding to all pixels in the t-th column of the image
Figure RE-GSB0000195688040000048
t represents the number of pixel columns of the central image instead of the number of pixel blocks;
4.2 sequence scrambling algorithm step
1. Based on the logistic parameter mu and the initial value X in 2.30；
2. Generating a chaos value X through one iteration1Judgment of X1The range R, if X1∈RhReplacing the pixel point of the first row with the pixel point of the h row; through
Figure RE-GSB0000195688040000049
And performing the operation on each row of pixel points in the second iteration, and finishing the centering of the image P3Scrambling and encrypting the column; the encrypted central image is marked as P4A size of
Figure RE-GSB00001956880400000410
The image pixel matrix is denoted as A4；
The fifth step: cat mapping encryption is carried out on central image
On the basis of preprocessing, re-encrypting the intermediate image based on cat mapping;
5.1 generalized cat mapping:
applying the cat mapping to image encryption, and discretizing the original cat mapping; i.e. pn，qnThe values of (n-0, 1, 2 …) are all positive integers, pn、qnRespectively representing the horizontal and vertical coordinates of the pixel points; the following generalized cat mapping is obtained:
Figure RE-GSB0000195688040000051
wherein a and b are positive integers, a and b are both smaller than M, and the determinant | C | ═ 1;
5.2 encryption step:
step 1: let process parameters
a＝mod(M，9)+1；
b＝mod(N，9)+1；
k＝(mod(M，9)+10)(mod(N，9)+10)；
Forming a matrix C;
Figure RE-GSB0000195688040000052
step 2: using matrix C and positive integer k as algorithm parameter, using formula (C) to image P4Scrambling the pixel point position; for the central image P in the order from line 1 to line N, then from column 1 to column M4Each pixel point A of4(i, j) operating to obtain the initial value (p) of (i, j)0，q0) Performing k iterations as initial values of the generalized cat mapping to obtain new positions (p) of the pixel points (i, j)k，qk) (ii) a Performing the operation on each pixel point of the central image to obtain a new encrypted image; recording the encrypted central image as P5A size of
Figure RE-GSB0000195688040000053
The image pixel matrix is denoted A5；
Thus, the whole encryption process is completed, and the encrypted image is marked as P6Size (M x M), the image pixel matrix is denoted A6And outputting the image;
step two, decryption
The first step is as follows: image blocking and central image extraction
Will P6Is divided into blocks with the size of
Figure RE-GSB0000195688040000061
256 pixel blocks; denoted Q (0, 0), Q (0, 1) … … Q (15, 15);
the gray image pixel block matrix is represented as
Figure RE-GSB0000195688040000062
Extracting an intermediate partial image P'5，P′5A size of
Figure RE-GSB0000195688040000063
Constructing a New Pixel matrix A'5；
Figure RE-GSB0000195688040000064
The second step is that: central image generalized cat mapping pixel scrambling decryption
Step 1: acquiring decryption keys a, b and k which are completely the same as the encryption parameters;
step 2: performing inverse pixel value transform by using inverse transform formula
Figure RE-GSB0000195688040000065
In a matrix C-1And the positive integer k is an algorithm parameter, and the image P 'is processed by a formula'5Scrambling the pixel point position; for center image P 'in order from bottom to top, right to left'5Of each pixel A'5(i, j) is operated, and the initial value (p 'of (i, j) is set'0，q′0) Performing k iterations as an initial value of the generalized cat mapping to obtain a new position (p ') of the pixel point (i, j)'k，q′k) (ii) a Performing the above operation on each pixel point of the central image to obtain a decrypted image, and recording the decrypted image as P'4；
The third step: central image column decryption
Step 1: obtaining decryption keys mu and X0The encryption parameter is completely the same as the encryption parameter and has the clock synchronization characteristic;
step 2: chaos value X generated by iteration using formula 21、X2…X3M/4Judgment of X3M/4The range R, if X3M/4∈RhThen will be
Figure RE-GSB0000195688040000071
The pixel point of the row is replaced with the pixel point of the ith row; through
Figure RE-GSB0000195688040000072
In the second iteration, the operation is carried out on each row of pixel points from right to left, and the center image P 'is completed'4Performing column scrambling and decryption; recording the decrypted image as P'3The size of the image is
Figure RE-GSB0000195688040000073
Image pixel matrix is represented as A'3；
The fourth step: image line decryption
Chaos value X generated by iteration using formula 21、X2…XMJudgment of XMThe range R, if XM∈RhReplacing the pixel point of the Mth row with the pixel point of the ith row; after M iterations, the operations are carried out on each line of pixel points from bottom to top, and the image P 'is completed'3Line scrambling and decrypting; recording the decrypted image as P'3， P′3A size of
Figure RE-GSB0000195688040000074
Image pixel matrix is represented as A'2；
Thereby completing the decryption process of the image, outputting the decrypted image P'2。
The invention adopts chaotic encryption, improves the rapidity of image encryption and decryption by a method of extracting a central image, and can complete the whole image transmission process by using a small amount of secret keys. The image encryption method of the invention gives consideration to the rapidity of the encryption process and the attack resistance of the encryption result, can greatly improve the security of image transmission, and can be used for the real-time transmission of missile images.
Drawings
FIG. 1 is a schematic row-column scrambling diagram;
FIG. 2 is an encryption flow chart of an encryption method of an airborne television guidance transmission image based on a chaos sequence according to the invention;
FIG. 3 is an original image to be encrypted;
FIG. 4 is a gray scale image of an original image;
FIG. 5 is a diagram of the effect of row scrambling;
FIG. 6 is a diagram of the effect of scrambling the center image column;
FIG. 7 is a diagram of a center image generalized cat mapping encryption effect;
fig. 8 is a decrypted image.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
First, encryption step
The first step is as follows: image graying and pixel filling
The original image size M × N to be encrypted is obtained M, N as a non-zero natural number equal to or greater than 16 and as a multiple of 16. Representing pixel points of the image as P (0, 0), P (0, 1).. P (i, j).. P (M, N); in this text, i and j represent the horizontal and vertical coordinates of a pixel point, that is, the pixel point is located in the ith row and the jth column. The original image is processed according to a weighted average formula
P(i，j)＝0.299*R(i，j)+0.578G(i，j)+0.114*B(i，j) ①
Carrying out image graying to obtain a grayscale image P0. The boundary complement 0 (black) operation is performed so that the image length and width are equal. The method specifically comprises the following steps: if M is less than or equal to N, supplementing the image into a new image of N x N in a graph supplementing mode; if M > N, the image is complemented into a new image of M by means of a complement. Suppose an image P obtained after supplementation1Size M x M, and pixel value matrix denoted A1。
The second step is that: line scrambling encryption
2.1 logical (Logistic) mapping
Nonlinear iterative equations of the mathematical model of the one-dimensional Logistic mapping:
Xk+1＝μXk(1-Xk) ②
wherein, mu belongs to [0, 4 ]]Referred to as Logistic parameters. When mu is not less than 3.57 and not more than 4, XkIs a random number generated by iteration according to a formula II, and k is any natural number more than or equal to 1. XkEntering a chaotic state. And outside this range, the number series X is generated0、X1、X2…XkWill necessarily converge to a certain specific value.
2.2 definition of the region R
Defining the interval length as
Figure RE-GSB0000195688040000091
Interval(s)
Figure RE-GSB0000195688040000092
Corresponding to all pixels in the first line of the image, interval
Figure RE-GSB0000195688040000093
Corresponding to all pixels in the second row of the image
Figure RE-GSB0000195688040000094
Corresponding to all pixels in the ith row of the image (i ═ 1, 2 … M).
2.3 line scrambling algorithm step
Giving Logistic mapping parameter mu and initial value X0. (mu with X)0Corresponding to the time constant T, see Table 1 for details
TABLE 1 Logistic parameters Table
Figure RE-GSB0000195688040000095
According to the formula II, generating a chaotic value X through one iteration1Judgment of X1The range R, if X1∈RhThen, the pixel point of the first row is replaced with the pixel point of the h-th row, and the schematic diagram is shown in fig. one.
After M iterations, the above operation is performed on each row of pixel points, and then the row encryption of the image is completed. Recording the encrypted image as P2The matrix of image pixels after line encryption is denoted A2。
The third step: image blocking and center image extraction
Will P2Is divided into blocks with the size of
Figure RE-GSB0000195688040000096
256 pixel blocks. Is shown as Q(0，0)、Q(0，1)……Q(15，15)。
The gray image pixel block matrix is represented as
Figure RE-GSB0000195688040000101
Extracting an intermediate partial image P3(image P)3A size of
Figure RE-GSB0000195688040000102
) Constructing a new pixel matrix A3。
Figure RE-GSB0000195688040000103
Thereby completing the pre-processing of the image.
The fourth step: encrypting a center image by line scrambling
4.1 definition of the region R'
Defining the interval length as
Figure RE-GSB0000195688040000104
Interval(s)
Figure RE-GSB0000195688040000105
Corresponding to all pixels in the first column of the image, interval
Figure RE-GSB0000195688040000106
Corresponding to all pixels in the second row of the image
Figure RE-GSB0000195688040000107
Corresponding to all pixels in the t-th column of the image
Figure RE-GSB0000195688040000108
t represents the number of pixel columns of the central image, not the number of pixel blocks.
4.2 sequence scrambling algorithm step
1. Based on 1OGisti in 2.3c parameter mu, initial value X0。
2. Generating a chaos value X through one iteration1Judgment of X1The range R, if X1∈RhThen the pixel point of the first column is replaced with the pixel point of the h column. Through
Figure RE-GSB0000195688040000109
And performing the operation on each row of pixel points in the second iteration, and finishing the centering of the image P3Is encrypted. The encrypted central image is marked as P4A size of
Figure RE-GSB00001956880400001010
The image pixel matrix is denoted as A4。
The fifth step: cat mapping encryption is carried out on central image
On the basis of preprocessing, the rapidity and the reliability of encryption are considered, and the intermediate image is re-encrypted based on cat mapping.
5.1 generalized cat mapping:
the nature of the cat map makes it very suitable for use in encryption systems, where the original cat map is discretized for application in image encryption. I.e. pn，qnThe values of (n-0, 1, 2 …) are all positive integers, pn、qnRespectively representing the horizontal and vertical coordinates of the pixel points. The following generalized cat mapping is obtained:
Figure RE-GSB0000195688040000111
wherein a and b are positive integers, a and b are both smaller than M, and the determinant | C | ═ 1. Adding modulo constraints to the cat map is still area-reversible, but this may also result in the map no longer being chaotic. The generalized cat mapping still has the property of stretching and folding in a geometric sense, i.e. the position of the original pixel of the image will be mapped to other positions and can therefore be applied to image encryption.
5.2 encryption step:
step 1: let process parameters
a＝mod(M，9)+1；
b＝mod(N，9)+1；
k＝(mod(M，9)+10)(mod(N，9)+10)；
Forming a matrix C.
Figure RE-GSB0000195688040000112
Step 2: using matrix C and positive integer k as algorithm parameter, using formula (C) to image P4The pixel point positions are scrambled. For the central image P in the order from line 1 to line N, then from column 1 to column M4Each pixel point A of4(i, j) operating to obtain the initial value (p) of (i, j)0，q0) Performing k iterations as initial values of the generalized cat mapping to obtain new positions (p) of the pixel points (i, j)k，qk). And performing the operation on each pixel point of the central image to obtain a new encrypted image. Recording the encrypted central image as P5A size of
Figure RE-GSB0000195688040000121
The image pixel matrix is denoted A5。
Thus, the whole encryption process is completed, and the encrypted image is marked as P6Size (M x M), the image pixel matrix is denoted A6And outputs an image.
Step two, decryption
The first step is as follows: image blocking and central image extraction
Will P6Is divided into blocks with the size of
Figure RE-GSB0000195688040000122
256 pixel blocks. Denoted as Q (0, 0), Q (0, 1) … … Q (15, 15).
The gray image pixel block matrix is represented as
Figure RE-GSB0000195688040000123
Extracting an intermediate partial image P'5，P′5A size of
Figure RE-GSB0000195688040000124
Constructing a New Pixel matrix A'5。
Figure RE-GSB0000195688040000125
The second step is that: central image generalized cat mapping pixel scrambling decryption
Step 1: and acquiring decryption keys a, b and k which are completely the same as the encryption parameters.
Step 2: performing inverse pixel value transform by using inverse transform formula
Figure RE-GSB0000195688040000126
In a matrix C-1And the positive integer k is an algorithm parameter, and the image P 'is processed by a formula'5The pixel point positions are scrambled. For center image P 'in bottom-to-top, right-to-left order (reverse order of encryption)'5Of each pixel A'5(i, j) is operated, and the initial value (p 'of (i, j) is set'0，q′0) Performing k iterations as an initial value of the generalized cat mapping to obtain a new position (p ') of the pixel point (i, j)'k，q′k). Performing the above operation on each pixel point of the central image to obtain a decrypted image, and recording the decrypted image as P'4。
The third step: central image column decryption
Step 1: obtaining decryption keys mu and X0The encryption parameter is identical to the encryption parameter and has a clock synchronization characteristic.
Step 2: chaos value X generated by iteration using formula 21、X2…X3M/4Judgment of X3M/4The range R, if X3M/4∈RhThen will be
Figure RE-GSB0000195688040000131
And the pixel point of the column is replaced with the pixel point of the ith column. Through
Figure RE-GSB0000195688040000132
In the second iteration, the operation is carried out on each row of pixel points from right to left, and the center image P 'is completed'4Is decrypted. Recording the decrypted image as P'3(image size of
Figure RE-GSB0000195688040000133
) Image pixel matrix is represented as A'3。
The fourth step: image line decryption
Chaos value X generated by iteration using formula 21、X2…XMJudgment of XMThe range R, if XM∈RhAnd replacing the pixel point of the M-th row with the pixel point of the ith row. After M iterations, the operations are carried out on each line of pixel points from bottom to top, and the image P 'is completed'3Line scrambling decryption. Recording the decrypted image as P'3， P′3A size of
Figure RE-GSB0000195688040000134
Image pixel matrix is represented as A'2。
Thereby completing the decryption process of the image, outputting the decrypted image P'2。
Examples of the applications
The encryption and decryption process is now performed by taking 256 × 256 images as an example.
First, decryption step
The first step is as follows: image graying and pixel filling
Acquiring an original image to be encrypted, as shown in fig. 3, the size of the original image is 256 × 256, and pixel points of the image are represented as P (0, 0), P (0, 1).. P (i, j).. P (256 ); the original image is processed according to a weighted average formula
P(i，j)＝0.299*R(i，j)+0.578G(i，j)+0.114*B(i，j) ①
The image is grayed. Obtaining a grayscale image P1256 × 256, as shown in FIG. 4, the matrix of pixel values is denoted A1。
The second step is that: line scrambling encryption
2.1 definition of the region R
Defining the interval length as
Figure RE-GSB0000195688040000141
Interval(s)
Figure RE-GSB0000195688040000142
Corresponding to all pixels in the first line of the image, interval
Figure RE-GSB0000195688040000143
Section corresponding to all pixels in the second row of the image
Figure RE-GSB0000195688040000144
Corresponding to all pixels in the ith row of the image ( i 1, 2.. 256).
2.2 line scrambling algorithm step
Given Logistic mapping parameter mu is 3.93 and initial value X0＝0.6。
Generating a chaos value X through one iteration1When X is 0.9432, X is judged1Interval of belongings, X1∈R242Then the pixel point of the first row is replaced with the pixel point of the 242 th row.
2.3 after 256 iterations, the above operation is performed on each row of pixel points, and then the row replacement of the image is completed. Recording the encrypted image as P2As shown in FIG. 5, the matrix of image pixels after row encryption is denoted A2。
The third step: image blocking and center image extraction
Will P2And partitioning into 256 pixel blocks with the size of 16 x 16. Denoted as Q (0, 0), Q (0, 1) … … Q (15, 15).
The gray image pixel block matrix is represented as
Figure RE-GSB0000195688040000145
Extracting an intermediate partial image P3(image P)3Size 192 × 192) to construct a new pixel matrix a3。
Figure RE-GSB0000195688040000146
The pre-processing of the image is completed.
The fourth step: encrypting a center image by line scrambling
4.1 definition of the region R'
Defining the interval length as
Figure RE-GSB0000195688040000151
Interval(s)
Figure RE-GSB0000195688040000152
Corresponding to all pixels in the first column of the image, interval
Figure RE-GSB0000195688040000153
Corresponding to all pixels in the second row of the image
Figure RE-GSB0000195688040000154
Corresponding to all pixels in the tth column of the image (t is 1, 2 … M).
4.2 sequence scrambling algorithm step
1. Based on the logistic parameter mu of 2.3 ═ 3.93 and the initial value X0＝0.6。
2. Generating a chaos value X through one iteration1When X is 0.9432, X is judged1Interval of belongings, X1∈R′182Then the pixel point in the first column is replaced with the pixel point in the 182 th column. After 192 iterations, the above operation is performed on each row of pixels, and the centering of the image P is completed3Is encrypted. The encrypted central image is marked as P4Size 192 × 192, as shown in fig. 6, the image pixel matrix is denoted as a4。
The fifth step: cat mapping encryption is carried out on central image
Step 1: order to
a＝mod(256，9)+1＝5；
b＝mod(256，9)+1＝5；
k＝(mod(256，9)+10)(mod(256，9)+10)＝225；
Forming a matrix C.
Figure RE-GSB0000195688040000155
Step 2: using matrix C and positive integer 225 as algorithm parameters, and using formula (C) to image P4The pixel point positions are scrambled. For the central image P in row-to-row order from top to bottom4Each pixel point A of4(i, j) operating to obtain the initial value (p) of (i, j)0，q0) Performing k iterations as initial values of the generalized cat mapping to obtain new positions (p) of the pixel points (i, j)k，qk). And carrying out the operation on each pixel point of the central image to obtain a new encrypted image. Recording the encrypted central image as P5Size 192 × 192, and image pixel matrix denoted as A5。
The whole encryption process is completed, and the encrypted image is marked as P6The size is 256 × 256 and the image pixel matrix is denoted a, as shown in fig. 76And outputs an image.
Step two, decryption
The first step is as follows: image blocking and central image extraction
Will P6And partitioning into 256 pixel blocks with the size of 16 x 16. Denoted as Q (0, 0), Q (0, 1) … … Q (15, 15).
The gray image pixel block matrix is represented as
Figure RE-GSB0000195688040000161
Extracting an intermediate partial image P'5(image P'5Size 192 x 192) constructs a new pixel matrix a'5。
Figure RE-GSB0000195688040000162
The second step is that: central image generalized cat mapping pixel scrambling decryption
Step 1: the decryption key a is 5, b is 5, and k is 225.
Step 2: performing inverse pixel value transform by using inverse transform formula
Figure RE-GSB0000195688040000163
In a matrix C-1And positive integer 225 is an algorithm parameter, and the image P 'is processed by a formula'5The pixel point positions are scrambled. For center image P 'in bottom-to-top, right-to-left order (reverse order of encryption)'5Of each pixel A'5(i, j) is operated, and the initial value (p 'of (i, j) is set'0，q′0) Performing k iterations as an initial value of the generalized cat mapping to obtain a new position (p ') of the pixel point (i, j)'k，q′k). Performing the above operation on each pixel point of the central image to obtain a decrypted image, and recording the decrypted image as P'4。
The third step: central image column decryption
Step 1: obtaining decryption key mu-3.93, X0＝0.6
Step 2: using iteratively generated chaotic values X1＝0.9432、X2＝0.2105448768...X192When X is 0.318312973691692, X is judged192The interval R', if X192∈R′62The pixel point in column 192 is replaced with the pixel point in column 62. After 192 iterations, the operation is performed on each column of pixel points from right to left, and then the center image P 'is completed'4In the column ofAnd (6) decrypting. Recording the decrypted image as P'3(image size 256 x 256) and image pixel matrix denoted A'3。
The fourth step: image line decryption
Using iteratively generated chaotic values X1、X2…X256Judgment of X256In the interval of 0.759766630703317, X256∈R195Then the pixel point of the 256 th row is replaced with the pixel point of the 195 th row. After 256 iterations, the above operation is performed on each row of pixel points from bottom to top, and the image P 'is completed'3Line scrambling decryption. Recording the decrypted image as P'3Size 192, image pixel matrix denoted A'2。
The decryption process of the image is completed, and the decrypted image P 'is output'2(see FIG. 7 below).
The advantages of the invention are not listed, but only two outstanding advantages are given as follows:
1. the method for extracting the intermediate image encryption is adopted to realize rapidity.
2. The number of the keys is reduced, and the memory occupation is reduced.

Claims (1)

1. A chaos sequence-based airborne television guidance transmission image encryption method is characterized by comprising the following steps:
first, encryption step
The first step is as follows: image graying and pixel filling
Acquiring the size M N of an original image to be encrypted, wherein M, N is a non-zero natural number which is greater than or equal to 16 and is a multiple of 16; representing pixel points of the image as P (0, 0), P (0, 1).. P (i, j).. P (M, N); i. j represents the horizontal and vertical coordinates of the pixel point, namely the pixel point is positioned in the ith row and the jth column; the original image is processed according to a weighted average formula
P(i，j)＝0.299*R(i，j)+0.578G(i，j)+0.114*B(i，j) ①
Carrying out image graying to obtain a grayscale image P0(ii) a A boundary complement 0 operation is performed, 0 representing black, so that the image length is equal toThe widths are equal; the method specifically comprises the following steps: if M is less than or equal to N, supplementing the image into a new image of N x N in a graph supplementing mode; if M is larger than N, supplementing the image into a new image of M by means of graph supplementing; suppose an image P obtained after supplementation1Size M x M, and pixel value matrix denoted A1；
The second step is that: line scrambling encryption
2.1 logical Logistic mapping
Nonlinear iterative equations of the mathematical model of the one-dimensional Logistic mapping:
Xk+1＝μXk(1-Xk) ②
wherein, mu belongs to [0, 4 ]]Referred to as Logistic parameter; k is an arbitrary natural number of 1 or more. When mu is not less than 3.57 and not more than 4, XkIs a random number, X, generated iteratively according to the formula-kEntering a chaotic state; and outside this range, the number series X is generated0、X1、X2…XkWill necessarily converge to a certain specific value;
2.2 definition of the region R
Defining the interval length as
Figure RE-FSB0000195688030000011
Interval(s)
Figure RE-FSB0000195688030000012
Corresponding to all pixels in the first line of the image, interval
Figure RE-FSB0000195688030000013
Corresponding to all pixels in the second row of the image
Figure RE-FSB0000195688030000021
All pixels (i is 1, 2 … M) in the ith row of the corresponding image;
2.3 line scrambling algorithm step
Giving Logistic mapping parameter mu and initial value X0(ii) a Mu and X0Corresponding to the time constant T, see table 2 for details.
TABLE 2 Logistic parameters Table
Figure RE-FSB0000195688030000022
According to the formula II, generating a chaotic value X through one iteration1Judgment of X1The range R, if X1∈RhReplacing the pixel point of the first row with the pixel point of the h row;
after M iterations, the operation is carried out on each row of pixel points, and then the row encryption of the image is completed; recording the encrypted image as P2The matrix of image pixels after line encryption is denoted A2；
The third step: image blocking and center image extraction
Will P2Is divided into blocks with the size of
Figure RE-FSB0000195688030000023
256 pixel blocks; denoted Q (0, 0), Q (0, 1) … … Q (15, 15);
the gray image pixel block matrix is represented as
Figure RE-FSB0000195688030000024
Extracting an intermediate partial image P3Constructing a new pixel matrix A3Picture P3A size of
Figure RE-FSB0000195688030000025
Figure RE-FSB0000195688030000031
Thereby completing the preprocessing of the image;
the fourth step: encrypting a center image by line scrambling
4.1 definition of the region R'
Defining the interval length as
Figure RE-FSB0000195688030000032
Interval(s)
Figure RE-FSB0000195688030000033
Corresponding to all pixels in the first column of the image, interval
Figure RE-FSB0000195688030000034
Corresponding to all pixels in the second row of the image
Figure RE-FSB0000195688030000035
Corresponding to all pixels in the t-th column of the image
Figure RE-FSB0000195688030000036
t represents the number of pixel columns of the central image instead of the number of pixel blocks;
4.2 sequence scrambling algorithm step
1. Based on the logistic parameter mu and the initial value X in 2.30；
2. Generating a chaos value X through one iteration1Judgment of X1The range R, if X1∈RhReplacing the pixel point of the first row with the pixel point of the h row; through
Figure RE-FSB0000195688030000037
And performing the operation on each row of pixel points in the second iteration, and finishing the centering of the image P3Scrambling and encrypting the column; the encrypted central image is marked as P4A size of
Figure RE-FSB0000195688030000038
The image pixel matrix is denoted as A4；
The fifth step: cat mapping encryption is carried out on central image
On the basis of preprocessing, re-encrypting the intermediate image based on cat mapping;
5.1 generalized cat mapping:
applying the cat mapping to image encryption, and discretizing the original cat mapping; i.e. pn，qnThe values of (n-0, 1, 2 …) are all positive integers, pn、qnRespectively representing the horizontal and vertical coordinates of the pixel points; the following generalized cat mapping is obtained:
Figure RE-FSB0000195688030000041
wherein a and b are positive integers, a and b are both smaller than M, and the determinant | C | ═ 1;
5.2 encryption step:
step 1: let process parameters
a＝mod(M，9)+1；
b＝mod(N，9)+1；
k＝(mod(M，9)+10)(mod(N，9)+10)；
Forming a matrix C;
Figure RE-FSB0000195688030000042
step 2: using matrix C and positive integer k as algorithm parameter, using formula (C) to image P4Scrambling the pixel point position; for the central image P in the order from line 1 to line N, then from column 1 to column M4Each pixel point A of4(i, j) operating to obtain the initial value (p) of (i, j)0，q0) Performing k iterations as initial values of the generalized cat mapping to obtain new positions (p) of the pixel points (i, j)k，qk) (ii) a Performing the operation on each pixel point of the central image to obtain a new encrypted image; recording the encrypted central image as P5A size of
Figure RE-FSB0000195688030000043
The image pixel matrix is denoted A5；
Thus, the whole encryption process is completed, and the encrypted image is marked as P6Size (M x M), the image pixel matrix is denoted A6And outputting the image;
step two, decryption
The first step is as follows: image blocking and central image extraction
Will P6Is divided into blocks with the size of
Figure RE-FSB0000195688030000044
256 pixel blocks; denoted Q (0, 0), Q (0, 1) … … Q (15, 15);
the gray image pixel block matrix is represented as
Figure RE-FSB0000195688030000051
Extracting an intermediate partial image P'5，P′5A size of
Figure RE-FSB0000195688030000052
Constructing a New Pixel matrix A'5；
Figure RE-FSB0000195688030000053
The second step is that: central image generalized cat mapping pixel scrambling decryption
Step 1: acquiring decryption keys a, b and k which are completely the same as the encryption parameters;
step 2: performing inverse pixel value transform by using inverse transform formula
Figure RE-FSB0000195688030000054
In a matrix C-1And the positive integer k is an algorithm parameter, and the image P 'is processed by a formula'5Scrambling the pixel point position; from bottom to top, fromRight to left order for center image P'5Of each pixel A'5(i, j) is operated, and the initial value (p 'of (i, j) is set'0，q′0) Performing k iterations as an initial value of the generalized cat mapping to obtain a new position (p ') of the pixel point (i, j)'k，q′k) (ii) a Performing the above operation on each pixel point of the central image to obtain a decrypted image, and recording the decrypted image as P'4；
The third step: central image column decryption
Step 1: obtaining decryption keys mu and X0The encryption parameter is completely the same as the encryption parameter and has the clock synchronization characteristic;
step 2: chaos value X generated by iteration using formula 21、X2…X3M/4Judgment of X3M/4The range R, if X3M/4∈RhThen will be
Figure RE-FSB0000195688030000055
The pixel point of the row is replaced with the pixel point of the ith row; through
Figure RE-FSB0000195688030000056
In the second iteration, the operation is carried out on each row of pixel points from right to left, and the center image P 'is completed'4Performing column scrambling and decryption; recording the decrypted image as P'3The size of the image is
Figure RE-FSB0000195688030000061
Image pixel matrix is represented as A'3；
The fourth step: image line decryption
Chaos value X generated by iteration using formula 21、X2…XMJudgment of XMThe range R, if XM∈RhReplacing the pixel point of the Mth row with the pixel point of the ith row; after M iterations, the operations are carried out on each line of pixel points from bottom to top, and the image P 'is completed'3Line scrambling and decrypting; recording the decrypted image as P'3，P′3A size of
Figure RE-FSB0000195688030000062
Image pixel matrix is represented as A'2；
Thereby completing the decryption process of the image, outputting the decrypted image P'2。
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