CN106570814B

CN106570814B - Hyperchaotic image encryption method

Info

Publication number: CN106570814B
Application number: CN201610908104.1A
Authority: CN
Inventors: 谢国波; 姜先值; 王朝阳
Original assignee: Guangdong University of Technology
Current assignee: Guangdong University of Technology
Priority date: 2016-10-17
Filing date: 2016-10-17
Publication date: 2020-09-29
Anticipated expiration: 2036-10-17
Also published as: CN106570814A

Abstract

The invention provides a hyperchaotic image encryption method which is mainly applied to the field of gray level image encryption. The algorithm mainly comprises the following contents: firstly, a plaintext image with the size of N multiplied by M is divided into M column vector groups, pixels in the obtained vector groups are subjected to bit conversion to obtain 8 multiplied by M vector groups, and then scrambling operation is carried out. And then remapping the obtained scrambled pixel values to the positions between [0, 255] to obtain an intermediate ciphertext. And finally, performing diffusion operation on the chaotic sequence generated by the Hyperhenon chaotic system and the intermediate ciphertext to obtain a final ciphertext. Experimental simulation shows that the algorithm can not only improve the defects of a low-dimensional chaotic system and resist statistical characteristic attack and differential attack, but also effectively resist four kinds of classical attack, well hide plaintext information and achieve a good encryption effect.

Description

Hyperchaotic image encryption method

Technical Field

The invention belongs to a gray level image encryption method, and particularly relates to a hyperchaotic image encryption method.

Background

With the rapid development of computer networks, the number of pictures transmitted in the networks is increasing, which brings about the attention of people to the safe transmission of pictures, and nowadays, scholars at home and abroad give high attention to how to encrypt pictures during image transmission.

Due to the characteristics of strong correlation of pixels of the image, high redundancy, large data volume and the like, the traditional text encryption method is difficult to be applied to image encryption. In recent years, experts point out that chaotic systems have the characteristics of high sensitivity to initial conditions, positive Lyapunov indexes, fractal and the like, can be applied to image encryption, and gradually provide some chaotic image encryption methods: such as one-time pad, bit encryption, mathematical model encryption and DNA sequence encryption

However, the above-identified methods have significant disadvantages:

such as the one-time pad key, presents great difficulties in delivery and distribution; the bit encryption method needs to convert all pixel values into binary system for image encryption during encryption, so that the encryption efficiency is low and time is consumed; the mathematical model encryption method is not beneficial to the realization of the encryption algorithm due to the comparison of factors which need to be considered; the pixel correlation coefficient in the DNA sequence encryption method is high and easy to be decrypted by an attacker.

Disclosure of Invention

Aiming at the defects of the encryption method, the invention provides a hyperchaotic image encryption method. The invention directly encrypts and generates the key according to the pixel value of the plaintext, can well solve the problems of image encryption efficiency and key transmission, and introduces the Hyperhenon hyper-chaotic system for encryption, thereby not only simplifying the realization of an encryption system, but also reducing the correlation of the pixel of the ciphertext image. Besides, the invention can effectively resist four classic attack methods and achieve good encryption effect.

The hyperchaotic image encryption method is characterized by comprising a key initialization process and a key encryption device

A chaotic transformation process and a Hyperhenon hyper-chaotic mapping diffusion process.

(1) Key initialization procedure

The encryption key K is mainly composed of a binary auxiliary key K with the length of 400 bits₁Inputting a secret key X₀，Y₀The three parts are as follows.

Step 1: firstly, a binary auxiliary secret K with the length of 400 bits is used₁Is divided into ten binary units of 40 bits in length, each of which is K₁₀，K₁₁，...，K₁₉。

Step 2: will input the key X₀，Y₀As an initial key of the Hyperhenon map, as shown in formula (1), where c is made 1.76, d is made 0.1, and X₀，Y₀And taking values between (0,1) to generate a group of hyperchaotic sequences for diffusion operation.

k＝0，1，2，... (1)

(2) Scrambling transformation process

Step 1: first, an N × M plaintext image is divided into M column vector groups, and pixels of each vector group are represented by 8-bit binary, so that 8 × M column vector groups can be obtained.

Step 2: according to the auxiliary key matrix K₁₀，K₁₁，...，K₁₉Two control parameters v and w in the cat map are calculated as shown in equation (2):

and step 3: combining v and w obtained in step 2, and substituting each column vector subscript as an input variable into an Arnold mapping, and obtaining s and t as shown in formula (3), wherein r is 0,1, 2. s is 0,1, 2.., 8 × M represents a new position scalar after the column vector is subjected to Arnold transformation; t is expressed as the number of bits of the column vector bit group that are rotationally shifted up.

And 4, step 4: and moving the column vector group represented by r into the column vector group represented by s according to the s obtained in the step 3. And circularly moving each element of the column vector group moved to the s position upwards by t according to the t obtained in the step 3.

And 5: and (5) repeating the steps 3 and 4 for 8 times multiplied by M times to obtain an intermediate ciphertext B.

(3) Hyperhenon hyper-chaotic map diffusion process

Step 1: and changing the obtained binary intermediate ciphertext B into a decimal ciphertext P with the size of N multiplied by M.

Step 2: setting an initial value X₀Is x₁，Y₀Is y₁Substituting the chaos sequence into a Hyperhenon hyperchaotic mapping system, discarding the previous 200 iteration results, and performing N × M iteration to obtain a chaos sequence L with the length of N × M ═ L₁，l₂，...，l_N×MSubstituting the obtained chaotic sequence L into formula (4) to transform the element value range to [0, 255 }]Get a new chaotic sequence Q ═ { Q ═ Q₁，q₂，...，q_N×M}。

q_i＝mod(l_i×10⁵，256)1≤i≤N×M (4)

And step 3: performing formula (5) operation on each pixel of the intermediate ciphertext P, and enabling c₀Is composed ofThe average value of the pixel values of the ciphertext P is increased, so that the correlation between the plaintext and the ciphertext is increased to achieve the pixel diffusion effect, and the final ciphertext C is obtained as { C {₁，c₂，...，c_N×M}。

The invention has the beneficial effects that:

the invention increases the length and combination of the key by forming the encryption key by the auxiliary key with the length of 400 bits and the input key, and makes exhaustive attack impossible. Then, plaintext scrambling operation is performed by means of the auxiliary key information, and plaintext (ciphertext attack) can be effectively resisted. And carrying out XOR operation on the obtained intermediate ciphertext and a hyper-henon hyperchaotic mapping to generate a chaotic sequence, and improving the poor characteristics of periodic windows and the like in the low-dimensional chaotic transformation. The invention can effectively resist classical attacks, ensures the security of channel transmission and has wide application prospect in the field of digital multimedia information security.

Drawings

FIG. 1 is an encryption flow diagram of the present invention

FIG. 2 shows a key K₁Composition diagram of

FIG. 3 is a block diagram of the intermediate ciphertext bit

FIG. 4(a) is a 256X 256 gray scale Lena diagram

FIG. 4(b) is the final encrypted image

FIG. 5(a) clear text grayscale histogram

FIG. 5(b) Gray histogram of ciphertext image

FIG. 6(a) is a plain text relationship diagram

FIG. 6(b) ciphertext relational graph

FIG. 7(a) K₂Decryption graph

FIG. 7(b) K₃Decryption graph

FIG. 7(c) K₄Decryption graph

Detailed Description

The specific implementation steps are shown in the encryption flowchart of fig. 1.

To implement image encryption, the present invention first implements a key initialization process, as shown in fig. 2.

k＝0，1，2，... (1)

After the key initialization process of fig. 2 is completed, the image encryption process of fig. 1 is performed, during which an intermediate bit cipher text matrix is also generated, as shown in fig. 3.

Step 6: and changing the obtained binary intermediate ciphertext B into a decimal ciphertext P with the size of N multiplied by M.

And 7: setting an initial value X₀Is x₁，Y₀Is y₁Substituting the chaos sequence into a Hyperhenon hyperchaotic mapping system, discarding the previous 200 iteration results, and performing N × M iteration to obtain a chaos sequence L with the length of N × M ═ L₁，l₂，...，l_N×MSubstituting the obtained chaotic sequence L into formula (4) to transform the element value range to [0, 255 }]Get a new chaotic sequence Q ═ { Q ═ Q₁，q₂，...，q_N×M}。

q_i＝mod(l_i×10⁵，256)1≤i≤N×M (4)

And 8: performing formula (5) operation on each pixel of the intermediate ciphertext P, and enabling c₀Is the average value of the pixel values of the intermediate ciphertext P, so that the correlation between the plaintext and the ciphertext is increased to achieve the pixel diffusion effect, and the final ciphertext C is obtained₁，c₂，...，c_N×M}。

Experimental simulations were performed using matlab 2014 on a gray scale Lena map of size 256 × 256, the plaintext image being shown in fig. 4(a), in whichThe system input keys are respectively: x₀＝0.314 852 2456，Y₀0.4258527320. The resulting encrypted image is shown in fig. 4 (b).

The image encryption method of the present invention is analyzed in terms of security as follows.

1. Histogram analysis

Fig. 5(a) and (b) are histogram diagrams of plaintext and ciphertext, respectively. As can be seen from the figure, the pixel value distribution of the image with the plaintext histogram distribution is quite uneven, and an attacker can obtain the image information according to the pixel distribution information. After the image is encrypted by the method, the histogram of the ciphertext image is distributed quite uniformly, the pixel value information is well hidden, and the encryption effect is achieved.

2. Statistical analysis

And randomly and respectively selecting two groups of adjacent pixel points in the horizontal direction, the vertical direction and the diagonal direction in the plaintext image and the ciphertext image to draw a pixel correlation diagram. Fig. 7(a) shows a plain text relationship diagram, fig. 7(b) shows a cipher text relationship diagram, and correlation coefficients between pixels are calculated according to equations (6) to (9).

Where x and y represent gray values of adjacent pixel groups of the image, E (.) -represents mathematical expectation, cov (.) -represents covariance, and γ represents_xyRepresented as the relation coefficient of the neighboring pixels. The calculation results are shown in table 1, and a correlation coefficient closer to 1 indicates stronger correlation, and a smaller correlation indicates less correlation.

TABLE 1 neighboring Pixel correlation coefficient Table

3. Sensitivity analysis of initial values

The decryption key K of the invention is composed of K ═ K₁，X₀，Y₀]In which the correct decryption key K is₂＝[K₁，X₀，Y₀]In which K is₁For a given 400-bit binary bit group, X₀＝0.314 852 2456，Y₀0.4258527320 when key X is input₀，Y₀The decryption keys K are respectively obtained by respectively changing slightly₃，K₄In which K is₃In (C) X₀Other values do not become a solution, K0.3148522457₄Middle Y₀Other values do not change to another solution, 0.4258527321. As can be seen from fig. 6, provided that the decryption key occurs 10^-10The small change of the data can not be decrypted successfully, and the method has extremely strong sensitivity to the initial value and can effectively resist differential attack.

4. Attack of classical type

The following four types are defined as classical attacks according to the Kerckhoff principle:

(1) ciphertext-only attack (Ciphertext only attack): the attacker has no other auxiliary information except the intercepted ciphertext.

(2) Known plaintext attack (knock plain attack): besides mastering the ciphertext, the attacker also masters the corresponding relation between partial plaintext and the ciphertext.

(3) Choose plaintext attack (Chosen plaintextattack): the attacker knows the encryption algorithm and can select the plaintext and obtain the ciphertext corresponding to the corresponding plaintext.

(4) Ciphertext attack (Chosen cipertext attack) was Chosen: the attacker knows the encryption algorithm and can select the ciphertext and obtain the corresponding plaintext.

Obviously, the plaintext attack is the most effective attack method, and the attack of the method can be effectively resisted by adding the encryption algorithm, and the attack of other methods can also be effectively resisted.

However, choosing a plaintext attack is not effective for the present invention, mainly for the following two reasons: firstly, the invention has extremely high sensitivity to the key, and the input key can not be decrypted normally as long as the input key has slight change; secondly, plaintext information is introduced when the diffusion operation is carried out, so that cracking through a two-dimensional matrix of all 0 is impossible. In conclusion, the invention can effectively resist the classical attack.

5. Clear text sensitivity analysis

Sensitivity to plaintext means that when the pixel values in an image change slightly, a distinct ciphertext image is obtained. Analysis is generally performed using two parameters, NPCR (pixel rate of change) and UACI (normalized average change in pixels).

And inputting the same key to obtain two identical ciphertexts. One of the ciphertext images is taken, and the pixel value 174 of (438,337) is changed to 173, which can be obtained from equations (10) and (11), where NPCR is 99.64% and UACI is 33.78%. The result shows that the method has strong sensitivity to the plaintext and can effectively resist differential attack.

6. Key space analysis

The input keys of the invention are all of double-precision floating point type, and the effective bits reach 16 bits, so the key space reaches 10³²If the length of the key space is considered in the 400-bit binary bit group in the auxiliary key, the key space of the invention becomes larger, and it is almost impossible to obtain the plaintext image information through exhaustive attack. Therefore, the key space of the invention can effectively resist exhaustive attack, achieve the effect of safe transmission and ensure that the image information is not leaked.

Claims

1. A hyperchaotic image encryption method sequentially comprises a key initialization process, a scrambling transformation process and a Hyperhenon hyperchaotic mapping diffusion process, and is characterized in that,

(1) key initialization procedure

The encryption key K is composed of a binary auxiliary key K with the length of 400 bits₁Inputting a secret key X₀，Y₀The three parts are as follows;

step 1: firstly, a binary auxiliary secret K with the length of 400 bits is used₁Cutting into ten binary units with the length of 40 bits to obtain an auxiliary key matrix K₁₀，K₁₁，...，K₁₉；

Step 2: will input the key X₀，Y₀As an initial key of the Hyperhenon map, the following formula (1) is shown, where c is 1.76, d is 0.1, and X₀，Y₀Taking values between (0,1), and generating a group of hyperchaotic sequences for diffusion operation;

(2) scrambling transformation process

Step 1: dividing the N multiplied by M plaintext image into M column vector groups, and expressing the pixels of each vector group by 8-bit binary to obtain 8 multiplied by M column vector groups;

step 2: according to the auxiliary key matrix K₁₀，K₁₁，...，K₁₉Two control parameters v and w in the cat map are calculated as shown in equation (2) below:

and step 3: combining v and w obtained in step 2, and substituting each column vector subscript as an input variable into an Arnold mapping, as shown in the following formula (3), obtaining s and t, wherein r is 0,1, 2. s ═ 0,1, 2.., 8 × M denotes a new position scalar after the column vector is subjected to Arnold transform; t represents the number of bits rotationally shifted up the column vector bit group;

and 4, step 4: moving the column vector group represented by r into the column vector group represented by s according to the s obtained in the step 3, and circularly moving each element of the column vector group moved to the position of s upwards by t according to the t obtained in the step 3;

and 5: repeating the steps 3 and 4 for 8 times multiplied by M times to obtain an intermediate ciphertext B;

(3) hyperhenon hyper-chaotic map diffusion process

Step 1: changing the obtained binary intermediate cryptograph B into a decimal cryptograph P with the size of N multiplied by M;

step 2: setting an initial value X₀Is x₁，Y₀Is y₁Substituting the chaos sequence into a Hyperhenon hyperchaotic mapping system, discarding the previous 200 iteration results, and performing N × M iteration to obtain a chaos sequence L with the length of N × M ═ L₁，l₂，...，l_N×MSubstituting the obtained chaotic sequence L into the following formula (4) to transform the element value range to [0, 255 }]Get a new chaotic sequence

Q＝{q₁，q₂，...，q_N×M}

q_i＝mod(l_i×10⁵，256) 1≤i≤N×M (4)

And step 3: the following equation (5) is applied to each pixel of the intermediate ciphertext P, let c₀Is the average value of the pixel values of the intermediate ciphertext P, so that the correlation between the plaintext and the ciphertext is increased to achieve the pixel diffusion effect, and the final ciphertext C is obtained₁，c₂，...，c_N×M}。