CN112737765A - Image encryption algorithm based on memristor chaotic neural network and improved Logistic chaotic mapping - Google Patents

Image encryption algorithm based on memristor chaotic neural network and improved Logistic chaotic mapping Download PDF

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CN112737765A
CN112737765A CN202110148355.5A CN202110148355A CN112737765A CN 112737765 A CN112737765 A CN 112737765A CN 202110148355 A CN202110148355 A CN 202110148355A CN 112737765 A CN112737765 A CN 112737765A
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李涵
葛斌
刘威
蔡威林
邰悦
陈壮
张延�
张宁
王婷
吴彩
彭曦晨
代高乐
沐李亭
宦立鑫
周衍庆
袁政
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Anhui University of Science and Technology
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Abstract

The invention relates to an image encryption algorithm based on a memristor chaotic neural network and improved Logistic chaotic mapping. According to the updated weight value of the chaotic neural network, the method introduces an exponential function exThe novel one-dimensional Logistic chaotic mapping is assigned, and the range of the chaotic random sequence value is adjusted to the range requirement met in different encryption stages through a nonlinear method; and performing pixel-level and bit-level scrambling operations on the plaintext by adopting a sorting algorithm on the corresponding replacement number group of the chaotic sequence, and finally performing two forward and reverse diffusion operations on the intermediate ciphertext by using two different groups of chaotic sequences to complete final encryption. Experiments show thatThe obtained chaotic sequence has good randomness, and the obtained ciphertext image can resist typical attacks, thereby achieving the effect of safe communication.

Description

Image encryption algorithm based on memristor chaotic neural network and improved Logistic chaotic mapping
Technical Field
The invention relates to the technical field of encryption, in particular to an image encryption algorithm based on a memristor chaotic neural network and improved Logistic chaotic mapping.
Background
With the development of computer network technology, images are widely used as an information carrier. However, due to the characteristics of large information amount and high redundancy, the security of the system also becomes a more and more concern of people. Because the traditional encryption algorithms, such as AES, DES, etc., for encrypting texts, have been completely unable to meet the requirements for encrypting images.
With the introduction of the chaos concept, the characteristics of the chaos mapping function such as sensitivity to initial values, pseudo-randomness, non-periodicity and the like are widely applied to the use of a random sequence generator. In recent years, the development of chaotic random sequences has led researchers to research chaotic encryption algorithms, and the randomness requirement of image encryption algorithms on key sequences makes chaotic mapping a new technology of encryption algorithms.
Disclosure of Invention
The invention aims to provide an image encryption algorithm based on a memristor chaotic neural network and improved Logistic chaotic mapping; the encryption system uses the weight value updated after the neural network convolves the plaintext image as the initial value of the chaotic system, improves the defect of one-dimensional chaotic mapping, performs double scrambling on pixels, and improves the safety of the encryption algorithm.
The invention adopts the following technical scheme for realizing the purpose:
in order to achieve the purpose, the technical scheme adopted by the invention is that the encryption steps of a double scrambling image encryption algorithm based on a memristor chaotic neural network and improved Logistic chaotic mapping are detailed as follows:
step 1: and completing feature extraction of the input image by the chaotic neural network based on the memristor, and obtaining the updated weight of the full connection layer as a key value of an image encryption algorithm.
Step 2: and the key value is used as an initial value of the improved Logistic chaotic mapping to generate a chaotic random sequence required in the encryption algorithm process.
And step 3: and respectively carrying out pixel level scrambling, bit level scrambling and diffusion stages in the encryption algorithm process by using the chaotic random sequence to finish image encryption.
1. Preferably, the memristor-based chaotic neural network provided by the invention derives a memristor equation according to voltage and current flowing through the memristor, and the resistance value m (t) of the memristor can be expressed as:
Figure BDA0002931102280000021
according to the characteristics of the memristor, when a small voltage can generate a large electric field, a chaotic field is generated, a Jokularr window function is selected to model the doping drift in the memristor device structure, and the nonlinear characteristic of the memristor is strongest when p is 1, which is expressed as:
f(x)＝4x-4x2 (2)
according to the relation between the memristance M (t) and the memristor conductance G (t), after differentiating the time t, an equation about the point-to-point change rate is obtained:
Figure BDA0002931102280000022
replacing the updated weight value delta w of the neural network with delta G, and combining the memristor and the Chebyshev chaotic polynomial as an activation function of a full connection layer of the convolutional neural network to enable the neural network to be converged quickly, so that the learning efficiency of the neural network is improved;
2. preferably, the improved Logistic chaotic map provided by the invention is improved by introducing an exponential function, as shown in formula (4), so that the randomness of the chaotic map is stronger, and the safety of an encryption algorithm is improved;
Figure BDA0002931102280000023
3. preferably, the double scrambling encryption algorithm provided by the invention comprises the following specific steps:
step 1: scanning a plaintext image into a one-dimensional plaintext pixel array P;
step 2: in the scrambling stage of the image, a key is used for generating a chaotic random sequence, the chaotic random sequence is sequenced through a sort function to obtain an index array, and pixel-level scrambling is carried out on a plaintext P according to the index array to obtain a scrambled sequence P';
and step 3: using the same method in the step 2, carrying out bit-level scrambling on the scrambled sequence P' to complete double scrambling to obtain a sequence A;
and 4, step 4: in the diffusion stage, mod and xor operators are used, a ciphertext feedback mechanism is introduced, two rounds of forward and reverse opposite diffusion are carried out on the scrambled image, the process is shown as follows, the image encryption is finally completed, and an encrypted image D2 is obtained;
(1) first round diffusion encryption
When the first round of diffusion encryption is carried out, a result A (l) after bit level scrambling is introduced and is used as the input of the first round of diffusion;
when l is equal to 1, the ratio of the total of the two,
Figure BDA0002931102280000031
when L is more than 1 and less than or equal to L,
Figure BDA0002931102280000032
(2) second round of diffusion
At the second round of diffusion, the result of the first round of diffusion D1(l) is introduced as input to the second round of diffusion;
when L is equal to L, the compound is,
Figure BDA0002931102280000033
when L is more than or equal to 1 and less than or equal to L,
Figure BDA0002931102280000034
has the advantages that:
compared with the prior art, the invention has the beneficial effects that:
(1) the update weight of the memristor-based chaotic neural network is used as a key of an encryption algorithm, the convergence speed of the neural network is considered, and the weights obtained according to different images have differences, so that the encryption algorithm is related to a plaintext;
(2) the chaotic mapping used by the method is the improved Logistic chaotic mapping, and the randomness and the sensitivity to the initial value are improved;
(3) the dual scrambling algorithm used by the invention enables scrambling to change the position of the pixel and the pixel value; the two rounds of diffusion algorithms with opposite forward and reverse directions ensure higher security of the encryption algorithm;
drawings
The invention will be further described with reference to the accompanying drawings.
FIG. 1 is an image encryption flow diagram based on a memristor chaotic neural network and an improved Logistic chaotic map;
FIG. 2 is a diagram of a memristor device architecture;
FIG. 3 is a bifurcation diagram of an improved Logistic chaotic map;
FIG. 4 is an original image
FIG. 5 is an encrypted image
Detailed Description
The following detailed description of the embodiments of the present invention is provided in connection with the accompanying drawings and examples.
Fig. 1 is an encryption flow diagram of the method.
The adopted programming software is Matlab R2018b, and a gray image with the size of 256 multiplied by 256 shown in FIG. 4 is selected as an original image P. The detailed process of encrypting the original image by using the method is described as follows.
Step 1: and inputting a plaintext image and a secret key, and obtaining an updated weight value through a memristor chaotic neural network to be used as the secret key of an encryption algorithm.
Step 2: inputting a secret key, using improved Logistic chaotic mapping, and respectively passing through N0And after + l times of iteration, obtaining a random sequence with the same size as the plain text pixel array, sequencing the random sequence to obtain an index array, and finishing pixel level scrambling of the original image.
And step 3: and (3) finishing bit-level scrambling of the image by using the same method in the step (2) to obtain a scrambled image A.
And 4, step 4: the two rounds of forward and reverse diffusion algorithms on the scrambled array are completed by using the formulas (5-8), and a final image encrypted image D2 is obtained, as shown in FIG. 5.

Claims (4)

1.一种基于忆阻器混沌神经网络和改进Logistic混沌映射的图像加密算法，其特征在于：1. an image encryption algorithm based on memristor chaotic neural network and improved Logistic chaotic mapping, is characterized in that: 加密过程如下：The encryption process is as follows: 步骤1：基于忆阻器的混沌神经网络完成对输入图像的特征提取，获得全连接层的更新后权值，作为图像加密算法的密钥值；Step 1: The memristor-based chaotic neural network completes the feature extraction of the input image, and obtains the updated weight value of the fully connected layer as the key value of the image encryption algorithm; 步骤2：密钥值作为改进Logistic混沌映射的初始值，产生加密算法过程中所需要的混沌随机序列；Step 2: The key value is used as the initial value of the improved Logistic chaotic map to generate the chaotic random sequence required in the process of the encryption algorithm; 步骤3：使用混沌随机序列分别进行加密算法过程中的像素级置乱、bit级置乱以及扩散阶段，完成图像加密。Step 3: Use chaotic random sequences to perform pixel-level scrambling, bit-level scrambling, and diffusion stages in the encryption algorithm process to complete image encryption. 2.根据权利要求1所述的一种基于忆阻器的混沌神经网络，其特征在于：根据电压和流过忆阻的电流推导忆阻方程，忆阻的阻值M(t)可以表示为：2. a kind of memristor-based chaotic neural network according to claim 1, is characterized in that: according to the voltage and the current flowing through the memristor, the memristor equation is deduced, and the resistance value M(t) of the memristor can be expressed as :
Figure FDA0002931102270000011
Figure FDA0002931102270000011
 根据忆阻器的特点，当小电压能够产生大电场时，混沌现场便产生了，选择Jokular窗口函数对忆阻器器件结构中的掺杂漂移进行建模，且p＝1时忆阻器的非线性特性最强，表示为：According to the characteristics of the memristor, when a small voltage can generate a large electric field, a chaotic scene occurs. The Jokular window function is selected to model the doping drift in the memristor device structure, and when p=1, the memristor's doping drift is The nonlinear characteristic is the strongest, which is expressed as: f(x)＝4x-4x2 (2)f(x)=4x-4x 2 (2) 根据忆阻值M(t)和忆阻器电导G(t)的关系，对时间t进行微分后，得到关于点到变化率的方程：According to the relationship between the memristor value M(t) and the memristor conductance G(t), after differentiating the time t, the equation for the point-to-change rate is obtained:
Figure FDA0002931102270000012
Figure FDA0002931102270000012
 使用ΔG代替神经网络更新的权值Δw，将忆阻器与Chebyshev混沌多项式结合作为卷积神经网络全连接层的激活函数，使得神经网络快速收敛，从而提高神经网络的学习效率。ΔG is used to replace the weight Δw updated by the neural network, and the memristor and the Chebyshev chaotic polynomial are combined as the activation function of the fully connected layer of the convolutional neural network, which makes the neural network converge quickly, thereby improving the learning efficiency of the neural network. 3.根据权利要求1所述的一种改进的Logistic混沌映射，其特征在于：通过引入指数函数，对Logistic混沌映射进行改进，如式(4)，使得混沌映射的随机性更强，提高加密算法的安全性；3. a kind of improved Logistic chaotic mapping according to claim 1 is characterized in that: by introducing exponential function, Logistic chaotic mapping is improved, such as formula (4), makes the randomness of chaotic mapping stronger, improves encryption the security of the algorithm;
Figure FDA0002931102270000013
Figure FDA0002931102270000013
 4.根据权利要求1所述的一种双重置乱扩散加密算法，其特征在于：具体步骤如下：4. a kind of double reset random diffusion encryption algorithm according to claim 1, is characterized in that: concrete steps are as follows: 步骤1：将明文图像扫描成一维明文像素数组P；Step 1: Scan the plaintext image into a one-dimensional plaintext pixel array P; 步骤2：在图像的置乱阶段，使用密钥产生混沌随机序列，通过sort函数对混沌随机序列排序得到索引数组，并按照索引数组对明文P进行像素级置乱，获得置乱后序列P′；Step 2: In the scrambling phase of the image, use the key to generate a chaotic random sequence, sort the chaotic random sequence through the sort function to obtain an index array, and scramble the plaintext P at the pixel level according to the index array to obtain the scrambled sequence P' ; 步骤3：使用步骤2中相同的方法，对置乱后序列P′进行bit级的置乱，完成双重置乱，得到序列A；Step 3: Using the same method as in Step 2, perform bit-level scrambling on the scrambled sequence P' to complete double scramble to obtain sequence A; 步骤4：在扩散阶段，使用mod以及xor运算符，引入密文反馈机制，对置乱后的图像进行两轮正逆方向相反的扩散，过程如下所示，最终完成图像加密，获得加密后图像D2；Step 4: In the diffusion stage, the mod and xor operators are used, and the ciphertext feedback mechanism is introduced to perform two rounds of forward and reverse diffusion on the scrambled image. The process is as follows. Finally, the image encryption is completed and the encrypted image is obtained. D2; (1)第一轮扩散加密(1) The first round of diffusion encryption 在第一轮扩散加密时，引入bit级置乱后的结果A(l)，作为第一轮扩散的输入；In the first round of diffusion encryption, the result A(l) after bit-level scrambling is introduced as the input of the first round of diffusion; 当l＝1时，When l=1,
Figure FDA0002931102270000021
Figure FDA0002931102270000021
 当1＜l≤L时，When 1<l≤L,
Figure FDA0002931102270000022
Figure FDA0002931102270000022
 (2)第二轮扩散(2) The second round of diffusion 在第二轮扩散时，引入第一轮扩散的结果D1(l)，作为第二轮扩散的输入；In the second round of diffusion, the result D1(l) of the first round of diffusion is introduced as the input of the second round of diffusion; 当l＝L时，When l=L,
Figure FDA0002931102270000023
Figure FDA0002931102270000023
 当1≤l＜L时，When 1≤l<L,
Figure FDA0002931102270000024
Figure FDA0002931102270000024
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CN117114959A (en) * 2023-09-13 2023-11-24 山东青橙数字科技有限公司 An image encryption method based on the key feedback mechanism of multi-parameter one-dimensional chaotic system

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