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CN109660695B - Color image encryption method based on genetic simulated annealing algorithm and chaotic mapping - Google Patents

Color image encryption method based on genetic simulated annealing algorithm and chaotic mapping Download PDF

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CN109660695B
CN109660695B CN201811488743.2A CN201811488743A CN109660695B CN 109660695 B CN109660695 B CN 109660695B CN 201811488743 A CN201811488743 A CN 201811488743A CN 109660695 B CN109660695 B CN 109660695B
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罗玉玲
欧阳雪
丘森辉
秦兴盛
刘俊秀
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Abstract

The invention discloses a color image encryption method based on a genetic simulated annealing algorithm and chaotic mapping, which is characterized by comprising the following steps of: 1) generating an integer sequence; 2) selecting and interleaving R, G, B layers in the plaintext image I; 3) scrambling operation based on a simulated annealing algorithm is carried out on each layer of the cross sequence; 4) judging whether to execute mutation operation; 5) a final encrypted image E is obtained. The method can enhance the security of image information, improve the efficiency of encryption processing, enhance the robustness of the image, has high security and can resist common image attacks.

Description

一种基于遗传模拟退火算法和混沌映射的彩色图像加密方法A Color Image Encryption Method Based on Genetic Simulated Annealing Algorithm and Chaos Mapping

技术领域technical field

本发明涉及图像加密技术领域，具体是一种基于遗传模拟退火算法和混沌映射的彩色图像加密方法。The invention relates to the technical field of image encryption, in particular to a color image encryption method based on a genetic simulated annealing algorithm and chaotic mapping.

背景技术Background technique

图像加密技术不仅能够增强图像信息传输的安全性和可靠性，还可以提高图像的抗攻击能力，确保重要的图像信息更加安全地传输。然而，由于图像相邻像素具有高度相关性，使得针对常规文本设计的传统加密算法(如AES和DES等)并不适用于图像加密。此外，由于混沌系统具有复杂非线性动力学性能，其拥有良好的伪随机特性、轨道的不可预测性以及对初始状态和控制参数极端敏感等特性，因此混沌系统适用于图像加密。Image encryption technology can not only enhance the security and reliability of image information transmission, but also improve the image's anti-attack ability to ensure more secure transmission of important image information. However, the traditional encryption algorithms (such as AES and DES, etc.) designed for regular text are not suitable for image encryption due to the high correlation between adjacent pixels in the image. In addition, chaotic systems are suitable for image encryption due to their complex nonlinear dynamics, good pseudo-random properties, unpredictability of orbits, and extreme sensitivity to initial states and control parameters.

在基于混沌系统的图像加密算法中，“置乱-扩散”的图像加密框架被广泛运用。其中，置乱操作可以改变像素的位置，扩散操作可以改变像素的灰度值。然而，单纯的置乱或扩散操作存在安全性低，易被单独攻击等问题。In the image encryption algorithm based on chaotic system, the "scrambling-diffusion" image encryption framework is widely used. Among them, the scrambling operation can change the position of the pixel, and the diffusion operation can change the gray value of the pixel. However, simple scrambling or diffusion operations have problems such as low security and easy to be attacked alone.

发明内容SUMMARY OF THE INVENTION

本发明的目的是针对现有技术的不足，而提供一种基于遗传模拟退火算法和混沌映射的彩色图像加密方法。这种方法能增强图像信息的安全性，提高加密处理的效率，能增强图像的鲁棒性，这种方法安全性高，可以抵抗常见图像攻击。The purpose of the present invention is to provide a color image encryption method based on genetic simulated annealing algorithm and chaotic mapping, aiming at the deficiencies of the prior art. This method can enhance the security of image information, improve the efficiency of encryption processing, and enhance the robustness of images. This method has high security and can resist common image attacks.

实现本发明目的的技术方案是：The technical scheme that realizes the object of the present invention is:

一种基于遗传模拟退火算法和混沌映射的彩色图像加密方法，与现有技术不同处在于，包括如下步骤：A color image encryption method based on genetic simulated annealing algorithm and chaotic mapping, which is different from the prior art in that it includes the following steps:

1)生成整数序列：将明文图像I作为MD5哈希的输入生成与明文相关的密钥，并作为混沌系统的初始值，依据混沌系统初始值迭代生成混沌序列并对其执行量化操作，生成六条整数混沌序列X1、Y1、Z1、X2、Y2和Z2；1) Generate an integer sequence: take the plaintext image I as the input of the MD5 hash to generate a key related to the plaintext, and as the initial value of the chaotic system, iteratively generate the chaotic sequence according to the initial value of the chaotic system and perform quantization operations on it to generate six an integer chaotic sequence X 1 , Y 1 , Z 1 , X 2 , Y 2 and Z 2 ;

2)对明文图像I中的R、G、B三层进行选择和交叉操作：对步骤1)得到的整数序列X1、Y1、Z1和明文图像I中的R、G、B三层进行二进制位平面分解产生8个位平面并重新组成一维向量，生成混沌二进制位序列，然后设置混沌二进制序列为掩码，通过掩码中“0”和“1”来选择和交叉明文图像，最后再将选择和交叉操作后的二进制图像序列恢复到像素级，生成交叉序列；2) Select and cross the three layers of R, G, and B in the plaintext image I: perform the integer sequence X 1 , Y 1 , Z 1 obtained in step 1) and the three layers of R, G, and B in the plaintext image I Perform binary bit plane decomposition to generate 8 bit planes and reconstitute a one-dimensional vector to generate a chaotic binary bit sequence, then set the chaotic binary sequence as a mask, and select and cross the plaintext image by "0" and "1" in the mask, Finally, restore the binary image sequence after selection and cross operation to the pixel level to generate a cross sequence;

3)对交叉序列各层执行基于模拟退火算法的置乱操作：设明文图像I的长和宽分别为M和N，首先对步骤1)生成的三条整数混沌序列X2、Y2和Z2相互进行减法操作得到大小为M×N的目标函数序列L1、L2和L3，然后判断目标函数序列：如果L1(t)≥0，则最优解

Figure GDA0002364015930000021
其中t为每个目标函数序列的索引，并且1≤t≤M×N；否则计算当前目标函数序列L1、L2和L3的阈值Pc和概率Pt，如果Pc≥Pt，则最优解
Figure GDA0002364015930000022
否则计算最优解
Figure GDA0002364015930000023
同理，最优解
Figure GDA0002364015930000024
和
Figure GDA0002364015930000025
可以由判断L2(t)与L3(t)获得，根据最优序列
Figure GDA0002364015930000026
和
Figure GDA0002364015930000027
对交叉序列I”R、I”G和I”B执行列置乱操作，得到置乱序列；3) Perform the scramble operation based on simulated annealing algorithm on each layer of the cross sequence: set the length and width of the plaintext image I to be M and N respectively, firstly perform the three integer chaotic sequences X 2 , Y 2 and Z 2 generated in step 1). Subtract each other to obtain the objective function sequence L 1 , L 2 and L 3 of size M×N, and then judge the objective function sequence: if L 1 (t)≥0, then the optimal solution
Figure GDA0002364015930000021
where t is the index of each objective function sequence, and 1≤t≤M×N; otherwise, the threshold P c and probability P t of the current objective function sequence L 1 , L 2 and L 3 are calculated, if P c ≥ P t , the optimal solution
Figure GDA0002364015930000022
Otherwise calculate the optimal solution
Figure GDA0002364015930000023
Similarly, the optimal solution
Figure GDA0002364015930000024
and
Figure GDA0002364015930000025
It can be obtained by judging L 2 (t) and L 3 (t), according to the optimal sequence
Figure GDA0002364015930000026
and
Figure GDA0002364015930000027
Perform a column scrambling operation on the cross sequence I" R , I" G and I" B to obtain a scrambling sequence;

4)判断是否执行变异操作：计算明文图像I和置乱图像各层的适应度，并通过明文图像I和置乱图像的适应度来判断是否执行变异操作，如果明文图像I的适应度大于置乱图像的适应度，则重新选择参数生成混沌序列并重新执行选择、交叉和置乱操作；否则根据置乱图像的适应度计算混沌系统的初始值并迭代混沌系统获得混沌序列，并对混沌系统进行量化处理得到整数序列；4) Determine whether to perform mutation operation: calculate the fitness of each layer of plaintext image I and scrambled image, and judge whether to perform mutation operation by the fitness of plaintext image I and scrambled image, if the fitness of plaintext image I is greater than If the fitness of the chaotic image is determined, the parameters are reselected to generate the chaotic sequence and the selection, crossover and scrambling operations are performed again; otherwise, the initial value of the chaotic system is calculated according to the fitness of the scrambled image, and the chaotic system is iterated to obtain the chaotic sequence, and the chaotic system is Perform quantization processing to obtain an integer sequence;

5)获得最终加密图像E：将各层置乱序列执行交互式变异操作并将变异序列合并获得最终加密图像E。5) Obtain the final encrypted image E: perform an interactive mutation operation on the scrambled sequences of each layer and combine the mutated sequences to obtain the final encrypted image E.

所述步骤1)的过程为：The process of described step 1) is:

将明文图像I作为MD5哈希的输入，并把MD5哈希生成的128位密钥H分成32个子密钥，每个块的长度是4位，如公式(1)所示：The plaintext image I is used as the input of the MD5 hash, and the 128-bit key H generated by the MD5 hash is divided into 32 sub-keys, and the length of each block is 4 bits, as shown in formula (1):

H＝h1,h2,h3,...,h32 (1)，H=h 1 , h 2 , h 3 ,...,h 32 (1),

然后，定义x'1、y'1、z'1和x'2、y'2、z'2的值，因此混沌系统的初始值x1(1)、y1(1)、z1(1)和x2(1)、y2(1)、z2(1)可以由公式(2)得到，依据混沌系统初始值迭代生成两组混沌序列x1、y1、z1和x2、y2、z2，并对其执行量化操作得到整数序列X1、Y1、Z1和X2、Y2、Z2，如公式(3)所示：Then, define the values of x' 1 , y' 1 , z' 1 and x' 2 , y' 2 , z' 2 , so the initial values of the chaotic system x 1 (1), y 1 (1), z 1 ( 1) and x 2 (1), y 2 (1), z 2 (1) can be obtained from formula (2), and iteratively generates two sets of chaotic sequences x 1 , y 1 , z 1 and x 2 according to the initial value of the chaotic system , y 2 , z 2 , and perform quantization operations on them to obtain integer sequences X 1 , Y 1 , Z 1 and X 2 , Y 2 , Z 2 , as shown in formula (3):

Figure GDA0002364015930000031
Figure GDA0002364015930000031

Figure GDA0002364015930000032
Figure GDA0002364015930000032

所述步骤2)的过程为：The process of described step 2) is:

对整数序列X1、Y1、Z1和明文图像I各层IR、IG、IB进行二进制位平面分解产生8个位平面并重新组成一维向量，生成二进制位序列，然后设置混沌二进制序列为掩码，通过掩码中“0”和“1”来选择和交叉图像，如果掩码值是“1”，则保持图像的位不变；否则翻转该图像的位来获得新的位，最后再将选择和交叉操作后的二进制图像序列恢复到像素级，生成交叉序列I”R、I”G和I”B。Perform binary bit plane decomposition on the integer sequence X 1 , Y 1 , Z 1 and each layer IR , IG , IB of the plaintext image I to generate 8 bit planes and reconstitute a one-dimensional vector, generate a binary bit sequence, and then set the chaos The binary sequence is a mask, and the image is selected and intersected by "0" and "1" in the mask. If the mask value is "1", the bits of the image are kept unchanged; otherwise, the bits of the image are flipped to obtain a new bits, and finally restore the binary image sequence after the selection and interleaving operations to the pixel level to generate the interleaving sequences I" R , I" G and I" B .

所述步骤3)的过程为：The process of described step 3) is:

采用模拟退火算法设计最优伪随机序列对交叉图像进行置乱操作来获得置乱图像，基于模拟退火算法的图像置乱步骤如下：The simulated annealing algorithm is used to design the optimal pseudo-random sequence to scramble the crossed image to obtain the scrambled image. The image scrambling steps based on the simulated annealing algorithm are as follows:

首先产生目标函数序列，根据步骤1)生成的三条整数混沌序列X2、Y2和Z2相互进行减法操作得到大小为M×N的目标函数序列L1、L2和L3，其中t为每个目标函数序列的索引，并且1≤t≤M×N：First, the objective function sequence is generated, and the three integer chaotic sequences X 2 , Y 2 and Z 2 generated in step 1) are mutually subtracted to obtain the objective function sequences L 1 , L 2 and L 3 of size M×N, where t is The index of each objective function sequence, and 1≤t≤M×N:

Figure GDA0002364015930000033
Figure GDA0002364015930000033

然后判断目标函数，令t＝1，执行以下操作：Then judge the objective function, let t=1, and perform the following operations:

a.可如果如果L1(t)≥0，则最优解

Figure GDA0002364015930000034
否则依据公式(5)计算当前目标函数序列L1、L2和L3的阈值Pc和概率Pt，如果Pc≥Pt，则最优解
Figure GDA0002364015930000041
否则依据公式(6)计算最优解
Figure GDA0002364015930000042
同理，最优解
Figure GDA0002364015930000043
和
Figure GDA0002364015930000044
可以由判断L2(t)与L3(t)获得，1≤t≤M×N，M和N分别为明文图像I的长和宽，a. If L 1 (t) ≥ 0, then the optimal solution
Figure GDA0002364015930000034
Otherwise, calculate the threshold P c and probability P t of the current objective function sequence L 1 , L 2 and L 3 according to formula (5). If P c ≥ P t , the optimal solution
Figure GDA0002364015930000041
Otherwise, calculate the optimal solution according to formula (6)
Figure GDA0002364015930000042
Similarly, the optimal solution
Figure GDA0002364015930000043
and
Figure GDA0002364015930000044
It can be obtained by judging L 2 (t) and L 3 (t), 1≤t≤M×N, M and N are the length and width of the plaintext image I, respectively,

Figure GDA0002364015930000045
Figure GDA0002364015930000045

Figure GDA0002364015930000046
Figure GDA0002364015930000046

b.令t＝t+1,并返回a步骤，直到t＝M×N，最终得到用于图像的置乱操作的三个最优序列

Figure GDA0002364015930000047
和
Figure GDA0002364015930000048
b. Let t=t+1, and return to step a until t=M×N, and finally get three optimal sequences for image scrambling operations
Figure GDA0002364015930000047
and
Figure GDA0002364015930000048

最后执行基于模拟退火算法的图像置乱操作，根据最优序列

Figure GDA0002364015930000049
和
Figure GDA00023640159300000410
对交叉序列I”R、I”G和I”B如公式(7)所示的列置乱，得到置乱序列
Figure GDA00023640159300000411
和
Figure GDA00023640159300000412
1≤i≤M×N：Finally, the image scrambling operation based on the simulated annealing algorithm is performed, and according to the optimal sequence
Figure GDA0002364015930000049
and
Figure GDA00023640159300000410
Scramble the columns of the cross sequences I" R , I" G and I" B as shown in formula (7) to obtain a scrambled sequence
Figure GDA00023640159300000411
and
Figure GDA00023640159300000412
1≤i≤M×N:

Figure GDA00023640159300000413
Figure GDA00023640159300000413

所述步骤4)的过程为：The process of described step 4) is:

将明文和置乱图像视为一个整体来计算其适应度，如公式(8)所示，其中，F表示适应度函数，Im g表示明文或置乱图像矩阵，通过公式(8)可以得到明文图像各层IR、IG、IB和置乱图像

Figure GDA00023640159300000414
和
Figure GDA00023640159300000415
的适应度值FR2、FG2、FB2的适应度值FR1、FG1、FB1，Take the plaintext and scrambled image as a whole to calculate its fitness, as shown in formula (8), where F represents the fitness function, Im g represents the plaintext or scrambled image matrix, and the plaintext can be obtained by formula (8) Image layers IR, IG , IB and scrambled images
Figure GDA00023640159300000414
and
Figure GDA00023640159300000415
The fitness values F R2 , F G2 , and F B2 of the fitness values F R1 , F G1 , and F B1 ,

Figure GDA00023640159300000416
Figure GDA00023640159300000416

然后，依据明文图像和置乱图像的适应度来判断是否执行变异操作，如果(FR1+FG1+FB1)×En1>(FR2+FG2+FB2)×En2，En1和En2为明文图像和置乱图像的信息熵，则重新选择参数x'1、y'1、z'1和x'2、y'2、z'2并返回步骤1)重新选择、交叉和置乱图像，否则由公式(9)计算混沌系统的初始值x3(1)、y3(1)、z3(1)并迭代混沌系统获得混沌序列x3、y3和z3，然后依据公式(10)对混沌系统进行量化处理得到整数序列X3、Y3和Z3，Then, according to the fitness of the plaintext image and the scrambled image, it is judged whether to perform the mutation operation. If (F R1 +F G1 +F B1 )×En 1 >(F R2 +F G2 +F B2 )×En 2 , En 1 and En 2 is the information entropy of the plaintext image and the scrambled image, then reselect the parameters x' 1 , y' 1 , z' 1 and x' 2 , y' 2 , z' 2 and return to step 1) reselect, cross and the scrambled image, otherwise calculate the initial values x 3 (1), y 3 (1), z 3 (1) of the chaotic system by formula (9) and iterate the chaotic system to obtain the chaotic sequence x 3 , y 3 and z 3 , Then quantize the chaotic system according to formula (10) to obtain integer sequences X 3 , Y 3 and Z 3 ,

Figure GDA0002364015930000051
Figure GDA0002364015930000051

Figure GDA0002364015930000052
Figure GDA0002364015930000052

所述步骤5)的过程为：The process of described step 5) is:

将置乱序列

Figure GDA0002364015930000053
和
Figure GDA0002364015930000054
执行如公式(11)变异操作，其中变异序列的初始值ER(1)、EG(1)和EB(1)如公式(12)表示，最后，将变异序列ER、EG和EB合并获得最终加密图像E，will scramble the sequence
Figure GDA0002364015930000053
and
Figure GDA0002364015930000054
Perform the mutation operation as in formula (11), where the initial values ER (1), EG (1) and EB (1) of the mutated sequence are expressed as in formula (12), and finally, the mutated sequence ER , EG and E and B are merged to obtain the final encrypted image E,

Figure GDA0002364015930000055
Figure GDA0002364015930000055

Figure GDA0002364015930000056
Figure GDA0002364015930000056

本技术方案的有益效果体现在：The beneficial effects of this technical solution are reflected in:

1)混沌系统的初始值分别由明文图像I的MD5哈希值和明文和置乱图像的适应度生成，它们是交叉和选择、置乱和变异过程中的重要组成部分，因此加密图像非常依赖明文图像I，并且对抵抗已知攻击和选择明文攻击是安全的；1) The initial value of the chaotic system is generated by the MD5 hash value of the plaintext image I and the fitness of the plaintext and scrambled images, respectively. They are an important part in the process of crossover and selection, scrambling and mutation, so encrypted images are very dependent on plaintext image I, and is secure against known attacks and chosen-plaintext attacks;

2)本技术方案对明文图像I进行选择和交叉操作，然后利用模拟退火算法生成的最优序列对图像进行置乱，通过这三个操作可以使置乱图像的直方图达到均衡，从而可以抵抗统计攻击；2) This technical solution selects and crosses the plaintext image I, and then uses the optimal sequence generated by the simulated annealing algorithm to scramble the image. Through these three operations, the histogram of the scrambled image can be balanced, so that it can resist statistical attack;

3)为了增强图像各层的相关性，本技术方案利用彩色图像交互的方法对置乱图像进行交互式变异操作，该操作由明文图像I和置乱图像的适应度来进行判断是否执行；3) in order to enhance the correlation of each layer of the image, this technical scheme utilizes the method of color image interaction to carry out an interactive mutation operation on the scrambled image, and this operation is judged by the fitness of the plaintext image I and the scrambled image whether to execute;

4)相比传统的“置乱-扩散”加密框架相比，本技术方案不仅可以增加加密系统的复杂度，而且可以增强加密算法对明文图像I的敏感性。4) Compared with the traditional "scrambling-diffusion" encryption framework, the technical solution can not only increase the complexity of the encryption system, but also enhance the sensitivity of the encryption algorithm to the plaintext image I.

本技术方案的加密方法具有大密钥空间、高安全性和对明文图像的高敏感性，因此可以抵抗常见的图像攻击。The encryption method of the technical solution has large key space, high security and high sensitivity to plaintext images, so it can resist common image attacks.

这种方法能增强图像信息的安全性，提高加密处理的效率，能增强图像的鲁棒性，这种方法安全性高，可以抵抗常见图像攻击。This method can enhance the security of image information, improve the efficiency of encryption processing, and enhance the robustness of images. This method has high security and can resist common image attacks.

附图说明Description of drawings

图1为实施例方法的流程示意图；1 is a schematic flowchart of an embodiment method;

图2为实施例中选择交叉过程示意图。FIG. 2 is a schematic diagram of a selection crossover process in an embodiment.

具体实施方式Detailed ways

下面结合附图和实施例对本发明内容作进一步的阐述，但不是对本发明的限定。The content of the present invention will be further described below with reference to the accompanying drawings and embodiments, but it is not intended to limit the present invention.

实施例：Example:

参照图1，一种基于遗传模拟退火算法和混沌映射的彩色图像加密方法，包括如下步骤：1)生成整数序列：将明文图像I作为MD5哈希的输入生成与明文相关的密钥，并作为混沌系统的初始值，依据混沌系统初始值迭代生成混沌序列并对其执行量化操作，生成六条整数混沌序列X1、Y1、Z1、X2、Y2和Z2；Referring to Fig. 1, a kind of color image encryption method based on genetic simulated annealing algorithm and chaotic mapping, comprises the steps: 1) generate integer sequence: use plaintext image I as the input of MD5 hash to generate the key relevant to plaintext, and as The initial value of the chaotic system, iteratively generates the chaotic sequence according to the initial value of the chaotic system and performs quantization operations on it, and generates six integer chaotic sequences X 1 , Y 1 , Z 1 , X 2 , Y 2 and Z 2 ;

2)对明文图像I中的R、G、B三层进行选择和交叉操作：对步骤1)得到的整数序列X1、Y1、Z1和明文图像I中的R、G、B三层进行二进制位平面分解产生8个位平面并重新组成一维向量，生成混沌二进制位序列，然后设置混沌二进制序列为掩码，通过掩码中“0”和“1”来选择和交叉明文图像I，最后再将选择和交叉操作后的二进制图像序列恢复到像素级，生成交叉序列；2) Select and cross the three layers of R, G, and B in the plaintext image I: perform the integer sequence X 1 , Y 1 , Z 1 obtained in step 1) and the three layers of R, G, and B in the plaintext image I Perform binary bit plane decomposition to generate 8 bit planes and recompose a one-dimensional vector to generate a chaotic binary bit sequence, then set the chaotic binary sequence as a mask, and select and cross the plaintext image I through the "0" and "1" in the mask , and finally restore the binary image sequence after selection and cross operation to the pixel level to generate a cross sequence;

3)对交叉序列各层执行基于模拟退火算法的置乱操作：设明文图像I的长和宽分别为M和N，首先对步骤1)生成的三条整数混沌序列X2、Y2和Z2相互进行减法操作得到大小为M×N的目标函数序列L1、L2和L3，然后判断目标函数序列：如果L1(t)≥0，则最优解

Figure GDA0002364015930000061
其中t为每个目标函数序列的索引，并且1≤t≤M×N；否则计算当前目标函数序列L1、L2和L3的阈值Pc和概率Pt，如果Pc≥Pt，则最优解
Figure GDA0002364015930000062
否则计算最优解
Figure GDA0002364015930000063
同理，最优解
Figure GDA0002364015930000064
和
Figure GDA0002364015930000065
可以由判断L2(t)与L3(t)获得，根据最优序列
Figure GDA0002364015930000071
和
Figure GDA0002364015930000072
对交叉序列I”R、I”G和I”B执行列置乱操作，得到置乱序列；3) Perform the scramble operation based on simulated annealing algorithm on each layer of the cross sequence: set the length and width of the plaintext image I to be M and N respectively, firstly perform the three integer chaotic sequences X 2 , Y 2 and Z 2 generated in step 1). Subtract each other to obtain the objective function sequence L 1 , L 2 and L 3 of size M×N, and then judge the objective function sequence: if L 1 (t)≥0, then the optimal solution
Figure GDA0002364015930000061
where t is the index of each objective function sequence, and 1≤t≤M×N; otherwise, the threshold P c and probability P t of the current objective function sequence L 1 , L 2 and L 3 are calculated, if P c ≥ P t , the optimal solution
Figure GDA0002364015930000062
Otherwise calculate the optimal solution
Figure GDA0002364015930000063
Similarly, the optimal solution
Figure GDA0002364015930000064
and
Figure GDA0002364015930000065
It can be obtained by judging L 2 (t) and L 3 (t), according to the optimal sequence
Figure GDA0002364015930000071
and
Figure GDA0002364015930000072
Perform a column scrambling operation on the cross sequence I" R , I" G and I" B to obtain a scrambling sequence;

4)判断是否执行变异操作：计算明文图像I和置乱图像各层的适应度，并通过明文图像I和置乱图像的适应度来判断是否执行变异操作，如果明文图像I的适应度大于置乱图像的适应度，则重新选择参数生成混沌序列并重新执行选择、交叉和置乱操作；否则根据置乱图像的适应度计算混沌系统的初始值并迭代混沌系统获得混沌序列，并对混沌系统进行量化处理得到整数序列；4) Determine whether to perform mutation operation: calculate the fitness of each layer of plaintext image I and scrambled image, and judge whether to perform mutation operation by the fitness of plaintext image I and scrambled image, if the fitness of plaintext image I is greater than If the fitness of the chaotic image is determined, the parameters are reselected to generate the chaotic sequence and the selection, crossover and scrambling operations are performed again; otherwise, the initial value of the chaotic system is calculated according to the fitness of the scrambled image, and the chaotic system is iterated to obtain the chaotic sequence, and the chaotic system is Perform quantization processing to obtain an integer sequence;

5)获得最终加密图像E：为了增强图像各层的相关性，将各层置乱序列执行交互式变异操作并将变异序列合并获得最终加密图像E。5) Obtain the final encrypted image E: In order to enhance the correlation of each layer of the image, perform an interactive mutation operation on the scrambled sequences of each layer and combine the mutated sequences to obtain the final encrypted image E.

所述步骤1)的过程为：The process of described step 1) is:

将明文图像I作为MD5哈希的输入，并把MD5哈希生成的128位密钥H分成32个子密钥，每个块的长度是4位，如公式(1)所示：The plaintext image I is used as the input of the MD5 hash, and the 128-bit key H generated by the MD5 hash is divided into 32 sub-keys, and the length of each block is 4 bits, as shown in formula (1):

H＝h1,h2,h3,...,h32 (1)，H=h 1 , h 2 , h 3 ,...,h 32 (1),

然后，定义x'1、y'1、z'1和x'2、y'2、z'2的值，因此混沌系统的初始值x1(1)、y1(1)、z1(1)和x2(1)、y2(1)、z2(1)可以由公式(2)得到，依据混沌系统初始值迭代生成两组混沌序列x1、y1、z1和x2、y2、z2，并对其执行量化操作得到整数序列X1、Y1、Z1和X2、Y2、Z2，如公式(3)所示：Then, define the values of x' 1 , y' 1 , z' 1 and x' 2 , y' 2 , z' 2 , so the initial values of the chaotic system x 1 (1), y 1 (1), z 1 ( 1) and x 2 (1), y 2 (1), z 2 (1) can be obtained from formula (2), and iteratively generates two sets of chaotic sequences x 1 , y 1 , z 1 and x 2 according to the initial value of the chaotic system , y 2 , z 2 , and perform quantization operations on them to obtain integer sequences X 1 , Y 1 , Z 1 and X 2 , Y 2 , Z 2 , as shown in formula (3):

Figure GDA0002364015930000073
Figure GDA0002364015930000073

Figure GDA0002364015930000074
Figure GDA0002364015930000074

参照图2，所述步骤2)的过程为：Referring to Fig. 2, the process of described step 2) is:

对整数序列X1、Y1、Z1和明文图像各层IR、IG、IB进行二进制位平面分解产生8个位平面并重新组成一维向量，生成二进制位序列，然后设置混沌二进制序列为掩码，通过掩码中“0”和“1”来选择和交叉图像，如果掩码值是“1”，则保持图像的位不变；否则翻转该图像的位来获得新的位，最后再将选择和交叉操作后的二进制图像序列恢复到像素级，生成交叉序列I”R、I”G和I”B。Perform binary bit plane decomposition on the integer sequence X 1 , Y 1 , Z 1 and each layer IR , IG , IB of the plaintext image to generate 8 bit planes and reconstitute a one-dimensional vector to generate a binary bit sequence, and then set the chaotic binary The sequence is a mask, and the image is selected and intersected by "0" and "1" in the mask. If the mask value is "1", the bits of the image are kept unchanged; otherwise, the bits of the image are flipped to obtain new bits , and finally restore the binary image sequence after selection and cross operation to the pixel level to generate cross sequences I" R , I" G and I" B .

所述步骤3)的过程为：The process of described step 3) is:

采用模拟退火算法设计最优伪随机序列对交叉图像进行置乱操作来获得置乱图像，基于模拟退火算法的图像置乱步骤如下：The simulated annealing algorithm is used to design the optimal pseudo-random sequence to scramble the crossed image to obtain the scrambled image. The image scrambling steps based on the simulated annealing algorithm are as follows:

首先产生目标函数序列，根据步骤1)生成的三条整数混沌序列X2、Y2和Z2相互进行减法操作得到大小为M×N的目标函数序列L1、L2和L3，其中t为每个目标函数序列的索引，并且1≤t≤M×N：First, the objective function sequence is generated, and the three integer chaotic sequences X 2 , Y 2 and Z 2 generated in step 1) are mutually subtracted to obtain the objective function sequences L 1 , L 2 and L 3 of size M×N, where t is The index of each objective function sequence, and 1≤t≤M×N:

Figure GDA0002364015930000081
Figure GDA0002364015930000081

然后判断目标函数，令t＝1，执行以下操作：Then judge the objective function, let t=1, and perform the following operations:

a.可如果如果L1(t)≥0，则最优解

Figure GDA0002364015930000082
否则依据公式(5)计算当前目标函数序列L1、L2和L3的阈值Pc和概率Pt，如果Pc≥Pt，则最优解
Figure GDA0002364015930000083
否则依据公式(6)计算最优解
Figure GDA0002364015930000084
同理，最优解
Figure GDA0002364015930000085
和
Figure GDA0002364015930000086
可以由判断L2(t)与L3(t)获得，1≤t≤M×N，M和N分别为明文图像I的长和宽，a. If L 1 (t) ≥ 0, then the optimal solution
Figure GDA0002364015930000082
Otherwise, calculate the threshold P c and probability P t of the current objective function sequence L 1 , L 2 and L 3 according to formula (5). If P c ≥ P t , the optimal solution
Figure GDA0002364015930000083
Otherwise, calculate the optimal solution according to formula (6)
Figure GDA0002364015930000084
Similarly, the optimal solution
Figure GDA0002364015930000085
and
Figure GDA0002364015930000086
It can be obtained by judging L 2 (t) and L 3 (t), 1≤t≤M×N, M and N are the length and width of the plaintext image I, respectively,

Figure GDA0002364015930000087
Figure GDA0002364015930000087

Figure GDA0002364015930000088
Figure GDA0002364015930000088

b.令t＝t+1,并返回a步骤，直到t＝M×N，最终得到用于图像的置乱操作的三个最优序列

Figure GDA0002364015930000089
和
Figure GDA00023640159300000810
b. Let t=t+1, and return to step a until t=M×N, and finally get three optimal sequences for image scrambling operations
Figure GDA0002364015930000089
and
Figure GDA00023640159300000810

最后执行基于模拟退火算法的图像置乱操作，根据最优序列

Figure GDA0002364015930000091
和
Figure GDA0002364015930000092
对交叉序列I”R、I”G和I”B如公式(7)所示的列置乱，得到置乱序列
Figure GDA0002364015930000093
和
Figure GDA0002364015930000094
1≤i≤M×N：Finally, the image scrambling operation based on the simulated annealing algorithm is performed, and according to the optimal sequence
Figure GDA0002364015930000091
and
Figure GDA0002364015930000092
Scramble the columns of the cross sequences I" R , I" G and I" B as shown in formula (7) to obtain a scrambled sequence
Figure GDA0002364015930000093
and
Figure GDA0002364015930000094
1≤i≤M×N:

Figure GDA0002364015930000095
Figure GDA0002364015930000095

所述步骤4)的过程为：The process of described step 4) is:

将明文和置乱图像视为一个整体来计算其适应度，如公式(8)所示，其中，F表示适应度函数，Img表示明文或置乱图像矩阵，通过公式(8)可以得到明文图像各层IR、IG、IB和置乱图像

Figure GDA0002364015930000096
和
Figure GDA0002364015930000097
的适应度值FR2、FG2、FB2的适应度值FR1、FG1、FB1，Consider the plaintext and scrambled image as a whole to calculate its fitness, as shown in formula (8), where F represents the fitness function, Img represents the plaintext or scrambled image matrix, and the plaintext image can be obtained by formula (8). Layers IR, IG , IB and scrambled images
Figure GDA0002364015930000096
and
Figure GDA0002364015930000097
The fitness values F R2 , F G2 , and F B2 of the fitness values F R1 , F G1 , and F B1 ,

Figure GDA0002364015930000098
Figure GDA0002364015930000098

然后，依据明文图像和置乱图像的适应度来判断是否执行变异操作，如果(FR1+FG1+FB1)×En1>(FR2+FG2+FB2)×En2，En1和En2为明文图像I和置乱图像的信息熵，则重新选择参数x'1、y'1、z'1和x'2、y'2、z'2并返回步骤1)重新选择、交叉和置乱图像，否则由公式(9)计算混沌系统的初始值x3(1)、y3(1)、z3(1)并迭代混沌系统获得混沌序列x3、y3和z3，然后依据公式(10)对混沌系统进行量化处理得到整数序列X3、Y3和Z3，Then, according to the fitness of the plaintext image and the scrambled image, it is judged whether to perform the mutation operation. If (F R1 +F G1 +F B1 )×En 1 >(F R2 +F G2 +F B2 )×En 2 , En 1 and En 2 is the information entropy of the plaintext image I and the scrambled image, then reselect the parameters x' 1 , y' 1 , z' 1 and x' 2 , y' 2 , z' 2 and return to step 1) to reselect, Cross and scramble the image, otherwise calculate the initial values x 3 (1), y 3 (1), z 3 (1) of the chaotic system by formula (9) and iterate the chaotic system to obtain the chaotic sequence x 3 , y 3 and z 3 , and then quantize the chaotic system according to formula (10) to obtain integer sequences X 3 , Y 3 and Z 3 ,

Figure GDA0002364015930000099
Figure GDA0002364015930000099

Figure GDA00023640159300000910
Figure GDA00023640159300000910

所述步骤5)的过程为：The process of described step 5) is:

将置乱序列

Figure GDA00023640159300000911
和
Figure GDA00023640159300000912
执行如公式(11)变异操作，其中变异序列的初始值ER(1)、EG(1)和EB(1)如公式(12)表示，最后，将变异序列ER,、EG和EB合并获得最终加密图像E，will scramble the sequence
Figure GDA00023640159300000911
and
Figure GDA00023640159300000912
Perform the mutation operation as in formula (11), in which the initial values of the mutated sequence ER (1), EG (1) and EB (1) are expressed as formula (12), and finally, the mutated sequence ER , EG Merge with E B to obtain the final encrypted image E,

Figure GDA0002364015930000101
Figure GDA0002364015930000101

Figure GDA0002364015930000102
Figure GDA0002364015930000102

Claims (6)

1. a color image encryption method based on a genetic simulation annealing algorithm and chaotic mapping is characterized by comprising the following steps:
1) generating an integer sequence: generating a key related to a plaintext by taking a plaintext image I as the input of MD5 Hash, taking the key as an initial value of the chaotic system, iteratively generating a chaotic sequence according to the initial value of the chaotic system and performing quantization operation on the chaotic sequence to generate six integer chaotic sequences X1、Y1、Z1、X2、Y2And Z2；
2) The selection and interleaving operations are performed on the R, G, B three layers in the plaintext image I: for the integer sequence X obtained in the step 1)1、Y1、Z1Decomposing binary bit planes with R, G, B layers in the plaintext image I to generate 8 bit planes, recombining the bit planes into one-dimensional vectors, generating a chaotic binary bit sequence, setting the chaotic binary bit sequence as a mask, selecting and crossing the plaintext image I through '0' and '1' in the mask, and finally restoring the binary image sequence after the selection and crossing operation to a pixel level to generate a crossing sequence;
3) scrambling operation based on a simulated annealing algorithm is carried out on each layer of the cross sequence: setting the length and width of a plaintext image I as M and N respectively, firstly, generating three integer chaotic sequences X in the step 1)2、Y2And Z2Mutually subtracting to obtain an objective function sequence L with the size of M multiplied by N1、L2And L3Then, judging the target function sequence: if L is1(t) is greater than or equal to 0, the optimal solution
Figure FDA0002363979680000011
Wherein t is the index of each target function sequence, and t is more than or equal to 1 and less than or equal to M multiplied by N; otherwise, calculating the current target function sequence L1、L2And L3Is a threshold value PcAnd probability PtIf P isc≥PtThen the optimal solution
Figure FDA0002363979680000012
Otherwise, calculating the optimal solution
Figure FDA0002363979680000013
By the same token, the optimal solution
Figure FDA0002363979680000014
And
Figure FDA0002363979680000015
can be judged by2(t) and L3(t) obtaining, according to the optimal sequence
Figure FDA0002363979680000016
And
Figure FDA0002363979680000017
for cross sequence I "R、I”GAnd I "BExecuting a column scrambling operation to obtain a scrambling sequence;
4) judging whether to execute mutation operation: calculating the fitness of each layer of the plaintext image I and the scrambled image, judging whether to execute mutation operation or not according to the fitness of the plaintext image I and the scrambled image, and if the fitness of the plaintext image I is greater than the fitness of the scrambled image, reselecting the parameters to generate a chaotic sequence and re-executing selection, crossing and scrambling operations; otherwise, calculating an initial value of the chaotic system according to the fitness of the scrambled image, iterating the chaotic system to obtain a chaotic sequence, and carrying out quantization processing on the chaotic system to obtain an integer sequence;
5) obtaining a final encrypted image E: and (4) performing interactive mutation operation on each scrambling sequence and merging the mutation sequences to obtain a final encrypted image E.
2. The color image encryption method based on the genetic simulated annealing algorithm and the chaotic mapping according to claim 1, wherein the process of the step 1) is as follows:
the plaintext image I is taken as an input of MD5 hash, and the 128-bit key H generated by MD5 hash is divided into 32 subkeys, each block being 4 bits in length, as shown in equation (1):
H＝h1,h2,h3,...,h32(1)，
then, define x'1、y′1、z′1And x'2、y'2、z'2Of the chaotic system, thus the initial value x of the chaotic system1(1)、y1(1)、z1(1) And x2(1)、y2(1)、z2(1) Can be obtained by formula (2), and two groups of chaotic sequences x are generated according to the initial value iteration of the chaotic system1、y1、z1And x2、y2、z2And performing a quantization operation thereon to obtain a sequence of integers X1、Y1、Z1And X2、Y2、Z2As shown in equation (3):
Figure FDA0002363979680000021
Figure FDA0002363979680000022
3. the color image encryption method based on the genetic simulated annealing algorithm and the chaotic mapping according to claim 1, wherein the process of the step 2) is as follows:
for integer sequence X1、Y1、Z1And layers I of plaintext image IR、IG、IBPerforming binary bit plane decomposition to generate 8 bit planes and recombining the bit planes into a one-dimensional vector to generate a binary bit sequence, then setting the chaotic binary sequence as a mask, selecting and crossing images through '0' and '1' in the mask, and if the mask value is '1', keeping the bits of the images unchanged; otherwise, the bit of the image is turned over to obtain a new bit, and finally the binary image sequence after the selection and the cross operation is restored to the pixel level to generate a cross sequence I'R、I”GAnd I "B。
4. The color image encryption method based on the genetic simulated annealing algorithm and the chaotic mapping according to claim 1, wherein the process of the step 3) is as follows:
adopting a simulated annealing algorithm to design an optimal pseudo-random sequence to carry out scrambling operation on the crossed images to obtain scrambled images, wherein the image scrambling step based on the simulated annealing algorithm is as follows:
firstly, generating an objective function sequence according to three integer chaotic sequences X generated in the step 1)2、Y2And Z2Mutually subtracting to obtain an objective function sequence L with the size of M multiplied by N1、L2And L3，Where t is the index of each sequence of objective functionsAnd t is more than or equal to 1 and less than or equal to M multiplied by N:
Figure FDA0002363979680000031
then, judging the target function, and making t equal to 1, executing the following operations:
a. can be if L1(t) is greater than or equal to 0, the optimal solution
Figure FDA0002363979680000032
Otherwise, calculating the current target function sequence L according to the formula (5)1、L2And L3Is a threshold value PcAnd probability PtIf P isc≥PtThen the optimal solution
Figure FDA0002363979680000033
Otherwise, calculating the optimal solution according to the formula (6)
Figure FDA0002363979680000034
By the same token, the optimal solution
Figure FDA0002363979680000035
And
Figure FDA0002363979680000036
can be judged by2(t) and L3(t) obtaining that t is more than or equal to 1 and less than or equal to M multiplied by N, M and N are respectively the length and the width of the plaintext image I,
Figure FDA0002363979680000037
Figure FDA0002363979680000038
b. let t be t +1 and return to step a until t be M × N, finally obtaining three optimal sequences for scrambling operation of image
Figure FDA0002363979680000039
Figure FDA00023639796800000310
And
Figure FDA00023639796800000311
finally, image scrambling operation based on simulated annealing algorithm is executed according to the optimal sequence
Figure FDA00023639796800000312
And
Figure FDA00023639796800000313
for cross sequence I "R、I”GAnd I "BThe column scrambling as shown in equation (7) is performed to obtain a scrambled sequence
Figure FDA00023639796800000314
And
Figure FDA00023639796800000315
1≤i≤M×N：
Figure FDA00023639796800000316
5. the color image encryption method based on the genetic simulated annealing algorithm and the chaotic mapping according to claim 1, wherein the process of the step 4) is as follows:
calculating the fitness of the plaintext image I by regarding the plaintext image and the scrambled image as a whole, as shown in formula (8), wherein F represents a fitness function, Img represents a plaintext or scrambled image matrix, and each layer I of the plaintext image I can be obtained through formula (8)R、IG、IBAnd scrambling the image
Figure FDA00023639796800000317
And
Figure FDA00023639796800000318
fitness value FR2、FG2、FB2Fitness value FR1、FG1、FB1，
Figure FDA00023639796800000319
Then, judging whether to execute mutation operation according to the fitness of the plaintext image I and the scrambled image, if (F)R1+FG1+FB1)×En1>(FR2+FG2+FB2)×En2，En1And En2For the entropy of the information of the plaintext image I and the scrambled image, the parameter x 'is reselected'1、y′1、z′1And x'2、y'2、z'2And returning to the step 1) to reselect, cross and scramble the image, otherwise, calculating the initial value x of the chaotic system by the formula (9)3(1)、y3(1)、z3(1) And iteration chaotic system obtains chaotic sequence x3、y3And z3Then, the chaotic system is quantized according to the formula (10) to obtain an integer sequence X3、Y3And Z3，
Figure FDA0002363979680000041
Figure FDA0002363979680000042
6. The color image encryption method based on the genetic simulated annealing algorithm and the chaotic mapping according to claim 1, wherein the process of the step 5) is as follows:
will scramble the sequence
Figure FDA0002363979680000043
And
Figure FDA0002363979680000044
performing mutation operation as shown in formula (11), wherein the initial value E of the mutated sequenceR(1)、EG(1) And EB(1) Finally, the variant sequence E is determined as shown in formula (12)R、EGAnd EBThe final encrypted image E is obtained by merging,
Figure FDA0002363979680000045
Figure FDA0002363979680000046
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