CN113595715A - Logistic-based double-pixel rectangular mapping color image encryption and decryption method - Google Patents

Logistic-based double-pixel rectangular mapping color image encryption and decryption method Download PDF

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CN113595715A
CN113595715A CN202110839190.6A CN202110839190A CN113595715A CN 113595715 A CN113595715 A CN 113595715A CN 202110839190 A CN202110839190 A CN 202110839190A CN 113595715 A CN113595715 A CN 113595715A
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image
color
logistic
encryption
color image
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莫佳
谭素琴
刘美香
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East China Jiaotong University
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    • 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
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • 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
    • H04N1/46—Colour picture communication systems
    • H04N1/56—Processing of colour picture signals

Abstract

The invention relates to the technical field of information security and image processing, and provides a color image encryption and decryption method. The method can quickly finish the encryption and decryption of various color images, and the encrypted ciphertext image destroys the structure of the plaintext image and can effectively resist the statistical attack of the image pixel frequency. The color image encryption method comprises the steps of firstly constructing a color key image for controlling an encryption algorithm and a decryption algorithm; secondly, preprocessing the plaintext color image by using a Logistic chaotic system, then searching ciphertext pixels in a rectangle formed by the key image by using double pixels as groups in each channel of the plaintext image, and finally outputting the ciphertext color image. The method has high encryption efficiency and strong practicability, can effectively resist frequency statistics attack and plaintext selection attack, has good encryption effect, can be applied to scenes such as generation, storage, transmission and the like of color images, and effectively protects the confidentiality of the color images.

Description

Logistic-based double-pixel rectangular mapping color image encryption and decryption method
Technical Field
The invention relates to the field of information security, in particular to a method for encrypting and decrypting a color image based on Logistic double-pixel rectangular mapping.
Background
At present, computer networks and multimedia technologies are rapidly developed, and people generally use various images to express information in work and life, wherein color images are used more frequently. The security of color images is challenging due to their widespread use. The encryption algorithms such as AES and RSA commonly used in the field of information security cannot be directly applied to the security implementation of color images. This is due to the fact that on the one hand the amount of color image data is very large, especially for high-resolution color images which are often used today; on the other hand, the traditional encryption algorithm mainly aims at text data during design, so that the encryption algorithm is complex, for example, the DES algorithm needs 16 iterations, the AES algorithm iterates at least 10 iterations, and the public key algorithm such as RSA is less efficient than the DES algorithm.
The attractor dimension of the chaotic system is fractal dimension, has a very complex fractal structure and good unpredictability, and the chaotic system has extreme sensitivity to initial conditions and parameters, so the chaotic system can be used in the field of data confidentiality. The existing chaos-based image security technology generally performs encryption processing on an image on the basis of chaos mapping. For example, patent publication No. CN108234813A discloses a plaintext associated image encryption algorithm based on hyperchaotic Chen system, which generates four pseudo-random sequence matrices through the Chen chaotic system, and then performs operations such as forward diffusion, scrambling and reverse diffusion on a plaintext image, thereby obtaining a final ciphertext image. Although the method solves the problem that the key space of the Logistic chaotic system is small, the process is complex, and the image encryption is not favorable. In general, the problems of the prior art are: the algorithm is complex, so that the efficiency is low when the image is encrypted and decrypted, the time is consumed, and the method is particularly suitable for encrypting the color image; the security of the algorithm needs to be further improved.
Disclosure of Invention
In order to solve the technical problems, the invention provides a method for encrypting a color image based on Logistic double-pixel rectangular mapping, which constructs a rectangular mapping function on the basis of a chaotic system and well balances the relationship between algorithm complexity and safety.
The technical purpose of the invention is realized by the following technical scheme:
a color image encryption method based on Logistic double-pixel rectangular mapping comprises the following steps:
step 101: according to the seed key k ═ k1,k2) K in (1)1Constructing a color key image IK；
Step 102: for the read-in plain text color image IPConverting into RGB color space, and further separating to R, G, B channels to obtain three plaintext subimages
Figure BDA0003178324900000021
Step 103: according to k2Disturbing the three plaintext sub-images obtained in the step 102 by using a Logistic chaotic system to obtain
Figure BDA0003178324900000022
Step 104: the sub-image obtained in step 103
Figure BDA0003178324900000023
Respectively executing rectangular mapping operation to obtain respective ciphertext sub-images
Figure BDA0003178324900000024
Step 105: three ciphertext sub-images obtained in the step 104
Figure BDA0003178324900000025
Synthesized into a final ciphertext image IC。
Preferably, the color key image I is constructed in step 101 according to the seed keyK(ii) a The seed key is composed of integers between 0 and 255, the length of the seed key is variable, the maximum length is 256, which is equivalent to 2048 bits long, and a constructed key image IKExpressed as RGB space of
Figure BDA0003178324900000026
Preferably, the RGB color model is used to represent the input plaintext color image in step 102, resulting in three component sub-images.
As a preferred scheme, the Logistic chaotic system mathematical model adopted in step 103 is as follows:
xk+1＝μxk(1-xk) (1)
wherein x isk，xk+1∈(0，1)，μ∈(0，4]When 3.5699456 < mu < 4, the system enters a chaotic state.
Preferably, the plaintext sub-images are processed in step 104
Figure BDA0003178324900000031
Respectively using two pixels as a group, inputting the two pixels into a rectangular function f to respectively obtain three ciphertext sub-images
Figure BDA0003178324900000032
The rectangular function f is defined as:
Figure BDA0003178324900000033
wherein row and col respectively represent the row number and the column number of the pixel pix; l, U denote pixels immediately to the left and top of the pixel, respectively.
As a preferred scheme, in step 105, the three ciphertext sub-images are synthesized into an image of one channel by using an RGB model, so as to obtain a final ciphertext image.
Preferably, the decryption algorithm is the inverse of the encryption algorithm.
In conclusion, the invention has the following beneficial effects:
1. the method for encrypting the color image based on Logistic double-pixel rectangular mapping can quickly finish encryption and decryption of various color images, and a ciphertext image obtained by encryption destroys the structure of a plaintext image, so that the statistical attack of the image pixel frequency can be effectively resisted;
2. the color image encryption method based on Logistic double-pixel rectangular mapping has high encryption efficiency and strong practicability, can effectively resist frequency statistics attack and plaintext selection attack, has good encryption effect, can be applied to scenes such as generation, storage, transmission and the like of color images, and effectively protects the confidentiality of the color images.
Drawings
FIG. 1 is a schematic diagram of an encryption process according to an embodiment of the present invention;
FIG. 2 is a block diagram illustrating a decryption process according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of key image construction scan in an embodiment of the invention;
fig. 4 is a diagram of encryption effect in the embodiment of the present invention.
Detailed Description
This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. "substantially" means within an acceptable error range, within which a person skilled in the art can solve the technical problem to substantially achieve the technical result.
The present invention will be described in further detail below with reference to the accompanying drawings, but the present invention is not limited thereto.
First, a color key image I is constructed from a seed keyKThe seeds of the optical fiber are composed of integers from 0 to 255, the length of the optical fiber is variable, the longest optical fiber is 256, and the length of the optical fiber is 2048 bits; constructed key image IKCan be expressed as RGB space
Figure BDA0003178324900000041
Wherein, the color key image IKThe construction method of (2) is as follows:
1. inputting a chaotic initial value;
2. generating a sequence L1 with the size of L (0< L <256) by using a Logistic chaotic system;
3. amplifying each value of the sequence obtained by the chaotic system by 1000 times, and then performing modulus selection on 256 to obtain L2;
4. filling L2 in the matrix of 16 x 16 in the order of FIG. 3 scanning, skipping repeated digits without writing, and filling the rest in the order of small to large in FIG. 3 until the whole matrix position is filled, to obtain the key image I of 16 x 16 sizeK。
Color key image IKThe construction principle of (1) is as follows: the key is a 16-order square matrix consisting of 256 gray-scale pixels. I isKThe derivation depends on the seed key k1, repeated unwritten, with the remainder filled in pixel-wise order from small to large.
Then, starting the image encryption process, and reading in the plaintext color image IPConverting into RGB color space, expressing the input plaintext color image by RGB color model, further separating to R, G and B channels to obtain three plaintext sub-images
Figure BDA0003178324900000051
Then according to k2Disturbing the three plaintext sub-images obtained in the step 102 by using a Logistic chaotic system to obtain
Figure BDA0003178324900000052
The Logistic chaotic system mathematical model comprises the following steps:
xk+1＝μxk(1-xk) (1)
wherein x isk,xk+1∈(0,1)，μ∈(0,4]When 3.5699456<μ<And 4, the system enters a chaotic state.
At the same time, the plaintext subimages are processed
Figure BDA0003178324900000053
Respectively inputting two pixels into a rectangular function f as a group, and respectively executing rectangular mapping operation to obtain respective ciphertext sub-images
Figure BDA0003178324900000054
The rectangular function f is defined as:
Figure BDA0003178324900000061
wherein row and col respectively represent the row number and the column number of the pixel pix; l, U denote pixels immediately to the left and top of the pixel, respectively.
And finally, obtaining three ciphertext sub-images by adopting an RGB (red, green and blue) model for the three ciphertext sub-images
Figure BDA0003178324900000062
Synthesizing into a channel image to obtain the final ciphertext image IC。
The above methods (algorithms) are all reversible, and the decryption algorithm is the inverse process of the above encryption algorithm.
The present embodiment is only for explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.

Claims (7)

1. A color image encryption method based on Logistic double-pixel rectangular mapping is characterized by comprising the following steps:
step 101: according to the seed key k ═ k1,k2) K in (1)1Constructing a color key image IK；
Step 102: for the read-in plain text color image IPConverting into RGB color space, and further separating to R, G, B channels to obtain three plaintext subimages
Figure FDA0003178324890000011
Step 103: according to k2And performing three plaintext sub-images obtained in the step 102 by using a Logistic chaotic systemDisorder to obtain
Figure FDA0003178324890000012
Step 104: the sub-image obtained in step 103
Figure FDA0003178324890000013
Respectively executing rectangular mapping operation to obtain respective ciphertext sub-images
Figure FDA0003178324890000014
Step 105: three ciphertext sub-images obtained in the step 104
Figure FDA0003178324890000015
Synthesized into a final ciphertext image IC。
2. The method for encrypting a color image based on Logistic double-pixel rectangular mapping according to claim 1, wherein the step 101 constructs a color key image I according to a seed keyK(ii) a The seed key is composed of integers ranging from 0 to 255, the length of the seed key is variable, the maximum length is 256, and a constructed key image IKExpressed as RGB space of
Figure FDA0003178324890000016
3. The method according to claim 1, wherein the step 102 represents the inputted plaintext color image by using an RGB color model to obtain three component sub-images.
4. The method for encrypting the color image based on Logistic double-pixel rectangular mapping according to claim 1, wherein the Logistic chaotic system mathematical model adopted in the step 103 is as follows:
xk+1＝μxk(1-xk) (1)
wherein x isk,xk+1∈(0,1)，μ∈(0,4]When 3.5699456<μ<And 4, the system enters a chaotic state.
5. The method of claim 1, wherein the plaintext sub-image is encrypted in step 104 according to a Logistic two-pixel rectangular mapping color image encryption method
Figure FDA0003178324890000021
Respectively using two pixels as a group, inputting the two pixels into a rectangular function f to respectively obtain three ciphertext sub-images
Figure FDA0003178324890000022
The rectangular function f is defined as:
Figure FDA0003178324890000023
wherein row and col respectively represent the row number and the column number of the pixel pix; l, U denote pixels immediately to the left and top of the pixel, respectively.
6. The method for encrypting the color image based on Logistic double-pixel rectangular mapping according to the claim 1, wherein the three ciphertext sub-images are synthesized into the image of one channel by adopting an RGB model in the step 105, and the final ciphertext image is obtained.
7. The method of encrypting a color image based on Logistic two-pixel rectangular mapping according to claim 1, wherein the decryption algorithm is the inverse process of the encryption algorithm.
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