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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chaotic
memristor
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image
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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. An image encryption algorithm based on a memristor chaotic neural network and improved Logistic chaotic mapping is characterized in that:
the encryption process is as follows:
step 1: completing feature extraction of an input image based on a chaotic neural network of a memristor, and obtaining an updated weight of a full connection layer as a key value of an image encryption algorithm;
step 2: the key value is used as an initial value of 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.
2. The memristor-based chaotic neural network according to claim 1, wherein: deducing a memristor equation according to the voltage and the current flowing through the memristor, wherein the resistance value M (t) of the memristor can be expressed as:
Figure FDA0002931102270000011
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 FDA0002931102270000012
and 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.
3. The improved Logistic chaotic map as claimed in claim 1, wherein: by introducing an exponential function, the Logistic chaotic mapping is improved, as shown in formula (4), so that the randomness of the chaotic mapping is stronger, and the safety of an encryption algorithm is improved;
Figure FDA0002931102270000013
4. a double scramble diffusion encryption algorithm according to claim 1, wherein: the method 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 FDA0002931102270000021
when L is more than 1 and less than or equal to L,
Figure FDA0002931102270000022
(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 FDA0002931102270000023
when L is more than or equal to 1 and less than L,
Figure FDA0002931102270000024
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Cited By (2)

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Publication number Priority date Publication date Assignee Title
CN114598782A (en) * 2022-04-01 2022-06-07 安徽大学 Image encryption method and system based on raspberry pi and memristor neural network
CN117114959A (en) * 2023-09-13 2023-11-24 山东青橙数字科技有限公司 Image encryption method based on key feedback mechanism of multi-parameter one-dimensional chaotic system

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CN109376540A (en) * 2018-09-11 2019-02-22 郑州轻工业学院 A kind of image encryption method based on Duffing mapping and genetic manipulation
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CN110766595A (en) * 2019-10-21 2020-02-07 中国石油大学(华东) Watermark encryption and decryption algorithm based on chaotic neural network
CN112084517A (en) * 2020-09-15 2020-12-15 郑州轻工业大学 Image encryption method based on chaotic mapping and bit-level permutation

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CN103227713A (en) * 2013-04-01 2013-07-31 杭州电子科技大学 Chaotic analog circuit and method for implementing nature exponential
CN106327414A (en) * 2016-08-16 2017-01-11 广东工业大学 Plaintext feature-based double-chaos image encryption method
CN109376540A (en) * 2018-09-11 2019-02-22 郑州轻工业学院 A kind of image encryption method based on Duffing mapping and genetic manipulation
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CN110766595A (en) * 2019-10-21 2020-02-07 中国石油大学(华东) Watermark encryption and decryption algorithm based on chaotic neural network
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Publication number Priority date Publication date Assignee Title
CN114598782A (en) * 2022-04-01 2022-06-07 安徽大学 Image encryption method and system based on raspberry pi and memristor neural network
CN117114959A (en) * 2023-09-13 2023-11-24 山东青橙数字科技有限公司 Image encryption method based on key feedback mechanism of multi-parameter one-dimensional chaotic system
CN117114959B (en) * 2023-09-13 2024-05-03 山东青橙数字科技有限公司 Image encryption method based on key feedback mechanism of multi-parameter one-dimensional chaotic system

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