CN116193041A - Image encryption method based on multistable memristor and four-dimensional chaotic neural network - Google Patents

Abstract

The invention relates to the field of image processing, in particular to an image encryption method based on a multistable memristor and a four-dimensional chaotic neural network. The memristive model and the traditional Hopfield neural network are coupled to form the memristive neural network, and the chaotic sequence is introduced into the image encryption and decryption process by utilizing the rich dynamic chaotic phenomenon of the memristive neural network; then introducing Arnold Cat Map to carry out image pixel scrambling, randomly selecting two numbers from the chaotic sequence to serve as control parameters of the Arnold Cat Map, and carrying out pixel diffusion encryption by exclusive OR operation. The method can be used for rapidly and effectively encrypting the image, can be successfully applied to the FPGA hardware chip, and has good development prospect in the aspects of large-scale internet of things multimedia communication confidentiality and the like in the future.

Description

Image encryption method based on multistable memristor and four-dimensional chaotic neural network

Technical Field

The invention relates to the field of image processing, in particular to an image encryption method based on a multistable memristor and a four-dimensional chaotic neural network.

Background

With the rapid development of computer technology and communication technology, information has become an important resource in the current society, and the information security problem caused by the information has become increasingly prominent. To secure information, cryptographic techniques are applied to information systems to achieve confidentiality, integrity, availability, controllability, and non-repudiation of information. In recent years, the development of networks is rapid, but problems are caused by the development of networks, and the problem of network security is one of the very serious problems. The image is an important carrier for the daily communication information transmission, and is a very critical part in the technical field of communication information. It plays an important role in the fields of information communication, medical imaging, digital multimedia systems, etc. It is known that image information and other text information differ in language information. The amount of information contained in the image pixels is large, the image pixels interact with each other, and the correlation between their different directions is also large, which results in that the text encryption technique will no longer be suitable for use in the image encryption technique.

In order to improve the performance of the image encryption algorithm, the research results of the neural network system and the chaotic system are applied to the image encryption technology, so that the safety of the image encryption system is improved, and the system effectively resists various attacks. Because the neural network has good nonlinear characteristics and associative memory functions, any data of the neural network can be stored and utilized after the number of neurons, the types of the neural network and the weight of the interconnection are determined. The data obtained through the neural network has good pseudo-randomness, and can be used for an image encryption algorithm to be a good choice. When the neural network is combined with the chaotic system, a larger random matrix is formed; compared with a single chaotic system, the system not only expands the key space, but also simultaneously generates larger space complexity.

Disclosure of Invention

The invention designs a novel memristor model, and simultaneously, the memristor model and a traditional Hopfield neural network are coupled to form a memristor neural network, and a chaotic sequence is introduced into an image encryption and decryption process by utilizing rich dynamic chaos phenomena of the memristor neural network; and then introducing an Amold Cat Map to carry out image pixel scrambling, randomly selecting two numbers from the chaotic sequence to serve as control parameters of the Arnold Cat Map, carrying out pixel diffusion encryption by exclusive OR operation, and finally outputting an encrypted image.

The technical scheme of the invention is as follows:

an image encryption method based on a multistable memristor and a four-dimensional chaotic neural network comprises the following steps:

the first step: in order to realize the rich nonlinear dynamic phenomenon of the memristor neural network of the encryption system, a novel multistable memristor is designed according to the definition of the universal memristor. The mathematical expression is as follows:

i＝G(x)v＝(cx+dcos(x))v， (1)

dx/dt＝g(x，v)＝abcos(x)tanh(x)-v， (2)

under sinusoidal external stimulus, the parameters of equations (1) and (2) are set as follows:

a is set to 10; b is set to 0.3, c is set to 500, d is set to 0.4; the arrangement can accord with three fingerprints of memristors to the greatest extent, and has the characteristics of multistability and the like, as shown in figure 2; meanwhile, the brain nerve synapse simulation device has good nonlinear property and is very suitable for simulating the brain nerve synapse of a human body.

Let v=0, then memristor state equation (2) becomes dx/dt=g (x, 0) =abcos (x) tanh (x), and by "POP" steady-state point analysis method, the memristor with infinite number of discrete steady-state points can be expressed as

In particular, the equilibrium steady-state point may be expressed as

The 'multistable' characteristic is further applied to a neural network model, so that the neural network model can generate coexisting chaotic attractors.

And a second step of: the memristor proposed in the previous step is coupled with a traditional Hopfield neural network to obtain the memristor neural network, and the mathematical expression is as follows:

wherein G is ₁ ＝500z ₁ +0.4cOs(z ₁ )，G ₂ ＝5002 ₂ +0.4cos(z ₂ )，G ₁ 、G ₂ Representing a multistable universal memristor, serving as a simulated nerve synapse, ρ ₁ 、ρ ₂ For the system coupling coefficient, represents the coupling strength of the memristor to the neural network, x _i Is used to represent the membrane voltage between the outside and inside of neuron i, tanh (x _i ) Is the activation function of the neuron. The memristive neural network topology structure diagram of the invention is shown in figure 3.

Meanwhile, by setting the right side of the formula (3) to 0, the memristive neural network can be found to have infinite discrete steady-state points, see the formula (4).

Where i=1, 2,3,4.K e (0, 1,2, 3.)

By modifying the phase space states, the memristive neural network has an infinite balance point along the z1 axis, which suggests that a unique multistable memristor synapse is critical for the formation of infinite balance.

At a given initiation, by adjusting the memristive coupling coefficient ρ of the neural network ₁ 、ρ ₂ And given different initial states, the memristive neural network can generate rich dynamic phenomena such as limit cycle motion, multicycle motion, chaos, hyperchaotic and the like (see figures 4 and 5).

Finally, according to the formula (4), a group of real numbers are selected

As an initial state of the memristive neural network, an ODE45 longge-kuta algorithm is used, and iteration is performed continuously, so that a chaotic sequence is generated.

And a third step of: an original image ORI is selected, the image size is (A multiplied by B), and 2D images are serialized in a column-first scanning mode to obtain a 1D image sequence O (i), and the sequence length is (A multiplied by B).

Fourth step: and a sequence K (i) with the length of (A multiplied by B) is intercepted from the chaotic sequence. Then, two numbers Ki and Li are randomly taken from K (i) to be used in the subsequent encryption process.

Where floor (x) represents the maximum integer less than or equal to x, randi (x, y) represents the length of the return K (i) sequence from between [ x, y ] back to a random integer, length (K (i)).

Fourth step: using Ki, li constructs the Anorld Cat Map (ACM) scrambling Map expression as follows:

where I and J represent the original pixel locations, and I 'and J' represent the scrambled pixel locations, and Ki, li are the system parameters of the ACM, N is equal to min (A, B).

All elements in the image sequence O (i) are subjected to scrambling, ACM scrambling mapping is carried out for sharing abs (Ki-Li)/2 times until scrambling is completed, and a scrambling sequence P (i) is obtained.

Fifth step: and performing bitwise exclusive OR operation on the P (i) and the K (i) to realize diffusion of the image encryption process and obtain an encryption sequence E (i).

Sixth step: e (i) is arranged in columns to form an encrypted image ENC of size (A×B).

The decryption process is the inverse of the encryption process, and the encryption related effect is shown in fig. 6.

In the invention, under the condition of setting the same initial value in the information entropy analysis of different encrypted images, the entropy values of the encrypted images are very close to the ideal value 8, the histogram distribution of the encrypted images is very uniform in the histogram analysis of the different encrypted images, the distribution characteristics of the pixel values of the images are well hidden, and a cracker can hardly acquire any useful information in the histogram. In the correlation analysis, the correlation coefficient of the encrypted image in the three directions of horizontal, vertical and diagonal is nearly 0, which indicates that the adjacent pixels of the encrypted image have little correlation. In addition, the image encryption and image decryption times on the FPGA platform were 0.240443s and 0.217897s, respectively. These times are much lower than the corresponding times 0.762345s and 0.671635s in MATLAB numerical simulations. The method can be used for rapidly and effectively encrypting the image, can be successfully applied to the FPGA hardware chip, and has good development prospect in the aspects of large-scale internet of things multimedia communication confidentiality and the like in the future.

Drawings

FIG. 1 is a workflow diagram of the present invention;

FIG. 2 (a) is a feature diagram of a novel memristor model;

FIG. 2 (b) is a feature diagram of a novel memristor model;

FIG. 2 (c) is a feature diagram of a novel memristor model;

FIG. 2 (d) is a feature diagram of a novel memristor model;

FIG. 3 is a diagram of a dynamic characteristic topology of a memristive neural network;

FIG. 4 (a) is a memristive neural network feature diagram;

FIG. 4 (b) is a memristive neural network feature diagram;

FIG. 4 (c) is a memristive neural network feature diagram;

FIG. 4 (d) is a memristive neural network feature diagram;

FIG. 5 (a) is a memristive neural network feature diagram;

FIG. 5 (b) is a memristive neural network feature diagram;

FIG. 6 (a) is a Lena plaintext image;

FIG. 6 (b) is a Lena ciphertext image;

FIG. 6 (c) is a Lena decrypted image;

FIG. 6 (d) is an Airplane plaintext image;

FIG. 6 (e) is an Airplane ciphertext image;

FIG. 6 (f) is an Airplane decrypted image;

FIG. 6 (g) is a Pepper plaintext image;

FIG. 6 (h) is a Pepper ciphertext image;

fig. 6 (i) is a Pepper decrypted image.

Detailed Description

Specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

The first step: a 512 x 512 image is selected and the 2D images are serialized in a column-first scan to obtain a 1D image sequence O (i), the sequence length being 26144.

And a second step of: selecting a set of real numbers (1, 7 pi, pi) ρ according to formula (4) ₁ ＝2.8、ρ ₂ =0.008 as the initial state of memristive neural network, solve equation (3) using ODE45 longge-kuta algorithm, iterate continuously, and generate chaotic sequence.

And a third step of: by the expression (5), a sequence K (i) of length (2626144) and two random numbers are obtained, and Ki, li are obtained by rounding operation.

Fourth step: using Ki, li uses equation (6) to traverse and scramble all elements in the image sequence O (i), and performs ACM scrambling mapping co abs (Ki-Li)/2 times until all scrambling is completed, resulting in a scrambled sequence P (i).

Fifth step: and performing bitwise exclusive OR operation on the P (i) and the K (i) to realize diffusion of the image encryption process and obtain an encryption sequence E (i).

Sixth step: e (i) is re-deserialized according to the original image size of 512×512 to obtain an encrypted image ENC.

The decryption process is the inverse of the encryption process.

Example 2:

image encryption and image decryption times on the FPGA platform were 0.240443s and 0.217897s, respectively. These times are much lower than the corresponding times 0.762345s and 0.671635s in MATLAB numerical simulations.

Claims (1)

1. An image encryption method based on a multistable memristor and a four-dimensional chaotic neural network is characterized by comprising the following steps:

the first step: the novel multistable memristor is designed, and the mathematical expression is as follows:

i＝G(x)υ＝(cx+dcos(x))υ， (1)

dx/dt＝g(x，υ)＝abcos(x)tanh(x)-υ， (2)

under sinusoidal external stimulus, the parameters of equations (1) and (2) are set as follows: a is set to 10; b is set to 0.3, c is set to 500, d is set to 0.4;

let v=0, then memristor state equation (2) becomes dx/dt=g (x, 0) =abcos (x) tanh (x), and by "POP" steady-state point analysis method, the memristor with infinite number of discrete steady-state points can be expressed as

The equilibrium steady-state point is expressed as

And a second step of: through coupling the memristor provided in the last step with a traditional Hopfield neural network, a memristor neural network is designed, and the mathematical expression is as follows:

wherein G is ₁ ＝500z ₁ +0.4cos(z ₁ )，G ₂ ＝500z ₂ +0.4cos(z ₂ ) Representing a multistable universal memristor, serving as a simulated nerve synapse, ρ ₁ 、ρ ₂ For the system coupling coefficient, represents the coupling strength of the memristor to the neural network, x _i Is used to represent the membrane voltage between the outside and inside of neuron i, tanh (x _i ) Is the activation function of neurons;

meanwhile, by setting the right side of the formula (3) as 0, the memristor neural network is found to have infinite discrete steady-state points, and the formula (4) is shown;

where i=1, 2,3,4.K e (0, 1,2, 3.)

According to formula (4), a group of real numbers is selected

As the initial state of the memristive neural network, an ODE45 Longge-Kutta algorithm is used, and iteration is carried out continuously, so that a chaotic sequence is generated;

and a third step of: selecting an original image ORI, wherein the size of the image is (A multiplied by B), and serializing the 2D images in a column-first scanning mode to obtain a 1D image sequence O (i), and the sequence length is (A multiplied by B);

fourth step: and intercepting a sequence K (i) with the length of (A multiplied by B) from the chaotic sequence; then, two numbers Ki and Li are randomly taken from K (i) to be used in a subsequent encryption process;

wherein floor (x) represents the maximum integer less than or equal to x, randi (x, y) represents the length of the return K (i) sequence from between [ x, y ] back to a random integer, length (K (i));

fourth step: using Ki, li constructs the Anorld Cat Map (ACM) scrambling Map expression as follows:

wherein I and J represent original pixel positions, I 'and J' represent scrambled pixel positions, ki, li are system parameters of ACM, and N is equal to min (A, B);

traversing and scrambling all elements in the image sequence O (i), and executing ACM scrambling mapping to commonly abs (Ki-Li)/2 times until scrambling is completed to obtain a scrambling sequence P (i);

fifth step: performing bitwise exclusive OR operation on the P (i) and the K (i) to realize diffusion of an image encryption process and obtain an encryption sequence E (i);

sixth step: e (i) is arranged in columns to form an encrypted image ENC of size (A×B).

Images