CN112543093B

CN112543093B - Image encryption method, device and storage medium based on double-entropy source hyperchaotic system

Info

Publication number: CN112543093B
Application number: CN202011362687.5A
Authority: CN
Inventors: 余飞; 乾帅; 陈曦; 张梓楠; 蔡烁
Original assignee: Changsha University of Science and Technology
Current assignee: Changsha University of Science and Technology
Priority date: 2020-11-27
Filing date: 2020-11-27
Publication date: 2022-06-10
Anticipated expiration: 2040-11-27
Also published as: CN112543093A

Abstract

The invention discloses an image encryption method, equipment and a storage medium based on a double-entropy source hyperchaotic system, wherein the method comprises the steps of firstly constructing a pseudo-random number generator based on a six-dimensional memristor hyperchaotic system and two-dimensional SF-SIMM hyperchaotic mapping, and obtaining a complex sequence with a double-entropy source structure; then, the pseudo-random number generator iterates to obtain a corresponding pseudo-random matrix; and finally, diffusing pixels of the original image based on the obtained pseudo-random matrix, and encrypting the original image into a ciphertext image. The method applies the six-dimensional memristor hyperchaotic system and the two-dimensional SF-SIMM hyperchaotic mapping to image encryption, and provides a new image encryption method, wherein the method has strong key sensitivity and strong differential attack resistance; the key space is far large, and violent attack can be effectively resisted; the information of the ciphertext image can be well hidden, and the safety of the ciphertext image is ensured; the information entropy values of the ciphertext images are very close to theoretical values, and the entropy attack resisting capacity is strong.

Description

Image encryption method, device and storage medium based on double-entropy source hyperchaotic system

Technical Field

The invention relates to the technical field of image encryption, in particular to an image encryption method, equipment and a storage medium based on a double-entropy source hyperchaotic system.

Background

With the rapid development of computer technology and communication technology, information has become an important resource in the society of today, and the problem of information security caused by the information becomes more and more prominent. To secure information, cryptographic techniques are applied to information systems to achieve confidentiality, integrity, availability, controllability, and non-repudiation of information.

The chaos is widely applied to the fields of complex networks, electronic circuits, image encryption, synchronous control, safe communication and the like due to good random characteristics, extreme sensitivity to initial values and parameters, and long-term unpredictability and ergodicity of tracks. The memristor is firstly proposed in 1971 by professor of zeiss begonia and is a novel passive two-port device. In 2008, hewlett packard first developed a physical device based on a titanium dioxide memristor in a laboratory. Since then, memristors have been receiving increasing attention from both academic and industrial circles. The memristor is used as a nonlinear part of the chaotic system, so that the randomness and the complexity of signals of the chaotic system can be improved, and the physical size of the system is reduced. Many scholars are engaged in the research of various memristor chaotic systems. Multistable is often referred to as the coexistence of stable states or attractors, the stability of which depends on the speed with which the system recovers to a state after a disturbance (which may be noise or even an initial condition). In recent years, it has been a very popular research topic and has achieved some meaningful research results. When the number of coexisting attractors generated by the chaotic system reaches infinity, the phenomenon that infinite attractors coexist depending on the initial conditions of state variables is called extreme multistability. In fact, a variety of super multistable systems with hidden features have been proposed.

For some special fields, such as military, business and medical, digital images require the transceivers to communicate according to high security standards during transmission to ensure the integrity, reliability and security of the digital images. Image encryption aims at changing the position of a pixel or the value of a pixel. Fridrich applies the chaos theory to image encryption for the first time, and gradually becomes a hot point of study of scholars. But the image encryption by the chaotic system at present has the following defects: (1) the key space is insufficient, which results in easy cracking by brute force attacks; (2) the sensitivity of the key is poor, and the capability of resisting differential attack is poor; (3) the resistance to entropy attack is poor.

Disclosure of Invention

The present invention is directed to solving at least one of the problems of the prior art. Therefore, the invention provides an image encryption method, equipment and a storage medium based on a double-entropy source hyper-chaotic system. The security of image encryption can be improved.

The invention provides an image encryption method based on a double-entropy source hyperchaotic system, which comprises the following steps:

s100, constructing a pseudo-random number generator based on a double-entropy source chaotic system according to a six-dimensional memristor hyperchaotic system and a two-dimensional SF-SIMM hyperchaotic mapping;

s200, generating a plurality of pseudo-random sequences by iterating the pseudo-random number generator based on the double-entropy source chaotic system, wherein a plurality of initial values of the six-dimensional memristive hyper-chaotic system and the two-dimensional SF-SIMM hyper-chaotic map are used as original keys;

s300, generating corresponding pseudo-random matrixes from the pseudo-random sequences;

s400, encrypting the original image based on the pseudo-random matrix to obtain a ciphertext image.

According to the embodiment of the invention, at least the following technical effects are achieved:

the method comprises the steps of firstly, constructing a pseudo-random number generator based on a six-dimensional memristor hyperchaotic system and two-dimensional SF-SIMM hyperchaotic mapping, and obtaining a complex sequence with a double-entropy source structure; secondly, generating a plurality of pseudo-random sequences by iterating a pseudo-random number generator based on a double-entropy source chaotic system, wherein a plurality of initial values of a six-dimensional memristor hyperchaotic system and a two-dimensional SF-SIMM hyperchaotic mapping are used as original keys; then, converting the pseudo-random sequence into a corresponding pseudo-random sequence matrix; and finally, diffusing the pixels of the original image based on the pseudo-random matrixes, changing the positions of the pixels or the values of the pixels, and encrypting the original image into a ciphertext image. The method applies a six-dimensional memristor hyperchaotic system and two-dimensional SF-SIMM hyperchaotic mapping to image encryption, provides a new image encryption method, and has stronger key sensitivity and strong differential attack resistance compared with the existing method for realizing image encryption by a chaos theory (such as a Liu chaotic system, a memristor hyperchaotic system and the like); the key space is large, so that violent attack can be effectively resisted; the information of the ciphertext image can be well hidden, and the safety of the ciphertext image is ensured; the information entropy values of the ciphertext images are very close to theoretical values, and the entropy attack resisting capacity is strong.

In a second aspect of the present invention, an image encryption device based on a dual-entropy source hyper-chaotic system is provided, which includes: at least one control processor and a memory for communicative connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the image encryption method based on the dual-entropy source hyper-chaotic system according to the first aspect of the present invention.

In a third aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores computer-executable instructions for causing a computer to execute the image encryption method based on the dual-entropy source hyper-chaotic system according to the first aspect of the present invention.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.

Drawings

The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 shows a six-dimensional memristor hyper-chaotic system x provided by an embodiment of the present invention₁-x₂Different values of x on the plane₆(0) Typical attractors of (1);

FIG. 2 is a chaotic attractor for a two-dimensional SF-SIMM system with different parameters, provided by an embodiment of the present invention;

fig. 3 is a schematic flow chart of an image encryption method based on a dual-entropy source hyper-chaotic system according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of an implementation of step S400 in FIG. 3;

FIG. 5 is a schematic diagram illustrating a diffusion flow in step S401 of FIG. 4;

FIG. 6 is a schematic view of the diffusion process in step S403 of FIG. 4;

FIG. 7 is a schematic diagram illustrating a comparison between a plaintext image encrypted and a plaintext image decrypted by using a correct key and an incorrect key respectively according to an embodiment of the invention;

FIG. 8 is a histogram of a plaintext image and a ciphertext image according to an embodiment of the invention;

fig. 9 is a schematic diagram illustrating a distribution of pixel points of a Lena plaintext image according to an embodiment of the present invention;

fig. 10 is a schematic diagram illustrating the distribution of pixel points of a Lena ciphertext image according to an embodiment of the present invention;

fig. 11 is a schematic diagram of pixel point distribution of a babon plaintext image according to an embodiment of the present invention;

fig. 12 is a schematic diagram of pixel point distribution of a babon ciphertext image according to an embodiment of the present invention;

fig. 13 is a schematic structural diagram of an image encryption device based on a dual-entropy source hyper-chaotic system according to an embodiment of the present invention;

fig. 14 is a schematic flowchart of an image encryption and decryption process according to a third embodiment.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.

For convenience of understanding, a six-dimensional memristive hyper-chaotic system and a two-dimensional SF-SIMM hyper-chaotic map are briefly introduced below;

(1) a six-dimensional memristive hyper-chaotic system;

a six-dimensional memristor hyperchaotic autonomous system with complex and implicit extreme multistability has the dynamics phenomena of hidden extreme multistability, transient chaos, blasting and migration enhancement on a line or a balance plane. The six-dimensional memristive hyper-chaotic system is the first high-order system to exhibit all these rich dynamic behaviors.

Using a memristor model of

Wherein

And β represent the flux variable and the positive parameter, respectively. x is the number of₁,x₂,x₃,x₄,x₅,x₆Representing the initial values, alpha, beta, a, b, c, d, e, f, r, k are control parameters of the system (1). When the initial point is (x)₁(0),x₂(0),x₃(0),x₄(0),x₅(0),x₆(0) -16, β -0.2, a-6.5, b-1.5, c-5.5, e-5, f-0.01, r-5, k-0.05 and d-1.122 and d-1.964, -lyapuloff indices (LE1, LE2, LE3, LE4, LE5, LE6) are (+, +, +, -, -) and it can be seen that system (1) is in a hyper-chaotic state. When f ≠ 0, the system (1) has a line balance point L (0,0,0,0,0, L), which is a plane balance point when L is any real constant. When some initial values are fixed, and the system parameter x₁(0) And x₆(0) While changing, it is easy to find that the system (1) has hidden attractors and multistable attractors. In FIG. 1, x is given here₆(0) Some typical attractors obtained at different values. When x is₆(0) 1.80 and x₆(0)＝-0.72，x₁-x₂The plane shows two period-2 limit cycles, when x₆(0) 0.02 and x₆(0) When equal to 0.36, x₁-x₂The planes exhibit twin chaotic attractors, all of which are initially conditioned by α 15.47, β 0.12, a 4.8, b 0.18, c 8.5, d-0.1, e1, f-0.1, r 0.1, k 0 and x₁(0)＝0.1，x₂(0)＝0，x₃(0)＝0.01，x₄(0)＝0.05，x₅(0) Completed under 0.07. FIG. 1(a) is the limiting attractor for cycle-2; FIG. 1(b) chaotic coexistence attractors.

(2) Two-dimensional SF-SIMM hyperchaotic mapping;

a new high-dimensional hyperchaotic map, sinusoidal feedback sinusoidal ICMIC modulation map (SF-SIMM), is proposed at present. The research results show that the chaotic model has complex phase space trajectories, infinite balance points, hyperchaotic behaviors, large maximum Lyapunov index, three typical branches and a plurality of attractors with odd symmetry and coexists. In addition, the method has the advantages of complexity, distribution characteristics, zero correlation and the like, and two independent random numbers can be generated. Therefore, the method has good application prospect in the pseudo-random number generator.

A two-dimensional hyperchaotic sinusoidal feedback modulation mapping (based on a closed-loop modulation coupling mode) based on sinusoidal mapping and wireless folding mapping is shown in equation (2).

y₁,y₂For the state variables, m, n, ω are the system control parameters, and m, n, ω ∈ (0, + ∞). m is the amplitude of the system and ω is the frequency. n is the internal disturbance frequency. In addition, in the case where m is 1, n is 3, and ω is pi, the system (2) is in a hyper-chaotic state. Fig. 2(a), (b) and (c) are attractor phase diagrams when m is 1, n is 3, m is 2, n is 5, m is 3 and n is 5, respectively. When m is 1, n is 3 and ω is 1, the system does not have any balance point; when the value of ω increases to ω 1.01, the system has an infinite balance point; when m omega is less than or equal to 1, the system (2) has no balance point; when m ω > 1, the system has an infinite point of equilibrium. Two-dimensional SF-SIMMs have high complexity, uniform distribution and zero correlation over the entire parameter range by kinetic analysis.

A first embodiment;

referring to fig. 3, an embodiment of the present invention provides an image encryption method based on a dual-entropy source hyper-chaotic system, which can be implemented in an MATLAB environment, and the method includes the following steps:

s100, constructing a pseudo-random number generator based on the double-entropy source chaotic system according to the six-dimensional memristor hyperchaotic system and the two-dimensional SF-SIMM hyperchaotic mapping.

S200, generating a plurality of pseudo-random sequences by iterating a pseudo-random number generator based on the double-entropy source chaotic system, wherein a plurality of initial values of a six-dimensional memristive hyper-chaotic system and a two-dimensional SF-SIMM hyper-chaotic map are used as original keys.

The initial value in the step refers to initial conditions or system parameters of a six-dimensional continuous memristive hyper-chaotic system and two-dimensional discrete SF-SIMM hyper-chaotic mapping, for example, an original key can be formed by the initial conditions { x ] of the six-dimensional continuous memristive hyper-chaotic system₁,x₂,x₃,x₄,x₅,x₆16 double-precision floating point numbers including system parameters (a, b, c, d, e, f, r, k, m and n) and initial conditions (y) of two-dimensional discrete SF-SIMM hyperchaotic mapping₁(n+1),y₂(n +1) } and mapping parameters m, n and omega are composed of 5 double-precision floating point numbers; for example, the original key can be formed by the initial condition { x ] of a six-dimensional continuous memristive hyper-chaotic system₁,x₂,x₃,x₄,x₅,x₆And initial conditions of two-dimensional discrete SF-SIMM hyperchaotic mapping { y }₁(n+1),y₂(n +1) } composition, which is not exhaustive here.

S300, generating corresponding pseudo-random matrixes from the pseudo-random sequences.

S400, encrypting the original image based on the pseudorandom matrix to obtain a ciphertext image.

In step S400, the pseudo-random matrix is used to change the positions of the pixels or the values of the pixels by diffusing the pixels of the original image, and encrypt the original image into a ciphertext image.

A second embodiment;

referring to fig. 4, as an implementation manner, the step S400 in the first embodiment includes the following steps:

s401, diffusing the plaintext image according to the corresponding pseudo-random matrix to generate a first image.

S402, scrambling the first image into a second image according to the corresponding pseudo-random matrix.

And S403, diffusing the second image from the last pixel point forward according to the corresponding pseudo-random matrix until the second image is diffused into a ciphertext image.

Of course, step S400 may also use a diffusion-scrambling encryption structure commonly used in the art. Compared with the existing diffusion-scrambling encryption structure, the encryption structure of scrambling-diffusion-scrambling is adopted in the method, so that the spatial distribution and the gray distribution of image pixels are more uniform, and the robustness of image encryption is improved.

A third embodiment;

referring to fig. 14, a specific example of an image encryption method based on a dual-entropy source hyper-chaotic system is provided, and the method includes the following steps:

S200, generating a plurality of pseudo-random sequences by iterating a pseudo-random number generator based on the double-entropy source chaotic system, wherein a plurality of initial values of the six-dimensional memristive hyper-chaotic system and the two-dimensional SF-SIMM hyper-chaotic mapping and iterated transition values are used as original keys. Note that The DECHCS in fig. 14 represents a pseudo-random number generator.

This example is as follows (x)₁(0),x₂(0),x₃(0),x₄(0),x₅(0),x₆(0),r₁,r₂,y₁(0),y₂(0) (0.05,0,0.2,1,0,0.5,35,201,1,1) as the original key, where r is₁,r₂Is the transition value of the iteration. In order to improve the sequence randomness and avoid the periodicity possibly generated by starting iteration, the front r is omitted in the iteration process₁+r₂And (4) performing iteration for the second time, and skipping the transition state of the pseudo random number generator hyperchaotic system based on the double-entropy source chaotic system. Wherein r is₁And r₂Two random numbers, 8b, are selected as the original key for this embodiment. This embodiment iterates r first₁+r₂After the next time, normal iteration is carried out again to generate a pseudo-random sequence.

And continuously iterating M x N times to obtain 8 pseudo-random sequences which are sequentially marked as { x_1,i},{x_2,i},{x_3,i},{x_4,i},{x_5,i},{x_6,i},{y₁(n+1)},{y₂(N +1) }, i ═ 1,2, …, M × N denotes the image block size of the plaintext image to be encrypted.

Randomly selecting 6 pseudo-random sequences, and sequentially generating integer pseudo-random matrixes X, Y, Z, W, U and V according to the following formula:

X(k,l)＝floor((x_1,(k-1)×N+l+500mod 1)×10¹³)mod 2^L (3)

Y(k,l)＝floor((x_2,(k-1)×N+l+500 mod 1)×10¹³)mod 2^L (4)

Z(k,l)＝(floor(x_3,(k-1)×N+l×10¹³)mod M)+1 (5)

W(k,l)＝(floor((x_4,(k-1)×N+l+500 mod 1)×10¹²)mod N)+1 (6)

U(k,l)＝(floor((x_5,(k-1)×N+l+500 mod 1)×10¹²)mod M)+1 (7)

where L denotes the grey level, floor denotes the rounding operation, k is 1,2, …, M, L is 1,2, …, N.

By incrementing j, the plaintext image P is diffusion transformed into matrix a according to the resulting integer pseudorandom matrix X. The matrix a is then converted to image a. The diffusion process is shown in fig. 5, where the formula is described as follows:

A(i,j)＝P(i,j)+X(i,j)+r₁mod2^L (9)

A(i,j)＝P(i,j)+A(i,j-1)+X(i,j)mod2^L (10)

A(i,j)＝P(i,j)+sum(A(i-1,1 to N)+X(i,j)mod2^L (11)

And scrambling the image A to generate an image B by disturbing the correlation of adjacent pixel points in the pixel points. For the coordinates (i, j) of any point pixel point in the image a, the value of (m, n) is obtained by equations (12) and (13).

m＝(U(i,j)+sum(A(Z(i,j),1 to N)modM))+1 (12)

n＝(V(i,j)+sum(A(1 to M,W(i,j))modN))+1 (13)

When the resulting m ═ i or Z (i, j), or n ═ j or W (i, j), or Z (i, j) ═ i, or W (i, j) ═ j (conversion takes place to the corresponding programming of i ═ m ═ Z (i, j) | n ═ j | n ═ Wi, jZi, j ═ iWi, j ═ j), the position of a (i, j) remains unchanged; otherwise, A (i, j) is interchanged with A (m, n). Thus, all pixel points in the image A are traversed from left to right and from top to bottom, and the image A is converted into an image B.

To further make the spatial distribution and the grey scale distribution of the image pixels more uniform, the image B is transformed into a matrix C by means of an integer pseudo-random matrix Y. And converting the matrix C into an image C, wherein the image C is the obtained ciphertext image. The difference between the diffusion algorithm used in this step and the diffusion algorithm used in step S401 is that the diffusion algorithm is forward diffused from the last pixel point of the image, and a specific diffusion process is shown in fig. 6, where a formula described in the figure is as follows:

C(i,j)＝B(i,j)+Y(i,j)+r₂mod 2^L (13)

C(i,j)＝B(i,j)+C(i,j+1)+Y(i,j)mod 2^L (14)

C(i,j)＝B(i,j)+sum(C(i+1,1 to N)+Y(i,j)mod 2^L (15)

by adopting a scrambling-diffusing-scrambling encryption structure, the spatial distribution and the gray distribution of image pixels can be changed, and the robustness of image encryption is improved.

As an alternative embodiment, after step S403, a decryption step of the ciphertext image is further included, where the decryption step of the ciphertext image is the inverse process of steps S401 to S403, and a person skilled in the art can derive the decryption process according to the encryption process, and details will not be described here.

Referring to FIG. 7, a set of simulation examples of the present implementation is provided;

given a correct set of original keys: (x)₁(0),x₂(0),x₃(0),x₄(0),x₅(0),x₆(0),r₁,r₂,y₁(0),y₂(0) (0.05,0,0.2,1,0,0.5,35,201,1,1) and a set of wrong original keys: (x)₁(0),x₂(0),x₃(0),x₄(0),x₅(0),x₆(0),r₁,r₂,y₁(0),y₂(0) (0.050000000001,0,0.2,1,0,0.5,35,201,1, 1); there is a slight difference between the correct original key and the wrong original key. Fig. 7 shows the correlation results, where fig. 7(a) and (e) show the plaintext images (Lena has a small amount of detail; Baboon has a medium level of detail). Fig. 7(b) and (f) show ciphertext images obtained by encrypting with the correct original key. Fig. 7(c) and (h) show the decrypted image that was successfully decrypted using the correct original key. Fig. 7(d) and (g) show decrypted images decrypted using the wrong original key. The method has strong key sensitivity, and the result shows that the implementation method has strong differential attack resistance.

Providing a set of key space analysis examples of the present embodiment method;

the larger the key space, the higher the encryption strength, and the more suitable it is for information encryption. One-dimensional continuous spatial chaotic mapping has a relatively small key space, which is not desirable in cryptography. Otherwise, a too small key space is vulnerable to brute force attacks and the key cipher is broken. The brute force attack is a standard attack and can be used for any blob cipher. The attack method will typically be based on certain policies and rules to exhaust all possible keys until the correct key is found. To resist brute force attacks, the size of the key space must be large. It is generally accepted that when the key space is less than 2¹²⁸Is not sufficiently secure.

The method adopts a six-dimensional continuous memristor hyperchaotic system and two-dimensional discrete mapping to construct a random number generator so as to increase the required key space. The key space is a set of all possible keys that can be used for the initial seed of the pseudo-random scheme. The high-dimensional chaotic system has numerous parameters, is sensitive to boundary conditions and system initial values, has large relative key space, and has better application prospect in information encryption application compared with a low-dimensional chaotic system.

According to the IEEE floating point operation standard, the key can be set to the initial condition { x ] of six-dimensional continuous memristor hyperchaotic system at most₁,x₂,x₃,x₄,x₅,x₆16 double-precision floating point numbers including system parameters (a, b, c, d, e, f, r, k, m and n) and initial conditions (y) of two-dimensional discrete SF-SIMM hyperchaotic mapping₁(n+1),y₂(n +1) } and a mapping parameter m, n, omega, which are 5 double-precision floating point numbers. That is, the key space of the method of the present embodiment is at most 2³¹⁵(precision 10)^-15) Is much greater than 2¹²⁸Thus, the violent attack can be effectively resisted.

Referring to fig. 8, a set of histogram analysis examples of the present embodiment method is provided;

histogram analysis provides information about the distribution of the number of pixels in an image for each value of pixel intensity, i.e. the distribution reflects the statistical properties of the image. If the probability of generating all intensity pixels is equal in the encrypted image histogram, the encryption symmetry is higher and there is good uniformity. Fig. 8(a), (c) show that the histograms of the original plaintext images Lena and Baboon fluctuate with non-uniformity, which means that the data can be visually extracted, as in fig. 8. However, in contrast to the original plaintext image, in fig. 8(b), (d), the histogram of the ciphertext image is uniformly distributed, similar to a straight line. By comparing the image histograms of the plaintext image and its corresponding ciphertext image, this indicates that each pixel intensity in the encrypted ciphertext image has an almost equal probability of being generated. This shows that the method of the present embodiment hides the statistical information of the image well, and ensures the security of the encrypted ciphertext image.

Referring to fig. 9 to 12, a set of examples of image correlation analysis of the method of the present embodiment is provided;

2000 pairs of adjacent pixel points on horizontal, vertical, right-angle and anti-angle lines are selected from the plaintext image and the ciphertext image respectively at random, and corresponding correlation coefficients are calculated. Fig. 9 and 13 show that the pairs of adjacent pixel points in each direction of the plaintext image are densely arranged on a line y-x, while fig. 10 and 14 show that the pairs of adjacent pixel points in each direction of the ciphertext image are uniformly distributed in the matrix area, which shows that the plaintext image has strong correlation in each direction, and the ciphertext image has no correlation in each direction. In addition, table 1 shows correlation values of the colored plaintext images and their respective encrypted versions used in the experiment. It can be seen from table 1 that the correlation coefficient value of the ciphertext image is close to 0. In a digital image, a ciphertext image generated by a good encryption algorithm has high correlation between adjacent pixel points in the plaintext image theoretically, and the correlation between the adjacent pixel points of the ciphertext image is close to 0 and is approximately zero. FIG. 9 shows a Lena plaintext image correlation case, wherein (a) is a horizontal direction; (b) is in the vertical direction; (c) is opposite to the direction of the angular line; (c) in the negative diagonal direction. Fig. 10 shows Lena ciphertext image dependent cases, in which (a) is in a horizontal direction; (b) is in the vertical direction; (c) is opposite to the direction of the angular line; (c) in the negative diagonal direction. FIG. 11 shows a Baboon clear text image correlation, wherein (a) is a horizontal direction; (b) is in the vertical direction; (c) is opposite to the direction of the angular line; (c) in the negative diagonal direction. Fig. 12 shows a case where a Baboon ciphertext image is related, where (a) is in a horizontal direction; (b) is in the vertical direction; (c) is opposite to the direction of the angular line; (c) in the negative diagonal direction.

TABLE 1

Providing a group of differential attack analysis examples of the method of the embodiment;

the principle of the differential attack is to analyze and utilize the influence of the tiny difference of the input plaintext on the difference of the corresponding image ciphertext. The seed values used for the same input vector differ only littleThe sequences produced are also completely different. But when two adjacent input vectors use the same seed value, great convenience may be brought to an attacker, and the differential attack is much simpler. Therefore, this situation is considered to be solved in the above image encryption method design, generating a secure output and avoiding differential attacks. If the two ciphertext images have obvious difference, the key sensitivity of the image encryption scheme is strong; otherwise, it is weak. A good image encryption scheme should have a rather strong key sensitivity. To verify key sensitivity in the proposed image encryption algorithm, two metrics commonly used in cryptography systems are used here to measure the ability of the system to resist differential attacks. The pixel change rate (NPCR) and the normalized average changing intensity (UACI) are used to quantify two adjacent initial seeds to generate two pseudorandom sequences. NPCR measures two pseudo-random number generators (P)_i) And (P)_i') how many elements differ from one another, and UACI measures (P)_i) And (P)_i') makes up for the NPCR measure the one-sidedness of the difference index of the two images. The definition expression of NPCR is as follows:

the probability that pixel points of two images with the same size at any position are different is

I.e. the theoretical value of NPCR for a given image versus a random image is also 99.6094%.

The UACI is defined as follows:

the average of the ratio of the difference between the pixel points at the corresponding positions of the given image and the random image to the maximum difference (255) is called UACI.

A difference image of two images of the same size is defined as D ═ P_i(i,j)-P_i' (i, j) |, and then the adjacent pixel points of the difference image are divided into a 2 × 2 matrix, which can be divided into (M-1) × (N-1) small image blocks (image size is M × N). The average of the absolute values of the differences of any two elements is:

the Block Average Changing Intensity (BACI) is calculated for all small image blocks Δ_iThe ratio of the maximum difference value of the pixel point is used for solving the defects that the image visual effect is similar, but the NPCR and UACI values are ideal.

In this experiment, 100 keys were randomly generated, and x was slightly changed in sequence₁(0),x₂(0),x₃(0) And y₁(0),y₂(0) And respectively encrypting the plaintext images by using two keys before and after changing, and then analyzing the NPCR, UACI and BACI between two corresponding ciphertext images obtained by encrypting the same plaintext image. The average values of NPCR, UACI and BACI for 100 trials are shown in Table 2. We can see that the value of NPCR is over 99% and the value of UACI is over 33%, very close to the ideal value. This means that the proposed pseudo random number generator has a high resistance against differential attacks. TABLE 2 secret Key x₁(0),x₃(0),x₄(0),x₆(0) NPCR, UACI, BACI test results with minor variations

TABLE 2

Providing a set of information entropy analysis examples of the method of the embodiment;

the information entropy of the image reflects the uncertainty of the image information and the richness of the contained information. It is generally considered that the larger the information contained in an image (the larger the uncertainty), the less the information that can be directly observed, and the larger the entropy value thereof. The calculation formula of the information entropy is as follows.

Where L is the number of gray levels of the image and p (i) is the probability of the occurrence of the gray value i. The possible values of the color image are 28 x 3, the ideal entropy value of each channel (R, G and B) is equal to 8 bits, and the ideal entropy value of the grayscale image is also equal to 8 bits. Therefore, in order to verify the effectiveness of the encryption mechanism of the pseudo random number generator chaotic system based on the dual-entropy source chaotic system, which is proposed by the image encryption method, the entropy value of the encrypted plaintext image should be close to 8. Table 3 lists the shannon entropy values of the plaintext images and their corresponding ciphertext images. Obviously, the information entropy of each plaintext image is obviously different from the theoretical value (i.e. 8), and the information entropy values of all the ciphertext images are very close to the theoretical value. Therefore, the method of the embodiment is safe to entropy attack.

TABLE 3

A fourth embodiment;

referring to fig. 13, an image encryption device based on a dual-entropy source hyper-chaotic system is provided, and the device may be any type of intelligent terminal, such as a mobile phone, a tablet computer, a personal computer, and the like. Specifically, the apparatus includes: one or more control processors and memory, here exemplified by a control processor. The control processor and the memory may be connected by a bus or other means, here exemplified by a connection via a bus.

The memory, as a non-transitory computer readable storage medium, may be used to store non-transitory software programs, non-transitory computer executable programs, and modules, such as program instructions/modules corresponding to the image encryption device based on the dual-entropy source hyper-chaotic system in the embodiment of the present invention. The control processor operates the non-transient software program, the instructions and the modules stored in the memory, so that the image encryption method based on the double-entropy source hyperchaotic system is realized.

The memory may include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function; the memory may include high speed random access memory, and may also include non-transitory memory, such as at least one magnetic disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory optionally includes a memory remotely disposed with respect to the control processor, and the remote memories may be connected to the image encryption device based on the dual-entropy source hyper-chaotic system through a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.

The one or more modules are stored in the memory and when executed by the one or more control processors, perform the image encryption method based on the dual-entropy source hyper-chaotic system in the above method embodiments.

The embodiment of the invention also provides a computer-readable storage medium, which stores computer-executable instructions, and the computer-executable instructions are used by one or more control processors to execute the image encryption method based on the double-entropy source hyper-chaotic system in the above method embodiments.

Through the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be implemented by software plus a general hardware platform. Those skilled in the art will appreciate that all or part of the processes in the methods for implementing the embodiments described above can be implemented by hardware related to instructions of a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes in the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read Only Memory (ROM), a Random Access Memory (RAM), or the like.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. An image encryption method based on a double-entropy source hyperchaotic system is characterized by comprising the following steps:

s300, generating a corresponding pseudo-random matrix from a plurality of pseudo-random sequences;

2. The image encryption method based on the dual-entropy source hyperchaotic system as claimed in claim 1, wherein the encrypting the original image based on the pseudo-random matrix to obtain the ciphertext image comprises the steps of:

s401, diffusing the plaintext image according to the corresponding pseudo-random matrix to generate a first image;

s402, scrambling the first image into a second image according to the corresponding pseudo-random matrix;

s403, diffusing the second image from the last pixel point forward according to the corresponding pseudo-random matrix until the second image is diffused into a ciphertext image.

3. The image encryption method based on the dual-entropy source hyperchaotic system according to claim 1, wherein the original key further includes iterative transition values.

4. The image encryption method based on the dual-entropy source hyperchaotic system according to claim 2, characterized in that it further comprises a decryption step, which is the inverse of steps S401 to S403.

5. An image encryption device based on a double-entropy source hyperchaotic system is characterized by comprising: at least one control processor and a memory for communicative connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the dual-entropy source hyper-chaotic system based image encryption method according to any one of claims 1 to 4.

6. A computer-readable storage medium storing computer-executable instructions for causing a computer to perform the image encryption method based on the dual-entropy source hyper-chaotic system according to any one of claims 1 to 4.