CN109660696B - New image encryption method - Google Patents

New image encryption method Download PDF

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CN109660696B
CN109660696B CN201811457278.6A CN201811457278A CN109660696B CN 109660696 B CN109660696 B CN 109660696B CN 201811457278 A CN201811457278 A CN 201811457278A CN 109660696 B CN109660696 B CN 109660696B
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image
pixel
mapping
matrix
scrambled
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CN109660696A (en
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范冬梅
卢志茂
王贺
姚念民
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Dalian University of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/44—Secrecy systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0643—Hash functions, e.g. MD5, SHA, HMAC or f9 MAC

Abstract

The invention belongs to the field of image processing, and provides a novel image encryption method based on image blocking and coupling mapping grids. And finally, performing exclusive OR operation on the chaotic sequence generated by coupling the mapping grid and the scrambled pixel stream to realize diffusion operation on the image and generate a ciphertext image. The provided encryption algorithm has high key sensitivity and key space, can effectively resist various statistical attacks and brute force attacks, and has high safety. Therefore, the invention has strong applicability and safety.

Description

New image encryption method
Technical Field
The invention belongs to the field of image processing, relates to an image encryption method based on image blocking and coupling mapping lattices, and is particularly applied to an image encryption process.
Background
With the rapid development of computer image transmission technology in networks, especially in Internet networks, the security of digital images is becoming the focus of attention. There are special requirements for image encryption compared to text encryption. Mainly because digital images have the characteristics of large data space, high correlation and the like, most of the traditional encryption technologies are difficult to design image encryption algorithms. Therefore, many novel image encryption algorithms have been proposed in recent years, and one possible solution is an image encryption algorithm based on the chaos theory.
The core of image encryption generally comprises two major principles, and an image encryption algorithm framework based on the chaos theory also takes scrambling and diffusion as the algorithm core. During the scrambling process, the positions of the pixel points are repositioned without changing the size of the pixel values. In the diffusion process, the size of the pixel values is changed without changing their position, just the opposite; moreover, slight changes to a pixel may cause a great deal of pixel value variation. Scrambling and diffusion are two independent and iterative processes, but there is a necessary association between the two operations and the sequence of pixel values they acquire. At present, many encryption algorithms have the defects of insufficient anti-attack capability and the like, and the algorithm in the chapter completes the encryption of images by combining a mature space-time chaotic system after pixel points are scrambled according to a rule of loop iteration on the basis of image blocking, so that the safety of the algorithm is obviously improved.
Wang et al propose an image alternate encryption algorithm (X Wang, K Guo. A new image encryption algorithm based on a random map. nonlinear Dynamics,2014,76(4):1943-1950) for L organic mapping, and Wang also propose an image encryption scheme (XY Wang, XM. A novel block encryption system based on the same mapped random map Dynamics,2013,72(4):707-715) for coupling a mapping grid and a selector, and security analysis can find that the correlation among pixels is not strong enough, and information also shows that the degree of chaos is not strong enough, so that the attack resistance is not strong.
Disclosure of Invention
The invention aims to solve the problems of improving the safety, efficiency and the like of an encryption algorithm and provides an image encryption method combined with a mature theory. The method has the main idea that firstly, the image is subjected to blocking processing, then pixels in each pixel block are diffused to the whole image to realize the scrambling operation of the pixels, and then the scrambled pixels are subjected to corresponding exclusive OR operation by combining the coupling mapping grids to realize the encryption processing of the image. The specific technical scheme of the invention is as follows:
firstly, calculating the average value of the pixel sum and the pixel of the image, using the average value as a part of a secret key, and calculating an initial value of the chaotic system through a secure hash algorithm.
Step two, scrambling operation: and iteratively coupling the mapping grids through the initial value obtained in the first step and the auxiliary function, converting the generated chaotic sequence into a two-dimensional pixel matrix, then carrying out blocking operation on the matrix according to a proper size, diffusing the pixels in each pixel block into the pixel matrix for storing the scrambled image, and after iteration, finishing the operation of the whole image to generate the scrambled image.
Thirdly, diffusion: and generating another three groups of chaotic sequences by taking the coupling mapping grids in the second step, performing exclusive OR operation on the chaotic sequences and the scrambled image pixel stream after data processing, wherein the obtained processing result is the diffused image pixel value, and the change of the pixel value is realized.
The secure hash algorithm used in the first step is SHA-512, which is a supplement to the SHA-1 and SHA-2 algorithms, and has higher initial value sensitivity and stronger security. In the invention, firstly, a 512-bit hash value closely related to plaintext information is generated on the basis of the pixel sum of a known image through an SHA-512 algorithm, and then all initial values required by an iterative coupling mapping grid are generated, wherein the formula is as follows:
h＝SHA3-512(sum) (1)
Figure BDA0001887997170000031
in the formula (d)1、d2、d3And d4Are extracted from the hash value h, where each diRepresenting one byte. It should be noted that the initial value required for chaos can be obtained by a formula after binary system is first converted into decimal system.
The chaos used in the second and third steps is a coupling mapping grid, which is a high-dimensional system, so that the chaos has more complex characteristics of nonlinearity and high randomness, and is suitable for image encryption operation.
Figure BDA0001887997170000032
Where j is the spatial index, n is the temporal index, which is the coupling parameter, L is the number of bins auxiliary function f (x) is the L logistic map as follows:
f(x)＝x＝μx(1-x),x∈(0,1),μ∈[3.57,4](4)
the scrambling operation in the second step is: firstly, a one-dimensional chaotic sequence needs to be converted into a two-dimensional pixel matrix with the same size as an image, then the matrix is subjected to blocking processing according to the proper size, and if the matrix cannot be uniformly blocked, pixels 0 are added to the matrix for reconstruction. And diffusing the pixels in the first pixel block into a matrix for storing the scrambled image, and circularly iterating each pixel block to finally completely scramble the pixel positions of the original image.
The diffusion step in the third step is specifically to obtain three chaotic sequence streams, perform xor operation on the two sequence streams to obtain a modulus, and perform xor operation on the two sequence streams, the third sequence stream and the scrambled pixel stream to change the size of the scrambled pixel value, where the obtained diffusion data is the final ciphertext pixel. The safety of the algorithm is enhanced by high-complexity calculation for the exclusive-or operation.
The method has the advantages that the provided encryption algorithm is more excellent in effect, strong in safety, capable of resisting various attacks and strong in key sensitivity. The invention is designed based on a mature theory and has strong applicability and safety.
Drawings
Fig. 1 is a diagram of an encryption process of the present invention.
FIG. 2 shows the effects of encryption and decryption of the present invention, (a) L ena plaintext image, (b) L ena ciphertext image, (c) L ena decrypted image;
fig. 3 shows the histogram distribution of the present invention, (a) a plaintext image L ena, (b) a histogram of a plaintext image L ena, (c) a ciphertext image L ena, and (d) a histogram of a ciphertext image L ena.
FIG. 4 is a key sensitivity test of the present invention. (a) A successfully decrypted image; (b) a decrypted image with a slightly changed key; (c) difference between the two ciphertext images.
Detailed Description
The encryption of the present invention is described in more detail below in conjunction with FIG. 1
The flow of the encryption algorithm is as follows:
to avoid loss of generality, let the grayscale image P be M × N, where M is the number of rows and N is the number of columns.
1) If the total number of pixel values is not a multiple of 64, the modification is made to be suitable for the size of the image, the sum of pixel values sum, and the average value ag of pixel values are calculated, and the corresponding calculation formula is as follows:
Figure BDA0001887997170000041
Figure BDA0001887997170000042
the one-dimensional array corresponding to the image is g (i), and i ∈ (1, M × N).
2) First, a 512-bit hash value closely related to the plaintext image P is generated by equation (1), and then an initial value x for coupling the mapping lattices is generated from the k-th bit according to the secure hash algorithm of equation (2)0(j),j∈0,1,2…L。
3) By means of an initial parameter x0(j) And two auxiliary functions are mapped by the logistic chaos represented by the formula (4), and chaos sequences for diffusion operation can be obtained by iterative coupling mapping grid formula (3). recording the generated value of each grid, M × N ×L chaos sequences are generated in total.
4) Taking a grid g generated in the previous step1(i) The total M × N chaotic sequences are processed according to the formula (7) and are used for scrambling the image, and then three grids g in the previous step are taken2(i),g3(i) And g4(i) The chaotic sequence of (a) is used for a diffusion operation, which is processed according to equation (8-10):
c(i)＝(g1(i)×1015+ag×1015)mod(M×N) (7)
e1(i)＝(g2(i)×1015+sum×106)mod 256 (8)
e2(i)＝(g3(i)×1015+ag×1013)mod 256 (9)
e3(i)＝(g4(i)×1015)mod256 (10)
5) one dimension to be used for scramblingThe chaotic sequence c (i), i ∈ 0,1, … M × N is converted into a two-dimensional matrix H with the same size as the plaintext image P1Reproducing a two-dimensional matrix H2And the method is used for storing the scrambled pixel points. Will matrix H1Is divided into Z blocks, each block contains 64 pixel points, and simultaneously the matrix H is divided into2Is divided into 64 blocks, each block has the size of Z1Sum/64 pixels, wherein Z and Z1Are equal in value. H is to be1Respectively storing 64 pixel points of the first block image in H2In the first position of each of the 64 images, then H will be1The 64 pixel points in the second image block are also stored in H2And in the second position of each block, after the cyclic operation is performed for Z times, scrambling operations of all pixel points are completed, and a scrambled image Pc is generated.
6) The chaos sequence generated by the equation (8-10) and the scrambled image pixel stream are subjected to exclusive-or operation, and the process is as follows:
Figure BDA0001887997170000051
Figure BDA0001887997170000061
where pc (i) is the image pixel value scrambled in step 5, and pe (i) is the encryption result of pc (i), i.e., the pixel value of the ciphertext image finally obtained.
So far, the image encryption operation of the algorithm is completely finished, and a ciphertext image Pe is generated.
The decryption of the invention is illustrated as follows:
the encryption algorithm provided by the chapter has reversibility, the decryption processing process of the algorithm is very similar to the encryption process, and some steps are executed reversely.
1) The method comprises the steps of firstly, calculating all parameters needed in the decryption process according to a secure hash algorithm, a coupling mapping grid and the like used in an encryption algorithm through a known secret key, and only executing according to an encryption step as the secret key comprises the sum of pixel values, an average value, an initial value of chaotic mapping and the like.
2) And carrying out XOR decryption operation on the ciphertext image through the inverse operation of the sixth step of the encryption step to obtain a scrambled image Pc.
3) And (3) carrying out decryption operation on the scrambling step, firstly dividing the scrambled image into 64 blocks, extracting the first pixel value of each block, taking the 64 pixel values as the first block of the plaintext image, and repeating iteration for a plurality of times to obtain a plaintext image pixel matrix.
4) And converting the pixel matrix into a plaintext image, wherein the obtained result is the decrypted image P.
3, the algorithm is analyzed by combining the data in the attached drawings and tables as follows:
TABLE 1 plaintext and ciphertext image correlation coefficients
Figure BDA0001887997170000062
TABLE 2 entropy of information of the invention and comparison with existing algorithms
Figure BDA0001887997170000071
TABLE 3 NPCR and UACI values for ciphertext images with a change of one bit in the plaintext image and comparison to existing algorithms
Figure BDA0001887997170000072
Table 1 shows correlation coefficients of adjacent pixels in three directions of a plain text and a cipher text of an L ena image, and it can be found from data in the table that the encryption algorithm proposed by the present invention well breaks strong correlation between the adjacent pixels and can well resist attacks such as statistical analysis, Table 2 shows a comparison result of the algorithm of this chapter with other algorithms, and under a completely random condition, the magnitude of the entropy of the image is 8, and it can be found from the table that the entropy of the information of the present invention is very close to a theoretical value, so the present invention can safely resist the attacks of the entropy analysis, in order to effectively resist differential attacks, a subtle change in the plain text image should make the cipher text image completely change, it can be known from the implementation data of Table 3 that the present invention has high security compared with other algorithms, it can effectively resist known plain text attacks, for the encryption system, the statistical characteristic of the cipher text image is an important index, the cipher text image should have a certain robustness to resist any arbitrary statistical analysis attacks, and it can be seen that the cryptographic key has a very good security of L images and a very high security of the cryptographic key is selected to resist a relatively strong statistical analysis of the cryptographic key of the cryptographic system, and a relatively high security of the cryptographic key of the cryptographic image, and the present invention can be considered that the cryptographic key has a very good security of a very good key of a very good cryptographic system, and a very good cryptographic key, and a very good cryptographic system, and a very good cryptographic key of this invention can be selected to show that the invention, and a very good cryptographic system has a very good key, and a very good key of this invention.

Claims (3)

1. A new image encryption method, comprising the steps of:
firstly, calculating the pixel sum of an image and the average value of the pixel, using the pixel sum as a part of a secret key, and calculating an initial value of a chaotic system through a secure hash algorithm;
step two, scrambling operation: iteratively coupling the mapping grids through the initial values and the auxiliary functions obtained in the first step, converting the generated one-dimensional chaotic sequence into a two-dimensional pixel matrix with the same size as the image, then carrying out blocking processing on the matrix according to the proper size, and adding pixels 0 to the matrix for reconstruction if the matrix cannot be uniformly blocked; diffusing the pixels in the first pixel block into a matrix for storing the scrambled image, then circularly iterating each pixel block, finally completely scrambling the pixel position of the original image, completing the operation of the whole image and generating the scrambled image;
thirdly, diffusion: and generating another three groups of chaotic sequence streams by taking the coupling mapping grid in the second step, performing exclusive OR operation on the two sequence streams to obtain a module, performing exclusive OR operation on the two sequence streams, the third sequence stream and the scrambled pixel stream, and changing the size of the scrambled pixel value to obtain diffusion data, namely the final ciphertext pixel.
2. A new image encryption method according to claim 1, characterized in that the coupling mapping grid used in the second and third steps is a typical CM L, the kinetic formula of which is:
Figure FDA0002416974120000011
where is the coupling parameter, n is the time index, j is the space index, L is the number of bins, and the mapping function f (x) is the L logistic mapping as follows:
f(x)＝x＝μx(1-x),x∈(0,1),μ∈[3.57,4](4)。
3. a new image encryption method according to claim 1 or 2, characterized in that the secure hash algorithm used in the first step is SHA-512, and the initial value for chaotic mapping is obtained by the following steps
h＝SHA3-512(sum) (1)
Figure FDA0002416974120000012
In the formula (d)1、d2、d3And d4Are extracted from the hash value h, where each diRepresenting one byte.
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