CN113129196B - Image encryption method based on DNA sequence and memristor chaos - Google Patents
Image encryption method based on DNA sequence and memristor chaos Download PDFInfo
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Abstract
The invention provides an image encryption method based on a DNA sequence and memristor chaos, which is used for improving the existing single DNA scrambling mode.
Description
Technical Field
The invention relates to an image encryption method based on a DNA sequence and memristor chaos.
Background
With the coming of the information era and the rapid development of the internet technology and the mobile communication technology, intelligent terminals such as smart phones are rapidly popularized and applied due to portability and practicability, and the life of people is greatly facilitated. Under the situation, digital images have become the main media for people to communicate information due to the characteristics of intuitiveness, large information carrying capacity and the like. However, due to the openness of the network, the digital image is at risk of being tampered and stolen during transmission, and people face a huge challenge on privacy security. In order to ensure the information security of digital images and protect the personal privacy of people, digital images are urgently required to be encrypted. However, due to the particularity of the image information, the existing algorithm suitable for text encryption is not suitable for encrypting the image information, and the encryption and decryption speed, real-time performance, format requirements before and after image encryption and fidelity of the algorithm are difficult to meet the requirements of image encryption.
The chaos is very suitable for image encryption due to the characteristics of initial value sensitivity, dimensionality, non-periodicity and the like. In recent years, as a unique image encryption technology, chaotic image encryption has become a research hotspot in the field of image encryption, and a plurality of chaotic-based image encryption algorithms appear at present. However, in these achievements, most of the adopted chaotic systems are discrete chaotic systems and general low-dimensional chaotic systems, and the chaotic systems have the problems of simple equation, small initial value and parameter quantity as keys, and the like, so that the key space is not large, and the encryption effect is not good.
In 1971, cai Shaotang proposed the concept of a memristor, which is a fourth component besides three traditional electronic components, namely a resistor, a capacitor and an inductor, and a physical memristor component was manufactured subsequently by the engineering community. The new element called as a memory resistor is applied to the research of chaotic circuits quickly because of the extremely strong sensitivity to the initial value, and a plurality of memristive chaotic systems are generated. Due to the memory function of the memristor and the complexity of the system, the memristor chaotic system has stronger noise-like characteristics and more complex dynamic characteristics than other chaotic systems, and has stronger confidentiality when being applied to image encryption, so that the application of the memristor chaotic system in the image encryption attracts the attention of some scholars. However, in general, the memristive chaotic image encryption research is still in a starting stage, and the research result is few and immature.
In the current research results of chaotic image encryption, most chaotic systems for generating chaotic pseudo-random series adopt a discrete chaotic system and a low-dimensional chaotic system, and documents for researching chaotic image encryption by applying a memristive chaotic system, namely a emerging chaotic system, are relatively few, and the main research results are as follows: document application of memristive chaotic circuit in image encryption (Chinese geological university, 2016) proposes an image encryption algorithm based on a charge-control memristive chaotic system, the algorithm takes parameters and initial state variable values of the memristive chaotic system as keys, a discrete chaotic pseudorandom sequence is obtained by sampling the memristive chaotic system in a certain step length, and then the chaotic pseudorandom sequence is encoded and then subjected to exclusive or operation with a pixel matrix, so that image encryption is realized. Shi Haonan et al, "multi-stable encryption of color image memristor system based on Python" (science of complex system and complexity, 2018) applies a four-dimensional magnetic control memristor chaotic system to image encryption, obtains four groups of chaotic pseudorandom series through iteration and discrete sampling by taking an initial value of a state variable of the memristor chaotic system as a key, and then obtains three groups of chaotic pseudorandom series to be respectively subjected to exclusive-or operation with a pixel matrix of three components of image RGB, thereby finally realizing image encryption. Cheng Yunlong design and implementation of a memristive hyper-chaotic system-based medical image encryption algorithm (university of Henan, 2016) proposes an image encryption algorithm combined with a memristive hyper-chaotic system, wherein a discrete chaotic pseudorandom series is generated by a four-dimensional memristive hyper-chaotic system constructed on the basis of a classical Chua circuit, then scrambling is performed twice by taking different chaotic pseudorandom sequences as parameters, and chaotic images are encrypted after single diffusion. The algorithm fully applies the pseudo-randomness of the memristive chaotic system, and the encryption effect is good. Min Fugong et al, "novel memristor chaotic circuit and application thereof in image encryption" (electronics and informatics, 2016 "), applies memristor chaos generated by a novel memristor chaotic circuit to image encryption, firstly sets a simple hyperbolic sine nonlinear curve by using a memristor model, carries out xor operation on an image to be encrypted for preprocessing, and then exchanges a chaotic sequence and a pixel value to finally realize image encryption. Yangkang design and implementation of chaos system-based image encryption algorithm (Henan university, 2017) combined with cellular automata, memristive chaos system and DNA technology, provides an image encryption algorithm. The algorithm has the advantages that the secret key can be dynamically selected, and the safety of the algorithm is enhanced.
In the study we found: the adoption of the memristor chaotic system greatly improves the security of chaotic image encryption, but the existing research result about memristor chaotic image encryption still has some points worth improvement:
(1) Some documents only use the chaotic sequence to carry out scrambling and diffusion operations on the image, and do not consider image encryption combined with other scrambling modes, and the algorithm is relatively single.
(2) Some documents adopt a single scrambling mode, do not use memristor chaos to control scrambling operation, and do not fully utilize a key space.
Therefore, other scrambling modes are combined with the memristive chaotic system camera, and the memristive chaotic is applied to control the scrambling operation so as to fully utilize the key space, so that the image encryption performance of the memristive chaotic is undoubtedly enhanced, and the attack resistance of the image encryption is improved.
For scrambling operation in image encryption, wei Anzheng research on image encryption method based on chaotic mapping and DNA coding (the university of western electronic technology, 2014) adopts a chaotic image encryption algorithm combining chaotic mapping and DNA technology. The algorithm image scrambling link adopts a method of combining a DNA base pair pairing rule with a DNA algorithm, and chaotic mapping is not used to participate in scrambling, so that the encoding rule is easy to be always solidified in one of the chaotic mapping, the diversity of the encoding rule is not combined with a chaotic sequence, and a certain key space is wasted.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an image encryption method based on a DNA sequence and memristive chaos, wherein an image pixel matrix and a chaotic matrix generated by a memristive chaotic system are subjected to an exclusive OR operation to generate a diffusion matrix, then a chaotic pseudorandom sequence generated by the memristive chaotic system is adopted as a parameter to dynamically extract a DNA code to generate a coding rule, and then the coding rule is utilized to scramble the diffusion matrix, so that chaotic image encryption is realized. MATLAB software is applied to simulate the method, and the algorithm is analyzed through image encryption performance indexes such as key space, histogram, information entropy, adjacent pixel correlation and the like, so that the method is proved to have good encryption performance.
The technical scheme of the invention is realized as follows:
an image encryption method based on a DNA sequence and memristor chaos comprises the following steps:
s1, reading an image to obtain a matrix A;
s2, selecting the Chua memristive chaotic system of the formula (1)
Wherein x, y, z and w are state variables, alpha, beta and xi are system parameters, the parameters are alpha =4, beta =0.7 and xi =0.1, the initial value of the state variables (0.01,0,0, -1.1) is iterated by a Runge-Kutta method with the step length of 0.1 to obtain a chaotic real number sequence x i ,y i ,z i ,w i ；
S3, according to the following formula
For chaotic real number sequence x i ,y i ,z i ,w i Processing to obtain a chaotic sequence K, KZ, and converting the chaotic sequence into a matrix H, HZ; wherein [. ]]Is a rounding function;
s4, performing pixel fusion on the original image matrix A and the chaotic sequence K to obtain a diffusion matrix P, and converting each pixel of P and HZ into a binary system;
s5, for the chaotic matrix x i ,y i ,z i ,w i Carrying out rounding treatment and then 8 modulus treatment so as to carry out DNA coding on the treated diffusion matrix P and the chaos matrix HZ corresponding to one coding mode in 8 coding rules of the DNA sequence to obtain DNA nucleotide strings PP and HH;
and S6, adding PP and HH according to the DNA addition rule to obtain a DNA ciphertext sequence LL. Repeating the fourth and fifth steps for N times;
and S7, decoding the ciphertext sequence LL into a binary sequence according to the coding rule in the fifth step, converting the binary sequence into a decimal system, and forming a two-dimensional matrix to obtain an encrypted image.
Preferably, the first 400 sets are removed when iterating with the Runge-Kutta method with a step size of 0.1 to avoid transient effects from affecting the results.
The invention has the following beneficial effects: (1) The chaos memristor pseudo-random sequence is adopted to dynamically select the DNA coding rule for scrambling, so that the confidentiality is high; (2) The chaotic pseudo-random system is generated by a Gao Weiyi chaotic system, and has more parameters and initial values as a secret key and large secret key space; and (3) the encryption calculation amount is small, and the encryption and decryption speed is high.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without paying creative efforts.
Fig. 1 is a schematic diagram of the encryption process of the present invention.
Fig. 2 is a schematic diagram of the decryption process of the present invention.
Fig. 3 shows images before and after encryption, where fig. 3 (a) shows an original image before encryption and fig. 3 (b) shows an image after encryption.
Fig. 4 is an image after key error decryption.
Fig. 5 is an image after the key is correctly decrypted.
Fig. 6 is histograms before and after encryption, where fig. 6 (a) is a gray level histogram of an original image and fig. 6 (b) is a gray level histogram of a ciphertext image.
Fig. 7 shows correlation diagrams in each direction before and after encryption, where fig. 7 (a) is a correlation diagram of an original Lena in the horizontal direction, fig. 7 (b) is a correlation diagram of a ciphertext image in the horizontal direction, fig. 7 (c) is a correlation diagram of an original Lena in the vertical direction, fig. 7 (d) is a correlation diagram of a ciphertext image in the vertical direction, fig. 7 (e) is a correlation diagram of an original Lena in the diagonal direction, and fig. 7 (f) is a correlation diagram of a ciphertext image in the diagonal direction.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the following embodiments of the present invention, and it should be apparent that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Before describing the present invention, the following rules for encoding and calculating the relevant DNA sequences to be used are introduced: 1. DNA sequence coding and calculation rules
(1) DNA sequence coding
The main constituent unit of DNA is deoxyribonucleotide, which consists of four different nucleotides, adenine (a), thymine (T), cytosine (C) and guanine (G), respectively. Although the pairing of DNA base pairs is simple, there are many sequences of pairing, and the information corresponding to different sequences is different, so that the DNA molecules composed of a plurality of nucleotides have diversity. Due to the base complementary principle, 4! Only 8 of the seed coding rules meet the standard as in table 1.
TABLE 18 coding rules for DNA sequences
| Model (II) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| A | 10 | 11 | 01 | 11 | 00 | 10 | 01 | 00 |
| C | 11 | 01 | 11 | 10 | 10 | 00 | 00 | 01 |
| G | 00 | 10 | 00 | 01 | 01 | 11 | 11 | 10 |
| T | 01 | 00 | 10 | 00 | 11 | 01 | 10 | 11 |
When a gray scale image is selected, a gray scale binary sequence can be represented by 4 DNA bases using one of the 8 coding rules described above, e.g., gray scale value 109 is converted to binary sequence 01101101, and the nucleotide sequence TACT can be obtained by the first coding rule in Table 1. However, if a different coding rule is used, such as the 2 nd type, a different nucleotide sequence CGAC is obtained. This feature can be applied to the processing of pixel values, where binarized pixel values are processed with the encoding rules of a particular DNA to form a string of nucleotides. The results obtained after the same picture is coded by using different coding rules are very different.
(2) Rule of calculation of DNA
Algebraic operations such as addition and subtraction can be performed between every two DNA sequences. Addition and subtraction of DNA sequences is still a mathematical operation on a two-digit binary number represented by a base pair. There are 8 corresponding relations based on DNA coding, and there are 8 corresponding addition and subtraction methods. As shown in the following figures, all the addition and subtraction results are unique and equal to the number of digits of the number to be operated.
TABLE 2 DNA sequence addition
The algebraic operation of the DNA sequence is applied to the image encryption, the pixel values can be scrambled, and the safety of the image encryption can be improved. After the image matrix is converted into a DNA sequence, a group of known DNA sequences with the same length and the same coding rule are used for carrying out the same algebraic operation with the DNA sequence, and finally the obtained sequence is subjected to DNA decoding, so that the image encryption effect is more remarkable than that of the chaos sequence encryption, and the decoding difficulty is higher.
TABLE 3 DNA sequence subtraction
| — | A | G | C | T |
| A | A | T | C | G |
| G | G | A | T | C |
| C | C | G | A | T |
| T | T | C | G | A |
2. Image encryption algorithm
First, the steps of the encryption algorithm are described. The encryption algorithm firstly carries out XOR operation on an image pixel matrix and a chaotic matrix generated by a memristive chaotic system to generate a diffusion matrix, then uses a chaotic pseudorandom sequence generated by the memristive chaotic system as a parameter to dynamically extract various codes, and then scrambles the diffusion matrix and the chaotic matrix according to an extracted coding rule, thereby realizing image encryption. As shown in fig. 1, the specific steps are as follows:
the first step is as follows: reading the image to obtain a matrix A.
The second step: selecting the following Chua memristive chaotic system
Wherein x, y, z and w are state variables, and alpha, beta and xi are system parameters. Taking parameters alpha =4, beta =0.7 and xi =0.1 of Chua memristive chaotic system in formula (1), carrying out iteration 10000 times by a Runge-Kutta method with the step size of 0.1 and taking initial values (0.01,0,0, -1.1) of state variables, removing the previous 400 groups to avoid the influence of transient effects on the result, and obtaining a chaotic real number sequence x i ,y i ,z i ,w i 。
The third step: according to the formula
For chaotic real number sequence x i ,y i ,z i ,w i Processing to obtain chaotic sequence K, KZ, and converting into 256 × 256 dimensional matrix H, HZ, wherein [ ·]Is a rounding function.
The fourth step: and carrying out pixel fusion on the original image matrix A and the chaotic sequence K to obtain a diffusion matrix P. And (4) converting each pixel of the P and the HZ into a binary system.
The fifth step: for the chaos matrix x i ,y i ,z i ,w i Rounding and modulo 8 are performed to select one of the encoding modes in Table 1, and the processed diffusion matrix P and mixture are processedThe chaos matrix HZ is used for DNA encoding to obtain DNA nucleotide strings PP and HH.
And a sixth step: PP and HH are added according to the DNA addition operation rule in the table 2 to obtain a DNA ciphertext sequence LL. Repeating the fourth and fifth steps for N times.
The seventh step: and decoding the ciphertext sequence LL into a binary sequence according to the coding rule in the fifth step, converting the binary sequence into a decimal system, and forming a 256 multiplied by 256 dimensional matrix to obtain an encrypted image.
3. Image decryption algorithm
The steps of the decryption algorithm shown in fig. 2 are the inverse of the encryption algorithm, and the decryption process is as follows:
the first step is as follows: first, the equation (1) is iterated (NxN/4) times according to the secret key to generate four groups of chaotic sequences, and the chaotic sequences are arranged in a pairwise crossing manner.
The second step is that: and (3) obtaining two groups of new pseudo-random sequences according to the formula (2), and arranging the two groups of obtained chaotic sequences into a two-dimensional matrix J, JM.
The third step: for the chaos matrix x i ,y i ,z i ,w i And (3) processing, namely, firstly taking the whole and then taking the module 8, correspondingly selecting one coding mode in the table 1, and carrying out DNA coding on the processed ciphertext matrix A and the chaos matrix J to obtain a DNA nucleotide string P, H.
The fourth step: and performing DNA subtraction operation on the DNA nucleotide string P, H to obtain the diffusion matrix W.
The fifth step: and carrying out pixel fusion on the diffusion matrix W and the chaotic sequence JM to obtain a plaintext matrix P. And (4) decoding the binary sequence to obtain a binary sequence, and repeating the third step and the fourth step for N times. And forming a 256 × 256 matrix by the obtained sequences, and converting the sequence into a decimal system to obtain a decrypted image.
4. Simulation result
In order to verify the effectiveness of the algorithm, MATLAB software is used for simulating the method, lena images are used during simulation, the algorithm provided by the chapter is used for encryption, the images are scrambled by using DNA sequence coding and computable properties, four chaotic sequences generated by a Chua memristive chaotic system with parameters of alpha =4, beta =0.7, xi =0.1 and initial values of state variables of (0.01,0,0, -1.1) are combined into two groups of sequences according to a certain rule, the two groups of sequences are subjected to exclusive OR operation with the images, coding rules are selected, DNA addition operation is carried out, and the images are finally encrypted, wherein the encryption effect is shown in figure 3.
As can be seen from fig. 3, the ciphertext image is directly observed with the naked eye, and no information related to the plaintext is obtained, so that the ciphertext image is a noise-like image.
If in the decryption process, if w in the initial value 0 Changing the image from-1.1 to-1.0999999, the decryption method is unchanged, the ciphertext image is decrypted, and the result obtained by simulation is shown in fig. 4; the result of decrypting the ciphertext using the initial value of the state variable during encryption is shown in fig. 5. Therefore, it can be seen that the sensitivity of the memristive chaotic system to the initial value is very different, and if the initial value is unknown, the original image cannot be recovered; the image encryption algorithm is proved to have high sensitivity to the key (initial value and parameter) and good encryption performance.
5. Algorithm performance analysis
The performance of the algorithm is analyzed by the image encryption performance indexes such as a cipher space, a histogram, information entropy, adjacent pixels and the like.
(1) Key space analysis
The key of the invention specifically comprises: system parameters alpha, beta, xi and system initial value x 0 ,y 0 ,z 0 ,w 0 If the simulation computer precision is 32 bits, the key space of the algorithm is about (2) 32 ) 3 ×(2 32 ) 4 ＝2 224 The global key space is much larger than 2 100 It is quite obvious that the key exhaustion value of the present algorithm is larger than 2 100 Therefore, the ability to resist brute force is described.
(2) Histogram analysis
Fig. 6 is a gray level histogram of an original Lena and an image encrypted by the algorithm in this chapter, and it can be seen that: the histogram 6 (a) of the original image has obvious height fluctuation, the frequency distribution of the occurrence of the pixels is extremely uneven, and the histogram 6 (b) of the right encrypted image is smoother and is similar to a rectangle with a little 'burr', which indicates that the frequency of the occurrence of each pixel is very close, and the related information of the original image is difficult to be directly analyzed from the frequency. Therefore, the encryption performance of the algorithm is better.
(3) Information entropy analysis
The more uniform the distribution of the pixel values of the picture is, the larger the value of the information entropy of the picture is, the uncertainty of the picture can be reflected through the information entropy, and the calculation formula of the information entropy is as follows:
wherein p is i For the probability of occurrence of the gray value i of the image, for 2 8 The encrypted image is the most ideal image, that is, the image with the strongest randomness, and the information entropy ideal value H (x) =8. According to the information in the histogram, through the calculation of the formula (3), the information entropy of the ciphertext image encrypted by using the algorithm in the chapter is 7.9991 which is very close to 8, which shows that the randomness of the ciphertext image is very good, and the algorithm has strong anti-attack capability.
(4) Neighboring pixel correlation analysis
The correlation analysis of adjacent pixels is performed on the original image and the encrypted image, and the image should be described from the horizontal direction, the vertical direction and the diagonal direction. It can be seen from fig. 7 that the original image correlation is very concentrated and has a strong correlation no matter from which of the three directions. By encryption, the characteristics and structure of the original image are changed, the correlation is dispersed, and the correlation of image pixels is greatly reduced, so that the algorithm can effectively defend statistical attacks.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (2)
1. An image encryption method based on a DNA sequence and memristor chaos is characterized by comprising the following steps:
s1, reading an image to obtain a matrix A;
s2, selecting a Chua memristive chaotic system of formula (1)
Wherein x, y, z and w are state variables, alpha, beta and xi are system parameters, the parameters are alpha =4, beta =0.7 and xi =0.1, the initial value of the state variables (0.01,0,0,1.1) is iterated by a Runge-Kutta method with the step length of 0.1 to obtain a chaotic real number sequence x i ,y i ,z i ,w i ；
S3, according to the following formula
For chaotic real number sequence x i ,y i ,z i ,w i Processing to obtain a chaotic sequence K, KZ, and converting the chaotic sequence into a matrix H, HZ; wherein [. ]]Is a rounding function;
s4, performing pixel fusion on the original image matrix A and the chaotic sequence K to obtain a diffusion matrix P, and converting each pixel of P and HZ into a binary system;
s5, for the chaotic matrix x i ,y i ,z i ,w i Performing rounding processing and then modulo 8 to perform DNA coding on the processed diffusion matrix P and the chaotic pseudorandom matrix HZ corresponding to one coding mode in 8 coding rules of the DNA sequence to obtain DNA nucleotide strings PP and HH;
s6, adding PP and HH according to the DNA addition operation rule to obtain a DNA ciphertext sequence LL, and repeating the steps of the fourth step and the fifth step for N times;
s7, decoding the ciphertext sequence LL into a binary sequence according to the coding rule in the fifth step, converting the binary sequence into a decimal system, forming a two-dimensional matrix, and obtaining an encrypted image.
2. The image encryption method based on the DNA sequence and the memristive chaos as claimed in claim 1, wherein the first 400 groups are removed to avoid the transient effect from influencing the result when iteration is performed by Runge-Kutta method with step size of 0.1.
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| CN115694784B (en) * | 2022-12-29 | 2023-05-02 | 北京厚方科技有限公司 | Data security storage method |
| CN116647327B (en) * | 2023-07-26 | 2023-10-13 | 傲拓科技股份有限公司 | Programmable edge controller communication method based on image encryption |
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