CN106023052B - Based on the image encryption method that memristor hyperchaotic system, cellular automata and DNA are calculated - Google Patents

Abstract

The present invention relates to a kind of resume image calculated based on memristor hyperchaotic system, cellular automata and DNA, first using the four-dimensional memristor hyperchaotic system based on Chua circuits, while plaintext image produces key by acting on SHA256 functions；The pseudo-random sequence of chaos system generation is determined into the rule of cellular dynamic evolution as the foundation of DNA dynamic codings and according to the DNA matrixes after diffusion, and during encryption, piecemeal treatment has been done to image；Finally, image is encrypted by pseudo- DNA computational methods, dispersion operation has been carried out while line shuffle is entered to image.One aspect of the present invention increased key space, enhance the ability that algorithm resists brute force attack, on the other hand cause that the generation of key is tightly depended in plain text again, improve the ability that algorithm resists chosen -plain attact, with stronger anti-exhaustive attack ability, it is easy to parallel computation, further improves operational efficiency, improves the security of algorithm.

Description

Based on the image encryption method that memristor hyperchaotic system, cellular automata and DNA are calculated

Technical field

It is more particularly to a kind of to be based on memristor hyperchaotic system, cellular automata and DNA the present invention relates to image encryption field The image encryption method of calculating.

Background technology

Now, along with the fast development and popularization of intelligent terminal, the most information in our lives, for example The picture shared on microblogging, using wechat video conversation etc., will be by the transmission of network.Image is due to raw with image Dynamic, simple, directly perceived the advantages of, have been developed as exchange way indispensable during we live.But, people pacify to network Full research does not have and reaches a cocksure stage, so image transmission in a network there is also huge safety Leak.The news report that information is divulged a secret is also of common occurrence, it is ensured that security of the information in network transmission into For the problem that researcher must face.As a rule, the image to be transmitted be usually constructed with some it is identical the characteristics of, all exist The features such as data volume is big, adjacent pixel correlation is strong, redundancy is high.Originally, research of the people to information security is mainly focused on In text message, they are all mostly, with one-dimensional data stream as design object, as DES, 3-DES and RSA etc., not consider The characteristics of to digital picture, if be encrypted to image using with text message identical cipher mode, its cipher round results Expected purpose is not reached.So find a kind of safe, reliable, practical image encryption method having put in people In front.At present, using chaos system and image is encrypted with reference to other cryptographic means has become information security research One focus, with huge application potential.

Past most of resume images are all based on the chaos system of low-dimensional, and Low-dimensional Chaotic Systems have structure letter The fast advantage of single, easily operated and calculating speed, but Low-dimensional Chaotic Systems are smaller due to key space, the pseudorandom sequence of generation Row complexity is not high and is easily subject to the shortcoming of phase space reconfiguration method attack and causes the safety of image of its encryption less high, with The raising of the computer speed of service and the proposition of New Algorithm, many AESs based on Low-dimensional Chaotic Systems by into Work(is cracked, and this just promotes more scholars to pass through the hyperchaotic system using higher-dimension to be encrypted image.Hyperchaotic system Attractor has the topological structure that is difficult to, and dynamic behavior is also more complicated than general chaos system and is difficult to predict, And the key space of respective encrypted algorithm is big, and this causes that hyperchaotic system possesses higher in communication encryption and information security field Use value.As the memristor that the scientist of HP Lab in 2008 successfully develops first physics realization starts, The various hyperchaotic systems based on memristor also have become a focus of academia's research.Memristor is a kind of non-linear nothing Source element, has the advantages that non-linear, non-volatile, small volume and low in energy consumption, and this all causes that memristor turns into chaotic sea The ideal chose of circuit.Chaos system based on memristor has following advantage：1. memristor has nano level chi It is very little, when the non-linear timesharing for being applied to chaos system can be substantially reduced the physical size of system；2. the resistance of memristor is Produced with the change of magnetic flux or electric charge, its VA characteristic curve can zero crossing, various non-linear song can be obtained Line, this provides for improved the complexity and the randomness of signal of chaos system；3. most of memristor materials can be simultaneous with CMOS technology Hold, this allows for memristor system with lower energy ezpenditure, and due to these advantages, memristor chaos system adds in communication and information Close field has broad application prospects.

In recent years, with deepening continuously that cellular automata is studied, cellular automata is applied to image encryption increasingly Favored by researcher.Cellular automata belongs to a kind of discrete dynamical system, with time, state and spatially all Discrete characteristic, in addition, structure cell is simple, concurrency is good, each cellular by simply with or wait logical operation group Into computing is simple, is especially suitable for the realization of image encryption, and especially two dimensional cellular automaton is even more in terms of parallel encryption and has Natural advantage, so it is also one new direction of image encryption that chaos system is combined for image encryption with cellular automata. However, the theory of current image encryption technology and correlation is perfect not enough, many algorithms only rely only on cellular automata or list Pure chaotic maps carry out figure encryption, security or not high enough, it is therefore necessary to find a kind of image of compound structure and add Close system.

Currently, another is exactly to calculate to be encrypted image using pseudo- DNA using more image encryption method, DNA encryptions are safe foundation mainly with the limitation of biology techniques, unrelated with computing capability, even therefore quantum calculation Machine cannot also break through the protection of DNA cryptographies, so that with security higher.Simultaneously as DNA is calculated with many other Characteristic not available for calculation, such as superelevation concurrency, super low energy consumption, but with superpower storage capacity, this causes that DNA is counted Calculate has inborn advantage in cryptography.But the existing AES based on DNA will depend on Bioexperiment to enter mostly Row operation, due to Bioexperiment apparatus expensive, experimental situation is difficult to control to, experiment sensitivity it is high the shortcomings of, cause based on DNA count The encryption method of calculation or theoretical being more than are put into practice, and Bioexperiment can be avoided by calculating to be encrypted image using puppet DNA. In addition, DNA encoding rule has 8 kinds, and most of AESs based on DNA are all using a certain coding rule therein Then, this has resulted in that algorithm is not strong to the resistivity of exhaustive attack, has seriously threatened the safety storage of information and has transmitted.

The content of the invention

To overcome deficiency of the prior art, the present invention propose it is a kind of based on memristor hyperchaotic system, cellular automata and The image encryption method that DNA is calculated, overcome that Low-dimensional Chaotic Systems key space is small, security is not high and algorithm lack with it is bright The shortcoming of system of Federation of Literary and Art Circles, while also eliminating, the DNA regular codings anti-exhaustive attack ability of rule is weaker and DNA encryptions are by complicated raw The drawbacks of difficulty is big is realized in thing operation, with stronger anti-exhaustive attack ability, and during encryption, image is done Piecemeal treatment, is easy to parallel computation, improves efficiency；Image is encrypted by pseudo- DNA computational methods, has broken away from the life of complexity Thing experimental implementation, and the algorithm is the encryption based on bit-level, and diffusion behaviour has been also carried out while line shuffle is entered to image Make, improve the security of algorithm.

According to design provided by the present invention, one kind is calculated based on memristor hyperchaotic system, cellular automata and DNA Image encryption method, comprise the following steps：

Step 1., for the plaintext image P of M × N is calculated, obtains the Kazakhstan of a group 256 using SHA256 function pairs size Wish value and using it as image key Key, the image key Key of 256 is scaled 32 decimal number k₁, k₂..., k₃₂, Calculate the initial state value of the memristor hyperchaotic system based on Chua circuits；

The initial state value that step 2. will be obtained is brought memristor hyperchaotic system into and is iterated, and obtains 4 sizes and is respectively 1 The state value matrix X=[x of × 4MN_1,1,x_1,2,...,x_1,4MN], Y=[y_1,1,y_1,2,...,y_1,4MN], Z=[z_1,1, z_1,2,...,z_1,4MN], W=[w_1,1,w_1,2,...,w_1,4MN], matrix X1=is modified to obtain to state value matrix X, Y, Z [x′_1,1,x′_1,2,...,x′_1,4MN], Y1=[y '_1,1,y′_1,2,...,y′_1,4MN], Z1=[z '_1,1,z′_1,2,...,z′_1,4MN], make Obtain x '_1,h、y′_1,h、z′_1,h∈ [1,8], is modified to obtain matrix W 1=[w ' to state value matrix W_1,1,w′_1,2,...,w′_1,4MN], So that w '_1,h∈ [0,1], h ∈ [Isosorbide-5-Nitrae MN], the matrix X_1, Y_ that size is M × 4N are reassembled as by X1, Y1, Z1, W1 by row respectively 1, Z_1, W_1；

Matrix X_1, Y_1, Z_1 after step 3. pair restructuring are grouped, note A1=[X_1, Y_1], A2=[X_1, Z_ 1], A3=[Y_1, Z_1], the regular matrix number needed for will being used for DNA dynamic codings is chosen using first pixel of plaintext R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3, wherein, the rule for choosing R1 and R2 is as follows：

Index=mod (P (1), 3)+1；

If index=1, then i=1, Ai=A1, now R1=X_1, R2=Y_1；

If index=2, then i=2, Ai=A2, now R1=X_1, R2=Z_1；

If index=3, then i=3, Ai=A3, now R1=Y_1, R2=Z_1；

Wherein, index is a variable of setting, and X_1, Y_1, Z_1 represent the state value matrix after amendment restructuring, P (1) First pixel value of plaintext image is represented, mod (a, b) represents a to b modulus, i ∈ [1,3]；

Step 4. launches plaintext image P step-by-steps, obtains eight bit planes and is reassembled as the matrix U that size is M × 8N, order D (i, j)=[U (i, 2*j-1), U (i, 2*j)], is one group by each two element in matrix U, as an element in D, i ∈ [1, M], j ∈ [Isosorbide-5-Nitrae N]；

Matrix D, R1, R2 are divided into p × q matrix in block form by step 5. respectively, and the size of each matrix in block form is m × n, And meet m × p=M, n × q=4N, and the matrix after segmentation is reassembled as one-dimensional matrix that size is 1 × pq simultaneously by row respectively D_1, R_1, R_2 are designated as, wherein representing the piecemeal square of kth block in D_1, R_1, R_2 respectively with D_1 [k], R_1 [k], R_2 [k] Battle array, k=1,2 ..., p × q；

Step 6. chooses 2mn element successively since first element of matrix W _ 1 by row, and reformulation size is m The matrix of × 2n, and the initial configuration C that the matrix is developed as cellular automata⁰；

Step 7. is to initial configuration C⁰Developed, wherein C^kThe configuration obtained after kth time is developed is represented, kth time is being carried out During differentiation, evolution rules are determined for -1 time by kth by the DNA matrix-blocks obtained after diffusion, k=1,2 ..., p × q；

Step 8. is by kth block matrix in block form D_1 [k] in D_1 according to the coding in kth block matrix in block form R_1 [k] in R_1 Rule carries out DNA encoding, and the matrix after coding is designated as into DNA (D_1 [k])；The cellular configuration C obtained to differentiation^kAccording to R_2 Corresponding coding rule carries out DNA encoding in middle kth block matrix in block form R_2 [k], and the matrix after coding is designated as into DNA (C^k), K=1,2 ..., p × q；

The encoder matrix DNA (D_1 [k]) that step 9. pair is obtained is diffused operation；

Step 10. makes k=k+1, and circulation performs step 7-10, until all of piecemeal all completes DNA encryptions；

Encrypted all piecemeal DNA matrixes are reassembled as the matrix of M × 4N and according in regular matrix number R1 by step 11. Corresponding regular number carries out DNA decoding operates, obtains the binary matrix Q1 that a size is M × 8N, and then matrix Q1 is entered Row decimal system conversion operation, obtains the decimal system ciphertext matrix Q2 that a size is M × N, the ciphertext graph picture after as encrypting.

Above-mentioned, the expression formula of the memristor hyperchaotic system based on Chua circuits is in the step 1：

Wherein, h (x)=m₁x+0.5(m₀-m₁) × (| x+1 |-| x-1 |), X, y, z, w represent the state variable of memristor hyperchaotic system, a, b, c, d, e, m₀、m₁It is the control parameter of memristor hyperchaotic system, And work as a=30, b=36, d=2.5, e=3.5, m₀=-0.5, m₁During=- 0.1 and c ∈ [0.073,0.162], system is in Hyperchaos state；And by formula：

Calculate the initial state value x of the state variable of the memristor hyperchaotic system based on Chua circuits₀, y₀, z₀And w₀, its In, sum (k₂₁,k₂₂,...,k₃₂) represent to k₂₁,k₂₂,...,k₃₂Sued for peace, max (k₂₁,k₂₂,...,k₃₂) represent and seek k₂₁, k₂₂,...,k₃₂Maximum,Representative takes the XOR of x and y.

Above-mentioned, the step 2 is specifically comprised the following steps：

Step 2.1, the initial state value x that will be calculated by step 1₀, y₀, z₀And w₀Bring into based on Chua circuits Memristor hyperchaotic system iteration N0 times, whereinObtain 4 sizes be respectively 1 × The state value matrix X=[x of 4MN_1,1,x_1,2,...,x_1,4MN], Y=[y_1,1,y_1,2,...,y_1,4MN], Z=[z_1,1,z_1,2,..., z_1,4MN], W=[w_1,1,w_1,2,...,w_1,4MN]；Step 2.2, state value matrix X, Y, Z, W are carried out by correction formula respectively Matrix X1, Y1, Z1, W1 are corrected to obtain, wherein correction formula is as follows：

X1=mod ((abs (x_1,h)-floor(x_1,h))×10¹⁴, 8) and+1,

Y1=mod ((abs (y_1,h)-floor(y_1,h))×10¹⁴), 8)+1,

Z1=mod ((abs (z_1,h)-floor(z_1,h))×10¹⁴, 8) and+1,

W1=mod ((abs (w_1,h)-floor(w_1,h))×10¹⁴, 2),

Wherein, x_1,h, y_1,h, z_1,h, w_1,hH-th value in state value matrix X, Y, Z, W, h ∈ [Isosorbide-5-Nitrae MN] are represented respectively； Abs (x) represents and x is taken absolute value that floor (x) is represented and taken the no more than maximum integer of x, and mod (a, b) represents modulus of a to b Computing；

Step 2.3, by X1, Y1, Z1, W1 respectively by row be reassembled as size be M × 4N matrix X_1, Y_1, Z_1, W_1.

Above-mentioned, step 7 is specifically comprised the following steps：

Step 7.1, by equation below：

Cellular automata evolution rules are determined, the state space for setting cellular is { 0,1 }, wherein,Represent in t+1 The state value of the center cellular in position (i, j) place is carved,Represent and be in the center cellular at position (i, j) place in moment t State value,It is illustrated respectively in upper, left, down, right the neighbours unit that moment t is in center cellular The state value of born of the same parents, L, VM, VT, VL, VD, VR are the variables that value is 0 or 1；If L=1, represent that rule is Non―linear programming, it is no It is exactly then linear programming, VM, VT, VL, VD, VR control whether middle, upper, five cellulars of left, down, right participate in cellular differentiation respectively Process, if corresponding value is 0 in VM, VT, VL, VD, VR, then it represents that its corresponding cellular is not involved in developing；L、VM、VT、VL、 The value of VD, VR is determined by evolution rules rule (k) in step 7.2；Step 7.2, by formula：

Determine cellular automata evolution rules number, wherein, rule (k) represents that cellular carries out regular number when kth time is developed, DNA (E (k-1)) represents the previous DNA matrix-blocks by being obtained after diffusion, and sum (DNA (E (k))) is represented and k-th is spread The ASCII character value summation of each element of DNA matrixes afterwards, as k=1, E (0)=C⁰, C⁰Represent the initial configuration of cellular, k =1,2 ..., p × q；

Step 7.3, the rule (k) that will be calculated in step 7.2 are changed into binary system, that is, try to achieve L, VM, VT, VL, VD, The value of VR, while according to step 7.1) determine the function that cellular is developed.

Above-mentioned, dispersion operation is specifically included in the step 9：By formula：

Encoder matrix DNA (D_1 [k]) to obtaining is diffused operation.

Beneficial effects of the present invention：

The present invention overcomes that Low-dimensional Chaotic Systems key space in the prior art is small, security is not high and algorithm lack with it is bright The shortcoming of system of Federation of Literary and Art Circles, while also eliminating, the DNA regular codings anti-exhaustive attack ability of rule is weaker and DNA encryptions are by complicated raw The drawbacks of difficulty is big is realized in thing operation；Using the memristor hyperchaotic system based on Chua circuits, while plaintext image is by effect Key is produced in SHA256 functions, increases key space, enhancing algorithm is resisted the ability of brute force attack, on the other hand caused again The generation of key is tightly depended in plain text, improves the ability that algorithm resists chosen -plain attact；Memristor hyperchaotic system is produced Raw pseudo-random sequence as DNA dynamic codings foundation and cellular dynamic evolution determined according to the DNA matrixes after diffusion Rule, encoded compared to the fixed dna used in current other many AESs for calculating with cellular automata with reference to DNA Rule and the single evolution rules of cellular, the algorithm have stronger anti-exhaustive attack ability, and during encryption, to figure As having done piecemeal treatment, it is easy to parallel computation, improves efficiency；Image is encrypted by pseudo- DNA computational methods, breaks away from multiple Miscellaneous biological experiment operating, and the algorithm is the encryption based on bit-level, is also carried out while line shuffle is entered to image Dispersion operation, improves the security of algorithm.

Brief description of the drawings：

Fig. 1 is schematic flow sheet of the invention；

Fig. 2 (a) is original image used by embodiment three；

Image after encryptions of the Fig. 2 (b) used by embodiment three；

Decrypted image when keys of the Fig. 2 (c) used by embodiment three is correct；

One of decrypted image when Fig. 2 (d) is the use false key used by embodiment three；

Fig. 2 (e) be embodiment three used by use false key when decrypted image two；

Fig. 2 (f) be embodiment three used by use false key when decrypted image three；

Fig. 3 (a) is the histogram of the original image used by embodiment three；

Fig. 3 (b) is the histogram of the encrypted image used by embodiment three；

The correlation analysis figure of Fig. 4 (a) adjacent pixels in the original image horizontal direction used by embodiment three；

The correlation analysis figure of Fig. 4 (b) adjacent pixels in the encrypted image horizontal direction used by embodiment three；

Fig. 5 (a) is original image used by example IV；

Image after encryptions of the Fig. 5 (b) used by example IV；

Decrypted image when keys of the Fig. 5 (c) used by example IV is correct；

One of decrypted image when Fig. 5 (d) is the use false key used by example IV；

Fig. 5 (e) be example IV used by use false key when decrypted image two；

Fig. 5 (f) be example IV used by use false key when decrypted image three；

Fig. 6 (a) is the histogram of the original image used by example IV；

Fig. 6 (b) is the histogram of the encrypted image used by example IV；

The correlation analysis figure of Fig. 7 (a) adjacent pixels in the original image horizontal direction used by example IV；

The correlation analysis figure of Fig. 7 (b) adjacent pixels in the encrypted image horizontal direction used by example IV；

Fig. 8 (a) is original image used by embodiment five；

Image after encryptions of the Fig. 8 (b) used by embodiment five；

Decrypted image when keys of the Fig. 8 (c) used by embodiment five is correct；

One of decrypted image when Fig. 8 (d) is the use false key used by embodiment five；

Fig. 8 (e) be embodiment five used by use false key when decrypted image two；

Fig. 8 (f) be embodiment five used by use false key when decrypted image three；

Fig. 9 (a) is the histogram of the original image used by embodiment five；

Fig. 9 (b) is the histogram of the encrypted image used by embodiment five；

The correlation analysis figure of Figure 10 (a) adjacent pixels in the original image horizontal direction used by embodiment five；

The correlation analysis figure of Figure 10 (b) adjacent pixels in the encrypted image horizontal direction used by embodiment five.

Specific embodiment：

The present invention is further detailed explanation with technical scheme below in conjunction with the accompanying drawings, and detailed by preferred embodiment Describe bright embodiments of the present invention in detail, but embodiments of the present invention are not limited to this.

Embodiment one, a kind of shown in Figure 1, image calculated based on memristor hyperchaotic system, cellular automata and DNA Encryption method, comprises the following steps：

Step 1., for the plaintext image P of M × N is calculated, obtains the Kazakhstan of a group 256 using SHA256 function pairs size Wish value and using it as image key Key, the image key Key of 256 is scaled 32 decimal number k₁, k₂..., k₃₂, Calculate the initial state value of the memristor hyperchaotic system based on Chua circuits；

The initial state value that step 2. will be obtained is brought memristor hyperchaotic system into and is iterated, and obtains 4 sizes and is respectively 1 The state value matrix X=[x of × 4MN_1,1,x_1,2,...,x_1,4MN], Y=[y_1,1,y_1,2,...,y_1,4MN], Z=[z_1,1, z_1,2,...,z_1,4MN], W=[w_1,1,w_1,2,...,w_1,4MN], matrix X1=is modified to obtain to state value matrix X, Y, Z [x′_1,1,x′_1,2,...,x′_1,4MN], Y1=[y '_1,1,y′_1,2,...,y′_1,4MN], Z1=[z '_1,1,z′_1,2,...,z′_1,4MN], make Obtain x '_1,h、y′_1,h、z′_1,h∈ [1,8], is modified to obtain matrix W 1=[w ' to state value matrix W_1,1,w′_1,2,...,w′_1,4MN], So that w '_1,h∈ [0,1], h ∈ [Isosorbide-5-Nitrae MN], the matrix X_1, Y_ that size is M × 4N are reassembled as by X1, Y1, Z1, W1 by row respectively 1, Z_1, W_1；

Matrix X_1, Y_1, Z_1 after step 3. pair restructuring are grouped, note A1=[X_1, Y_1], A2=[X_1, Z_ 1], A3=[Y_1, Z_1], the regular matrix number needed for will being used for DNA dynamic codings is chosen using first pixel of plaintext R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3, wherein, the rule for choosing R1 and R2 is as follows：

Index=mod (P (1), 3)+1；

If index=1, then i=1, Ai=A1, now R1=X_1, R2=Y_1；

If index=2, then i=2, Ai=A2, now R1=X_1, R2=Z_1；

If index=3, then i=3, Ai=A3, now R1=Y_1, R2=Z_1；

Wherein, index is a variable of setting, and X_1, Y_1, Z_1 represent the state value matrix after amendment restructuring, P (1) First pixel value of plaintext image is represented, mod (a, b) represents a to b modulus, i ∈ [1,3]；

Step 4. launches plaintext image P step-by-steps, obtains eight bit planes and is reassembled as the matrix U that size is M × 8N,

D (i, j)=[U (i, 2*j-1), U (i, 2*j)] is made, is one group by each two element in matrix U, as in D Individual element, i ∈ [1, M], j ∈ [Isosorbide-5-Nitrae N]；

Matrix D, R1, R2 are divided into p × q matrix in block form by step 5. respectively, and the size of each matrix in block form is m × n, And meet m × p=M, n × q=4N, and the matrix after segmentation is reassembled as one-dimensional matrix that size is 1 × pq simultaneously by row respectively D_1, R_1, R_2 are designated as, wherein representing the piecemeal square of kth block in D_1, R_1, R_2 respectively with D_1 [k], R_1 [k], R_2 [k] Battle array, k=1,2 ..., p × q；

Step 6. chooses 2mn element successively since first element of matrix W _ 1 by row, and reformulation size is m The matrix of × 2n, and the initial configuration C that the matrix is developed as cellular automata⁰；

Step 7. is to initial configuration C⁰Developed, wherein C^kThe configuration obtained after kth time is developed is represented, kth time is being carried out During differentiation, evolution rules are determined for -1 time by kth by the DNA image block obtained after diffusion, k=1,2 ..., p × q；

Step 8. is by kth block matrix in block form D_1 [k] in D_1 according to the coding in kth block matrix in block form R_1 [k] in R_1 Rule carries out DNA encoding, and the matrix after coding is designated as into DNA (D_1 [k])；The cellular configuration C obtained to differentiation^kAccording to R_2 Corresponding coding rule carries out DNA encoding in middle kth block matrix in block form R_2 [k], and the matrix after coding is designated as into DNA (C^k), K=1,2 ..., p × q；

The encoder matrix DNA (D_1 [k]) that step 9. pair is obtained is diffused operation；

Step 10. makes k=k+1, and circulation performs step 7-10, until all of piecemeal all completes DNA encryptions；

Encrypted all piecemeal DNA matrixes are reassembled as the matrix of M × 4N and according in regular matrix number R1 by step 11. Corresponding regular number carries out DNA decoding operates, obtains the binary matrix Q1 that a size is M × 8N, and then matrix Q1 is entered Row decimal system conversion operation, obtains the decimal system ciphertext matrix Q2 that a size is M × N, the ciphertext graph picture after as encrypting.

Embodiment two, a kind of shown in Figure 1, image calculated based on memristor hyperchaotic system, cellular automata and DNA Encryption method, comprises the following steps：

Step 1., for the plaintext image P of M × N is calculated, obtains the Kazakhstan of a group 256 using SHA256 function pairs size Wish value and using it as image key Key, the image key Key of 256 is scaled 32 decimal number k₁, k₂..., k₃₂, The initial state value of the memristor hyperchaotic system based on Chua circuits is calculated, the memristor hyperchaotic system of Chua circuits is specifically based on Expression formula be：

, wherein, h (x)=m₁x+0.5(m₀-m₁) × (| x+1 |-| x-1 |),X, y, z, w represent the state variable of memristor hyperchaotic system, a, b, c, d, e, m₀、m₁It is the control parameter of memristor hyperchaotic system, and works as a=30, b=36, d=2.5, e=3.5, m₀=-0.5, m₁=- During 0.1 and c ∈ [0.073,0.162], system is in hyperchaos state；And by formula：

, calculate the initial state value x0, y of the state variable of the memristor hyperchaotic system based on Chua circuits₀, z₀And w₀, its In, sum (k₂₁,k₂₂,...,k₃₂) represent to k₂₁,k₂₂,...,k₃₂Sued for peace, max (k₂₁,k₂₂,...,k₃₂) represent and seek k₂₁, k₂₂,...,k₃₂Maximum,Representative takes the XOR of x and y；

The initial state value that step 2. will be obtained is brought memristor hyperchaotic system into and is iterated, and obtains 4 sizes and is respectively 1 The state value matrix X=[x of × 4MN_1,1,x_1,2,...,x_1,4MN], Y=[y_1,1,y_1,2,...,y_1,4MN], Z=[z_1,1, z_1,2,...,z_1,4MN], W=[w_1,1,w_1,2,...,w_1,4MN], matrix X1=is modified to obtain to state value matrix X, Y, Z [x′_1,1,x′_1,2,...,x′_1,4MN], Y1=[y '_1,1,y′_1,2,...,y′_1,4MN], Z1=[z '_1,1,z′_1,2,...,z′_1,4MN], make Obtain x '_1,h、y′_1,h、z′_1,h∈ [1,8], is modified to obtain matrix W 1=[w ' to state value matrix W_1,1,w′_1,2,...,w′_1,4MN], So that w '_1,h∈ [0,1], h ∈ [Isosorbide-5-Nitrae MN], the matrix X_1, Y_ that size is M × 4N are reassembled as by X1, Y1, Z1, W1 by row respectively 1, Z_1, W_1, specifically comprise the following steps：

Step 2.1, the initial state value x that will be calculated by step 1₀, y₀, z₀And w₀Bring into based on Chua circuits Memristor hyperchaotic system iteration N0 times, whereinObtain 4 sizes be respectively 1 × The state value matrix X=[x of 4MN_1,1,x_1,2,...,x_1,4MN], Y=[y_1,1,y_1,2,...,y_1,4MN], Z=[z_1,1,z_1,2,..., z_1,4MN], W=[w_1,1,w_1,2,...,w_1,4MN]；

Step 2.2, matrix X1, Y1, Z1, W1 are modified to obtain by correction formula respectively to state value matrix X, Y, Z, W, Wherein correct

Formula is as follows：

X1=mod ((abs (x_1,h)-floor(x_1,h))×10¹⁴, 8) and+1,

Y1=mod ((abs (y_1,h)-floor(y_1,h))×10¹⁴), 8)+1,

Z1=mod ((abs (z_1,h)-floor(z_1,h))×10¹⁴, 8) and+1,

W1=mod ((abs (w_1,h)-floor(w_1,h))×10¹⁴, 2),

Wherein, x_1,h, y_1,h, z_1,h, w_1,hH-th value in state value matrix X, Y, Z, W, h ∈ [Isosorbide-5-Nitrae MN] are represented respectively； Abs (x) represents and x is taken absolute value that floor (x) is represented and taken the no more than maximum integer of x, and mod (a, b) represents modulus of a to b Computing；

Step 2.3, by X1, Y1, Z1, W1 respectively by row be reassembled as size be M × 4N matrix X_1, Y_1, Z_1, W_1；

Matrix X_1, Y_1, Z_1 after step 3. pair restructuring are grouped, note A1=[X_1, Y_1], A2=[X_1, Z_ 1], A3=[Y_1, Z_1], the regular matrix number needed for will being used for DNA dynamic codings is chosen using first pixel of plaintext R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3；

The rule for choosing R1 and R2 is as follows：

Index=mod (P (1), 3)+1；

If index=1, then i=1, Ai=A1, now R1=X_1, R2=Y_1；

If index=2, then i=2, Ai=A2, now R1=X_1, R2=Z_1；

If index=3, then i=3, Ai=A3, now R1=Y_1, R2=Z_1.

Wherein, index is the variable that we set, and X_1, Y_1, Z_1 represent the state value matrix after amendment restructuring, P (1) represents first pixel value of plaintext image, and mod (a, b) represents a to b modulus, i ∈ [1,3]；

Step 4. launches plaintext image P step-by-steps, obtains eight bit planes and is reassembled as the matrix U that size is M × 8N, order D (i, j)=[U (i, 2*j-1), U (i, 2*j)], is one group by each two element in matrix U, as an element in D, i ∈ [1, M], j ∈ [Isosorbide-5-Nitrae N]；

Matrix D, R1, R2 are divided into p × q matrix in block form by step 5. respectively, and the size of each matrix in block form is m × n, And meet m × p=M, n × q=4N, and the matrix after segmentation is reassembled as one-dimensional matrix that size is 1 × pq simultaneously by row respectively D_1, R_1, R_2 are designated as, wherein representing the piecemeal square of kth block in D_1, R_1, R_2 respectively with D_1 [k], R_1 [k], R_2 [k] Battle array, k=1,2 ..., p × q；

Step 6. chooses 2mn element successively since first element of matrix W _ 1 by row, and reformulation size is m The matrix of × 2n, and the initial configuration C that the matrix is developed as cellular automata⁰；

Step 7. is to initial configuration C⁰Developed, wherein C^kThe configuration obtained after kth time is developed is represented, kth time is being carried out During differentiation, evolution rules are determined for -1 time by kth by the DNA matrix-blocks obtained after diffusion, k=1,2 ..., p × q, specific bag Containing following steps：

Step 7.1, by equation below：

Cellular automata evolution rules are determined, the state space for setting cellular is { 0,1 }, wherein,Represent in t+1 The state value of the center cellular in position (i, j) place is carved,Represent and be in the center cellular at position (i, j) place in moment t State value, It is illustrated respectively in upper, left, down, right the neighbours unit that moment t is in center cellular The state value of born of the same parents, L, VM, VT, VL, VD, VR are the variables that value is 0 or 1；If L=1, represent that rule is Non―linear programming, it is no It is exactly then linear programming, VM, VT, VL, VD, VR control whether middle, upper, five cellulars of left, down, right participate in cellular differentiation respectively Process, if in VM, VT, VL, VD, VR it is corresponding value be 0, then it represents that its corresponding cellular be not involved in develop, L, VM, VT, VL, The value of VD, VR is determined by evolution rules rule (k) in step 7.2；

Step 7.2, by formula：

Determine cellular automata evolution rules number, wherein, rule (k) represents that cellular carries out regular number when kth time is developed, DNA (E (k-1)) represents the previous DNA matrixs in block form by being obtained after diffusion, and sum (DNA (E (k))) is represented and k-th is expanded The ASCII character value summation of each element of the DNA matrixes after dissipating, as k=1, E (0)=C⁰, C⁰The initial configuration of cellular is represented, K=1,2 ..., p × q；

Step 7.3, the rule (k) that will be calculated in step 7.2 are changed into binary system, that is, try to achieve L, VM, VT, VL, VD, The value of VR, while according to step 7.1) determine the function that cellular is developed；

Step 8. is by kth block matrix in block form D_1 [k] in D_1 according to the coding in kth block matrix in block form R_1 [k] in R_1 Rule carries out DNA encoding, and the matrix after coding is designated as into DNA (D_1 [k])；The cellular configuration C obtained to differentiation^kAccording to R_2 Corresponding coding rule carries out DNA encoding in middle kth block matrix in block form R_2 [k], and the matrix after coding is designated as into DNA (C^k), K=1,2 ..., p × q；

The encoder matrix DNA (D_1 [k]) that step 9. pair is obtained is diffused operation, by formula：

It is diffused operation；

Step 10. makes k=k+1, and circulation performs step 7-10, until all of piecemeal all completes DNA encryptions；

Encrypted all piecemeal DNA matrixes are reassembled as the matrix of M × 4N and according in regular matrix number R1 by step 11. Corresponding regular number carries out DNA decoding operates, obtains the binary matrix Q1 that a size is M × 8N, and then matrix Q1 is entered Row decimal system conversion operation, obtains the decimal system ciphertext matrix Q2 that a size is M × N, the ciphertext graph picture after as encrypting.

Embodiment three, referring to Fig. 2 (a)~4 (b) Suo Shi, in the present embodiment, the programming software for using is Matlab R2014a, the Lena gray level images for choosing size for 256 × 256 are experimental subjects, and specific ciphering process is as follows：

Step 1. input original size is 256 × 256 Lena gray level images, is read with P=imread (' lena.bmp') Take image information, calculated using SHA256 function pair plaintext images P, obtain one group 256 cryptographic Hash and using it as Image key Key, is then scaled 32 decimal number k by the Key of 256₁, k₂..., k₃₂, for calculating memristor hyperchaos The initial state value of system is comprised the following steps that：

1.1) use based on the memristor hyperchaotic system of Chua circuits to produce the pseudo-random sequence needed for AES, its Expression formula is as follows：

, wherein：H (x)=m₁x+0.5(m₀-m₁) × (| x+1 |-| x-1 | |),Work as a=30, b=36, c=0.1, d=2.5, e=3.5, m₀=-0.5, m₁=- When 0.1, system is in hyperchaos state.

1.2) calculated using SHA256 function pair plaintext images, (16 enter can to obtain the cryptographic Hash of a group 256 Tabulation is shown as [a c 3 of 26288 f e, 130 c of e e e e, 625 f of b a a f 8 d a, 1 c, 8 c 5 The e 9 of 69 a, 0994656 d, 59 e, 4605 e, 3 d 047672 3]), and using it as image Key, the cryptographic Hash of 256 is then converted into 32 decimal numbers (38 40 143 225 62 238 224 198 186 175 141 161 200 194 95 90 195 105 160 153 70 86 213 158 70 5 227 208 71 103 35 233), and are defined as k₁,k₂,...,k₃₂, the original state of memristor hyperchaotic system is calculated followed by equation below Value：

, by the initial state value x for being calculated memristor hyperchaotic system₀=1.3359, y₀=0.2813, z₀= 0.9297, w₀=0.1984.

The initial state value that step 2. will be obtained is brought memristor hyperchaotic system into and is iterated, and can obtain 4 sizes point Not Wei 1 × 262144 state value matrix X=[x_1,1,x_1,2,...,x_1,262144], Y=[y_1,1,y_1,2,...,y_1,262144], Z= [z_1,1,z_1,2,...,z_1,262144], W=[w_1,1,w_1,2,...,w_1,262144], then state matrix X, Y, Z for obtaining are repaiied Just obtain matrix X1=[x '_1,1,x′_1,2,...,x′_1,262144], Y1=[y '_1,1,y′_1,2,...,y′_1,262144], Z1=[z '_1,1, z′_1,2,...,z′_1,262144] so that x '_1,h、y′_1,h、z′_1,h∈ [1,8], is modified to obtain matrix W 1=to state value matrix W [w′_1,1,w′_1,2,...,w′_1,262144] so that w '_1,h∈ [0,1], h ∈ [1,262144], and then again by X1, Y1, Z1, W1 by row Matrix X_1, Y_1, Z_1, W_1 that size is 256 × 1024 are reassembled as, it is comprised the following steps that：

2.1) in order to avoid adverse effect, (the x that we will be first calculated by step 1₀,y₀,z₀,w₀) bring memristor into Hyperchaotic system iteration N0 times, whereinAnd then again to memristor hyperchaos system System is iterated and can obtain state value matrix X, Y, Z, W that three sizes are respectively 256 × 1024.

2.2) state value matrix X, Y, Z, the W by correction formula respectively to obtaining are modified, obtain X1, Y1, Z1, W1, correction formula is as follows：

X1=mod ((abs (x_1,h)-floor(x_1,h))×10¹⁴,8)+1

Y1=mod ((abs (y_1,h)-floor(y_1,h))×10¹⁴),8)+1

Z1=mod ((abs (z_1,h)-floor(z_1,h))×10¹⁴,8)+1

W1=mod ((abs (w_1,h)-floor(w_1,h))×10¹⁴,2)

, wherein x_1,h, y_1,h, z_1,h, w_1,hRepresent h-th value in state value matrix X, Y, Z, W respectively, h ∈ [1,256 × 1024]；Abs (x) represents and x is taken absolute value that floor (x) is represented and taken the no more than maximum integer of x, and mod (a, b) represents a to b Modulo operation.

2.3) to revised matrix X1, Y1, Z1, W1 by row reassemble into size be 256 × 1024 matrix X_1, Y_1, Z_1、W_1。

Its whole process is as follows：

Matrix X_1, Y_1, Z_1 after step 3. pair amendment restructuring are grouped, note A1=[X_1, Y_1], A2=[X_1, Z_1], A3=[Y_1, Z_1] chooses the rule needed for will being used for DNA dynamic codings followed by first pixel of plaintext Then matrix number R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3；

Selection rule matrix number R1's and R2 is regular specific as follows：

Index=mod (P (1), 3)+1；

If index=1, then i=1, Ai=A1, now R1=X_1, R2=Y_1；

If index=2, then i=2, Ai=A2, now R1=X_1, R2=Z_1；

If index=3, then i=3, Ai=A3, now R1=Y_1, R2=Z_1.

Wherein, index is the variable that we set, and X_1, Y_1, Z_1 represent the state value matrix after amendment restructuring, P (1) represents first pixel value of plaintext image, and mod (a, b) represents a to b modulus, i ∈ [1,3].

In the present embodiment, the value of P (1) is 162, and the value that index is obtained by selection rule is 1, so R1=X_1, R2 =Y_1.

Eight bit planes of plaintext image P are reassembled as the matrix U that size is 256 × 2048 by step 4.,

D (i, j)=[U (i, 2*j-1), U (i, 2*j)] is made, will each two element be one group as in D in U Element, i ∈ [1,256], j ∈ [1,1024], detailed process is as follows：Plaintext image

Wherein, P represents plaintext image, and P0~P7 represents 8 bit planes of plaintext image P, and U is represented and pressed 8 bit planes The matrix obtained after row restructuring, D represents the matrix that each two element in U is seen as acquisition after a group,Represent plaintext image P (i, j) individual element be converted to the t bit values after binary system, t ∈ [0,7].

Matrix D, R1, R2 are divided into 4 × 16 matrixs in block form by step 5. respectively, the size of each matrix in block form for 64 × 64, and by the matrix after segmentation respectively by row be reassembled as size be 1 × 64 one-dimensional matrix and be designated as D_1, R_1, R_2, wherein Represent the matrix in block form of kth block in D_1, R_1, R_2 respectively with D_1 [k], R_1 [k], R_2 [k], here k=1,2 ..., 64, Detailed process is as follows：

Piecemeal is carried out to matrix D：

D_1 [k] is recombinated to obtain by row

Similarly, with reference to the method for obtaining D_1 [k], it is also possible to obtain R_1 [k], the corresponding matrixs in block form of R_2 [k], wherein p ∈1,4,∈1,16。

Step 6. is chosen 2mn=2 × 64 × 64=8192 unit successively since first element of matrix W _ 1 by row Element, reformulates the matrix that size is for 64 × 128, and the initial configuration C that the matrix is developed as cellular automata⁰, wherein, Cellular automata (Cellular Automata, abbreviation CA) is a kind of dynamical system all discrete over time and space, is had The advantages of simple structure, concurrency are good.Each cellular by simply with or wait logical operation to constitute, computing is simple.Cellular is automatic Machine can represent with the four-tuple of formula CA=(C, S, V, F), wherein：C represents cellular space, and S represents cellular state space, V The neighborhood combination of cellular is represented, F represents local transitions function.For the one-dimensional cellular automatic machine of radius of neighbourhood r=1, it State transition function can be by formulaTo represent,It is three input variables, difference table Show cellular state of the cellular in t at position i-1, i and i+1,Represent cellular of the cellular at the t+1 moment at the i of position State, their value can only be 0 or 1 two states.

Two dimensional cellular automaton is that cellular space is divided into square net, for the Von Neumann neighbours that radius is 1 For the two dimensional cellular automaton of type, its state transition function can be by formula To represent, in formula Represent respectively t cellular position (i, j), (i-1, j), (i, j- 1), (i+1, j), the state at (i, j+1) place,Represent state of the t+1 moment cellular at position (i, j) place.

The evolution properties of cellular automata are determined by rule, and rule is otherwise known as local state transfer letter here Number.For the one-dimensional cellular automatic machine of radius of neighbourhood r=1, its state valueValue can only be 0 or 1, because This it one have 2⁸=256 kinds of rules.If by f_iEvery kind of form that may arrange into truth table, it is possible to determine f_iBelong to several Number rule, wherein the truth table of No. 80 evolution rules is as shown in the table：The radius of neighbourhood of table 1 is 1 one-dimensional cellular automatic machine 80 Regular truth table

The rule number that cellular is developed can be represented with 8 bits, as shown in No. 80 regular truth tables of upper table, turned to Binary system is (01010000)₂=(80)₁₀, regular number is expressed as simplified decimal form such as formulaInstitute Show.Similarly, the Else Rule of one-dimensional cellular automatic machine can also determine after the same method.

Obtain cellular initial configuration C⁰Whole process it is as follows：

8192 elements (shown in dotted line) are chosen as row since first element of W_1, then it is reassembled as 64 × 128 matrix, as C⁰：

Step 7. is to initial configuration C⁰Developed, wherein C^kThe configuration obtained after kth time is developed is represented, is specifically existed When carrying out kth time and developing, evolution rules are determined by kth -1 time by the DNA matrix-blocks obtained after diffusion, k=1,2 ..., 64, wherein, improved two dimensional cellular automaton as one-dimensional cellular automatic machine, also may be used by the size of two dimensional cellular automaton neighborhood To be represented with radius r, but complex and evolution rule the quantity of definition and complexity can be with cellular numbers in neighborhood Increase forms exponential increase, and this enhances the security of algorithm to a certain extent, but also significantly increases algorithm simultaneously Amount of calculation, state transition function is modified and obtains formula：

, the rule that cellular is developed is determined by the formula, wherein,Represent and be in position (i, j) place at the t+1 moment Center cellular state value,The state value that the center cellular at position (i, j) place is in moment t is represented,The state value that upper, left, down, right neighbours' cellular of center cellular is in moment t is represented, L, VM, VT, VL, VD, VR are the variables that value is 0 and 1.If L=1, represent that rule is Non―linear programming, be otherwise exactly linear Rule.VM, VT, VL, VD, VR represent middle, upper, five cellulars of left, down, right respectively, and which unit is the value of this five variables determine Born of the same parents participate in the renewal of middle cellular state value.We just determine every kind of possible rule with this 6 values of variable.For example (L, VM, VT, VL, VD, VR)=(001110)₂=(14)₁₀, the rule be known as rule 14, state transition function is carried out by above-mentioned The simplified formula that modification is obtained is formula：Due to there is six variables, so one has 2⁶=64 Rule is planted, on the premise of security is ensured, amount of calculation is greatly reduced, encryption efficiency is improve.Wherein, L, VM, VT, The value of VL, VD, VR variable can be tried to achieve by previous DNA matrixs in block form, equivalent to determined by cryptographic block cellular update Rule, regular number by equation below obtain：

, wherein, rule (k) represents that cellular carries out regular number when kth time is developed, and DNA (E (k-1)) represents previous warp The DNA matrix-blocks obtained after diffusion are crossed, sum (DNA (E (k))) represents each element of the DNA matrixes after being spread to k-th ASCII character value is sued for peace, as k=1, E (0)=C⁰, k=1,2 ..., p × q.

Next rule (k) is changed into binary system, formula is obtained according to above-mentioned being modified to state transition function Content can try to achieve the value of L, VM, VT, VL, VD, VR, and the function that now cellular is developed also has determined that.

One specific example is as follows：

It is assumed thatAs k=1, rule (1)=mod (sum (C⁰), 64)=11, by (11)₁₀ It is changed into binary system (001011)₂, L=0, VM=0, VT=1, VL=0, VD=1, VR=1 can be obtained, according to L, VM, VT, VL, The value of VD, VR can obtain the formula that now cellular is developed and be changed into：Cellular is entered according to this rule Row is developed for the first timeIt is assumed that the DNA matrixes obtained after first time spreads are represented bySo

Rule (2)=mod (sum (DNA (E (1))), 64)

=mod ((84+65+84+67+84+67+67+67+65+71+71+67), 64)

=27

, by (27)₁₀It is changed into binary system (011011)₂, L=0, VM=1, VT=1, VL=0, VD=1, VR=1 can be obtained, Value according to L, VM, VT, VL, VD, VR can obtain the formula that now cellular is developed：

Then carrying out second differentiation to cellular can obtain：

And then any cellular configuration of differentiation can also be tried to achieve.

Kth block matrix in block form D_1 [k] in D_1 is carried out into DNA encoding according to the coding rule in R_1 [k] in step 8, and Matrix after coding is designated as DNA (D_1 [k])；The cellular configuration C obtained to differentiation^kAccording to correspondence in matrix in block form R_2 [k] Coding rule carry out DNA encoding, and the element after coding is designated as DNA (C^k) comprise the following steps that：

A specific example for carrying out DNA encoding to D_1 [k] (now k is assumed to 5) is as follows：

It is assumed thatSo according in D_1 [5] Element in R_1 [5] corresponding coding rule can obtainSimilarly, arbitrary D_1 [k], R_1 [k] can also be tried to achieve.

The encoder matrix DNA (D_1 [k]) that step 9. pair is obtained is diffused operation, and it is comprised the following steps that：

Operation is diffused by the DNA matrixes as follows to obtaining,

DNA (E [k]) represents DNA encoding matrix of the kth block by the image after encryption, and DNA (E [k-1]) represents that its is previous DNA encoding matrix after individual encryption, DNA (C^k) represent that cellular is developed and by the coding square after DNA encoding by kth time Battle array, DNA (D_1 [k]) represents the DNA matrix encoded to kth block matrix in D_1, k=1,2 ..., 64.

Step 10. makes k=k+1, and circulation performs step 7-10, until all of piecemeal all completes DNA encryptions.

Encrypted all piecemeal DNA matrixes are reassembled as 256 × 1024 matrix and according to coding rule square by step 11. The corresponding regular numbers of battle array R1 carry out DNA decoding operates, can obtain the binary matrix Q1 that a size is 256 × 2048, so Decimal system conversion operation is carried out to matrix Q1 afterwards, the decimal system ciphertext matrix Q2 that a size is 256 × 256 can be obtained, i.e., It is the ciphertext graph picture after encryption.

One specific example is as follows：

It is assumed that the DNA matrixes after encrypted have two, respectively Decoding rule in correspondence R1 is respectivelyWith It is by decoded matrixWithThen it is converted into The decimal system is respectivelyWith

One good AES should be able to resist various attacks, and key space is sufficiently large, and the sensitiveness of key is enough It is high.Safety analysis is carried out to resume image of the invention below.

1. key space is sufficiently large, it is sufficient to resist exhaustive attack

Sensitivity of the chaos system to primary condition and control parameter extremely, any small initial deviation all can be exponential Amplify, therefore the security of chaos encryption algorithm has much relations with key space.In general, key space is bigger, and it is supported The ability of anti-exhaustive attack is also stronger.This paper keys are specifically included：1) 256 cryptographic Hash produced by SHA256 functions.2) The number N0 of the memristor chaos sequence given up.3) (noted for choosing the pixel value P (1) of DNA encoding regular matrix R1 and R2：P (1) first pixel value of plaintext image is represented).If it is 10 to set precision^-14, then key space be at least 2¹²⁸, it is seen that key Space is sufficiently large, can effectively resist exhaustive attack.

2. key sensitiveness is high

The security of chaos encryption, is its sensitiveness to key, that is to say, that when attacker with one with key very When close data carry out image and crack, original image can not be recovered.Accompanying drawing 2 (d), 2 (e), 2 (f) are sensitive key Property experiment, wherein four-dimensional memristor Chaotic system control parameter a=30, b=36, c=0.1, d=2.5, e=3.5, m₀=-0.5, m₁=-0.1, (ten enter for the pixel value P (1)=162 and correct 256 cryptographic Hash keys of matrix R1, R2 needed for selection encryption Tabulation is shown) Key=38 40 143 225 62 238 224 198 186 175 141 161 200 194 95 90 195 105 160 153 70 86 213 158 70 5 227 208 71 103 35 233.Accompanying drawing 2 (d) is to work as remaining initial value not Become, make decrypted image during systematic parameter e=3.50000000001.Fig. 2 (e) and 2 (f) are when remaining initial value is constant, respectively Decrypted image after key Key first (being changed to 39 by 38) and last position (being changed to 234 by 233) are changed.From decryption From the point of view of effect picture, this AES is high to the sensitiveness of key, and cryptographic security is also more preferable.

3. the grey level histogram of ciphertext graph picture is smooth and uniform, and anti-Statistical Analysis Attacks ability is strong.

Histogram describes the frequency that the pixel of all gray levels in digital picture occurs.One good resume image After being encrypted to image, the grey level histogram of the ciphertext graph picture for obtaining should be smooth and uniform, can so prevent The person of stealing secret information cracks image by histogrammic leak.Accompanying drawing 3 (a) represents the histogram of plaintext image；Fig. 3 (b) represents encryption The histogram of image.It can be seen that the pixel value distributed pole of image is uneven before encryption, and the pixel value after encrypting is put down Slide and be evenly distributed in [0,255], can effectively resist the attack of statistical analysis.

4. original image adjacent pixel height correlation, after encryption image adjacent pixel coefficient correlation close to 0, not phase substantially Close.

In order to analyze plaintext image and ciphertext graph as the correlation of adjacent pixel, the coefficient correlation of adjacent pixel is introduced.Phase Relation number is bigger, illustrates that the correlation of adjacent pixel is bigger；Conversely, the correlation of adjacent pixel is smaller.From image respectively with Machine chooses 10000 pairs of levels, vertical and diagonally opposed adjacent pixels pair, and the phase relation of adjacent pixel is quantitatively calculated with equation below Number：

In formula, x, y represent the pixel value of two neighboring pixel in image respectively, and D (x) represents the mean square deviation of pixel value, E X () is the average value of pixel value, cov (x, y) is correlation function, R_x,yIt is the coefficient correlation of two neighboring pixel.

Wherein, point (x, y) place test result such as accompanying drawing 4 (a) and 4 (b) are shown, and Fig. 4 (a) is in original image horizontal direction The correlation analysis figure of adjacent pixel, Fig. 4 (b) is the correlation analysis figure of adjacent pixel in encrypted image horizontal direction.

In plain text, ciphertext correlation contrast see the table below：

Adjacent direction	Original image	Encrypted image
			Horizontal direction	0.9588	-0.0016
Vertical direction	0.9260	-0.0033
			It is diagonally opposed	0.9025	0.0130

It can be seen that plaintext image adjacent pixel is height correlation, coefficient correlation is close to 1.And the adjacent phase of encrypted image Close to 0, correlation is obviously reduced relation number between adjacent pixel, and now the statistical property of plaintext has been diffused into random ciphertext In, can effectively resist statistical attack.

5.NPCR is more than 33% more than 99%, UACI, and resisting differential attacking ability is strong.

Algorithm is stronger to the sensitiveness of plaintext, and the ability for resisting differential attack is also stronger, can use pixel count rate of change NPCR (Number of Pixels Change Rate) and normalization pixel value averagely change intensity UACI (Unified Average Changing Intensity) measure sensitiveness of the AES to plaintext.Computing formula is as follows：

In formula, M and N represents the line number and columns of image, C₁Represent original ciphertext graph picture, C₂Represent and obtained after changing in plain text The ciphertext graph picture for arriving, C₁(i, j) represents pixel value of the plaintext image at coordinate (i, j) place, C₂(i, j) represents that ciphertext graph picture is being sat Mark the pixel value at (i, j) place.D represents with ciphertext graph that as equirotal matrix the value of D (i, j) is by C₁(i, j) and C₂(i, j) determines It is fixed.If C₁(i, j)=C₂(i, j), then D (i, j)=0；If C₁(i,j)≠C₂(i, j), then D (i, j)=1.In the present invention, First pixel value of original plaintext image is changed to after 223 to obtain a new plaintext image, then the two images is used Same key is encrypted to form corresponding ciphertext graph as C₁And C₂.NPCR the and UACI values for calculating ciphertext graph picture are as shown in the table, can It is more than 33% with value of the value more than 99%, UACI for seeing NPCR.This shows, even if doing small change to original image, leads to Cross after this algorithm is encrypted, ciphertext graph picture also has obvious difference.Therefore, this algorithm can be effective against differential attack, NPCR the and UACI values of ciphertext graph picture：

	Ciphertext graph picture
		NPCR	0.9961
UACI	0.3342

6. the comentropy of ciphertext graph picture closely ideal value 8, AES security is good.

Comentropy is the important measure index of reflection information randomness, and the comentropy computing formula of information source m is：

Wherein, p (m_i) represent symbol m_iThe probability of appearance, 2ⁿIt is total status number of information source m.After information encryption, information The desired value of entropy is 8.If encrypted image comentropy closely 8, shows the ciphertext graph picture close to random distribution.

Lena images to standard 256 × 256 are encrypted with inventive algorithm, and the comentropy of ciphertext graph picture is 7.9971, closely ideal value 8, this shows that the AES of present invention offer has good security.

Example IV：Referring to Fig. 5 (a)~7 (b) Suo Shi, in the present embodiment, the programming software for using for MatlabR2014a, the Baboon images for choosing size for 512 × 512 are experimental subjects, and the process of image encryption is as follows：

Step 1., for 512 × 512 Baboon gray level images P is calculated, obtains one using SHA256 function pairs size (hexadecimal representation is the [e of 8 e, 49 f b, 50 a of c c d, 5 a a c 680505 to the cryptographic Hash of group 256 4 c 0 1 9 9 2 c e e 4 9 e 5 f c 8 4 1 7 2 4 5 6 8 6 c d b d e e 4 7 c 2 5 4 a 6 5]), and using it as image key Key, the Key of 256 is then scaled 32 decimal number k₁, k₂..., k₃₂ (142 73 251 92 205 10 90 172 104 5 5 228 192 25 146 206 228 158 95 200 65 114 69 104 108 219 222 228 124 37 74 101), for calculating the initial state value of memristor hyperchaotic system.

Initial state value (the x that step 2. will be obtained₀=0.5664, y₀=1.0664, z₀=1.0430, w₀=0.2008) Bring memristor hyperchaotic system into be iterated, the state value matrix X=that 4 sizes are respectively 1 × 1048576 can be obtained [x_1,1,x_1,2,...,x_1,1048576], Y=[y_1,1,y_1,2,...,y_1,1048576], Z=[z_1,1,z_1,2,...,z_1,1048576], W= [w_1,1,w_1,2,...,w_1,1048576], matrix X1=[x ' are then modified to obtain to state matrix X, Y, Z for obtaining_1,1,x ′_1,2,...,x′_1,1048576], Y1=[y '_1,1,y′_1,2,...,y′_1,1048576], Z1=[z '_1,1,z′_1,2,...,z′_1,1048576], So that x '_1,h、y′_1,h、z′_1,h∈ [1,8], is modified to obtain matrix W 1=[w ' to state value matrix W_1,1,w′_1,2,..., w′_1,1048576] so that w '_1,h∈ [0,1], h ∈ [1,1048576], and then X1, Y1, Z1, W1 be reassembled as size and be by row again 512 × 2048 matrix X_1, Y_1, Z_1, W_1.

Matrix X_1, Y_1, Z_1 after step 3. pair amendment restructuring are grouped, note A1=[X_1, Y_1], A2=[X_1, Z_1], A3=[Y_1, Z_1] chooses the rule needed for will being used for DNA dynamic codings followed by first pixel of plaintext Then matrix number R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3.

Eight bit planes of plaintext image P are reassembled as the matrix U that size is 512 × 4096 by step 4., make D (i, j)= [U (i, 2*j-1), U (i, 2*j)], will each two element be one group as an element in D, i ∈ [1,512], j ∈ in U [1,2048]。

Matrix D, R1, R2 are divided into 8 × 32 matrixs in block form by step 5. respectively, the size of each matrix in block form for 64 × 64, and the matrix after segmentation is designated as D_1, R_1, R_2, wherein represented respectively with D_1 [k], R_1 [k], R_2 [k] D_1, R_1, The matrix in block form of kth block in R_2, here k=1,2 ..., 256.

Step 6. chooses 8192 elements successively since first element of state value matrix W _ 1 by row, reformulates Size is 64 × 128 matrix, and the initial configuration C that it is developed as cellular automata⁰。

Step 7. is to initial configuration C⁰Developed, wherein C^kThe configuration obtained after kth time is developed is represented, is specifically existed When carrying out kth time and developing, evolution rules are determined by kth -1 time by the DNA matrixes obtained after diffusion, k=1,2 ..., 256。

Kth block matrix in block form D_1 [k] in D_1 is carried out DNA encoding by step 8. according to the coding rule in R_1 [k], and Matrix after coding is designated as DNA (D_1 [k])；The cellular configuration C obtained to differentiation^kAccording to correspondence in matrix in block form R_2 [k] Coding rule carry out DNA encoding, and the element after coding is designated as DNA (C^k)。

The encoder matrix DNA (D_1 [k]) that step 9. pair is obtained is diffused operation.

Step 10. makes k=k+1, and circulation performs step 7-10, until all of piecemeal all completes DNA encryptions.

Encrypted all piecemeal DNA matrixes are reassembled as 512 × 2048 matrix and according to coding rule square by step 11. The corresponding regular numbers of battle array R1 carry out DNA decoding operates, can obtain the binary matrix Q1 that a size is 512 × 4096, so Decimal system conversion operation is carried out to matrix Q1 afterwards, the decimal system ciphertext matrix Q2 that a size is 512 × 512 can be obtained, i.e., It is the ciphertext graph picture after encryption.

Specific steps are referred to described in embodiment two.Security point is carried out to resume image of the invention below Analysis.

1. key space is sufficiently large, it is sufficient to resist exhaustive attack

2. key sensitiveness is high

Accompanying drawing 5 (d), 5 (e), 5 (f) are initial value sensitivity experiments, wherein four-dimensional memristor chaos system parameter a=30, b =36, c=0.1, d=2.5, e=3.5, m₀=-0.5, m₁=-0.1, chooses the pixel value P (1) of matrix R1, R2 needed for encryption =147 and correct 256 cryptographic Hash keys (decimal representation) Key=142 73 251 92 205 10 90 172 104 5 5 228 192 25 146 206 228 158 95 200 65 114 69 104 108 219 222 228 124 37 74 101.Accompanying drawing 5 (d) is, when remaining initial value is constant, to make initial value m₀Decrypted image when=- 0.500000000001. Fig. 5 (e) and 5 (f) are when remaining initial value is constant, respectively by first (being changed to 143 by 142) of key Key and last position Decrypted image after (being changed to 102 by 101) change.From the point of view of the effect picture of decryption, AES is calculated key extreme sensitivity Method security is also more preferable.

3. the grey level histogram of ciphertext graph picture is smooth and uniform, and anti-Statistical Analysis Attacks ability is strong.

Accompanying drawing 6 (a) represents the histogram of plaintext image；Fig. 6 (b) represents the histogram of encrypted image.Can from figure Go out, the pixel value distributed pole of image is uneven before encryption, and the pixel value after encrypting is smoothed and is evenly distributed in [0,255] In, can effectively resist the attack of statistical analysis.

4. original image adjacent pixel height correlation, after encryption image adjacent pixel coefficient correlation close to 0, not phase substantially Close.

Shown in point (x, y) place test result such as accompanying drawing 7 (a) and 7 (b).Fig. 7 (a) is adjacent in original image horizontal direction The correlation analysis figure of pixel, Fig. 7 (b) is the correlation analysis figure of adjacent pixel in encrypted image horizontal direction.In plain text, ciphertext Correlation contrast see the table below：

Adjacent direction	Original image	Encrypted image
			Horizontal direction	0.7569	-0.0042
Vertical direction	0.8587	0.0076
			It is diagonally opposed	0.7184	-0.0010

It can be seen that plaintext image adjacent pixel is height correlation, coefficient correlation is close to 1.And the adjacent picture of encrypted image Close to 0, correlation is obviously reduced plain coefficient correlation between adjacent pixel, and now the statistical property of plaintext has been diffused into random In ciphertext, statistical attack can be effectively resisted.

5.NPCR is more than 33% more than 99%, UACI, and resisting differential attacking ability is strong.

In the present invention, first pixel value of original plaintext image is changed to after 148 to obtain a new plaintext image, so Afterwards the two images are encrypted to form corresponding ciphertext graph as C with same key₁And C₂.Calculate ciphertext graph picture NPCR and UACI values are as shown in the table, it can be seen that value of the value of NPCR more than 99%, UACI is more than 33%.This shows, even if to original Image does small change, and after being encrypted by this algorithm, ciphertext graph picture also has obvious difference.Therefore, this algorithm can To be effective against differential attack.NPCR the and UACI values of ciphertext graph picture：

	Ciphertext graph picture
		NPCR	0.9961
UACI	0.3353

6. the comentropy of ciphertext graph picture closely ideal value 8, AES security is good.

Baboon images to standard 512 × 512 are encrypted with inventive algorithm, and ciphertext image information entropy is 7.9992, closely ideal value 8, this shows that the AES of present invention offer has good security.

Embodiment five：Referring to Fig. 8 (a)~10 (b) Suo Shi, in the present embodiment, the programming software for using for MatlabR2014a, the City images for choosing size for 256 × 320 are experimental subjects, and the process to City image encryptions is as follows：

Step 1., for 256 × 320 City gray level images P is calculated, obtains one group using SHA256 function pairs size (hexadecimal representation is the [c of 90 e of c b, 3 c, 14 f b b, 11 b a e of c e c e c 2 to the cryptographic Hash of 256 6 9 e 8 7 2 3 c 2 2 1 c a f 9 0 5 e c 0 d 2 d 6 5 3 0 3 1 a c 9 9 c 8 1 0 f d F]), and then the Key of 256 is scaled 32 decimal number k by it as image key Key₁, k₂..., k₃₂(203 144 227 193 79 187 28 236 236 27 174 44 105 232 114 60 34 28 175 144 94 192 210 214 83 3 26 201 156 129 15 223), for calculating the initial state value of memristor hyperchaotic system.

Initial state value (the x that step 2. will be obtained₀=0.4883, y₀=1.2656, z₀=0.6055, w₀=0.2166) Bring memristor hyperchaotic system into be iterated, the state value matrix X=[x that 4 sizes are respectively 1 × 327680 can be obtained_1,1, x_1,2,...,x_1,327680], Y=[y_1,1,y_1,2,...,y_1,327680], Z=[z_1,1,z_1,2,...,z_1,327680], W=[w_1,1, w_1,2,...,w_1,327680], matrix X1=[x ' are then modified to obtain to matrix X, Y, Z for obtaining_1,1,x′_1,2,..., x′_1,327680], Y1=[y '_1,1,y′_1,2,...,y′_1,327680], Z1=[z '_1,1,z′_1,2,...,z′_1,327680] so that x '_1,h、 y′_1,h、z′_1,h∈ [1,8], is modified to obtain matrix W 1=[w ' to state value matrix W_1,1,w′_1,2,...,w′_1,327680] so that w′_1,h∈ [0,1], h ∈ [1,327680], so again by X1, Y1, Z1, W1 by row be reassembled as size be 256 × 1280 matrix X_1、Y_1、Z_1、W_1。

Matrix X_1, Y_1, Z_1 after step 3. pair amendment restructuring are grouped, note A1=[X_1, Y_1], A2=[X_1, Z_1], A3=[Y_1, Z_1] chooses the rule needed for will being used for DNA dynamic codings followed by first pixel of plaintext Then matrix number R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3.

Eight bit planes of plaintext image P are reassembled as the matrix U that size is 256 × 2560 by step 4., make D (i, j)= [U (i, 2*j-1), U (i, 2*j)], will each two element be one group as an element in D, i ∈ [1,256], j ∈ in U [1,1280]。

Matrix D, R1, R2 are divided into 4 × 20 matrixs in block form by step 5. respectively, the size of each matrix in block form for 64 × 64, and the matrix after segmentation is designated as D_1, R_1, R_2, wherein represented respectively with D_1 [k], R_1 [k], R_2 [k] D_1, R_1, The matrix in block form of kth block in R_2, here k=1,2 ..., 80.

Step 6. chooses 8192 elements successively from state value matrix W 1, reformulates the matrix that size is for 64 × 128, And the initial configuration C that the matrix is developed as cellular automata⁰。

Step 7. is to initial configuration C⁰Developed, wherein C^kThe configuration obtained after kth time is developed is represented, is specifically existed When carrying out kth time and developing, evolution rules are determined by kth -1 time by the DNA matrix-blocks obtained after diffusion, k=1,2 ..., 80。

Kth block matrix in block form D_1 [k] in D_1 is carried out DNA encoding by step 8. according to the coding rule in R_1 [k], and Matrix after coding is designated as DNA (D_1 [k])；The cellular configuration C obtained to differentiation^kAccording to correspondence in matrix in block form R_2 [k] Coding rule carry out DNA encoding, and the matrix after coding is designated as DNA (C^k)。

The encoder matrix DNA (D_1 [k]) that step 9. pair is obtained is diffused operation.

Step 10. makes k=k+1, and circulation performs step 7-10, until all of piecemeal all completes DNA encryptions.

Encrypted all piecemeal DNA matrixes are reassembled as 256 × 1280 matrix and according to coding rule square by step 11. The corresponding regular numbers of battle array R1 carry out DNA decoding operates, can obtain the binary matrix Q1 that a size is 256 × 2560, so Decimal system conversion operation is carried out to matrix Q1 afterwards, the decimal system ciphertext matrix Q2 that a size is 256 × 320 can be obtained, i.e., It is the ciphertext graph picture after encryption.

Specific steps are referred to described in embodiment two.Security point is carried out to resume image of the invention below Analysis：

1. key space is sufficiently large, it is sufficient to resist exhaustive attack；

2. key sensitiveness is high, and accompanying drawing 8 (d), 8 (e), 8 (f) are initial value sensitivity experiments, wherein four-dimensional memristor chaos System control parameters a=30, b=36, c=0.1, d=2.5, e=3.5, m₀=-0.5, m₁=-0.1, chooses square needed for encryption The pixel value P (1)=102 of battle array R1, R2 and correct 256 cryptographic Hash keys Key (decimal representation)=203 144 227 193 79 187 28 236 236 27 174 44 105 232 114 60 34 28 175 144 94 192 210 214 83 3 26 201 156 129 15 223.Accompanying drawing 8 (d) is, when remaining initial value is constant, to make initial value e= Decrypted image when 3.500000000001.Fig. 8 (e) and 8 (f) are when remaining initial value is constant, respectively by the first of key Key Decrypted image behind position (being changed to 204 by 203) and the change of last position (being changed to 224 by 223).Come from the effect picture of decryption See, this AES is extremely sensitive to key, and algorithm security is also more preferable；

3. the grey level histogram of ciphertext graph picture is smooth and uniform, and anti-Statistical Analysis Attacks ability is strong, and accompanying drawing 9 (a) represents bright The histogram of texts and pictures picture；Fig. 9 (b) represents the histogram of encrypted image.It can be seen that the pixel value of image divides before encryption Cloth is extremely uneven, and the pixel value after encrypting is smoothed and is evenly distributed in [0,255], can effectively resist statistical analysis Attack；

4. original image adjacent pixel height correlation, after encryption image adjacent pixel coefficient correlation close to 0, not phase substantially Close, shown in point (x, y) place test result such as accompanying drawing 10 (a) and 10 (b).Figure 10 (a) is adjacent picture in original image horizontal direction The correlation analysis figure of element, Figure 10 (b) is the correlation analysis figure of adjacent pixel in encrypted image horizontal direction.In plain text, ciphertext Correlation contrast see the table below：

Adjacent direction	Original image	Encrypted image
			Horizontal direction	0.7789	0.0025
Vertical direction	0.6197	0.0036
			It is diagonally opposed	0.5907	-0.0090

It can be seen that plaintext image adjacent pixel is height correlation, and the coefficient correlation of the adjacent pixel of encrypted image connects It is bordering on correlation between 0, adjacent pixel to be obviously reduced, now the statistical property of plaintext has been diffused into random ciphertext, can be with Effectively resist statistical attack；

5.NPCR is more than 33% more than 99%, UACI, and resisting differential attacking ability is strong, in the present invention, by original plaintext image First pixel value be changed to after 148 obtain a new plaintext image, then the two images are encrypted with same key Corresponding ciphertext graph is formed as C₁And C₂.NPCR the and UACI values for calculating ciphertext graph picture are as shown in the table, it can be seen that the value of NPCR Value more than 99%, UACI is more than 33%.This is shown, even if doing small change to original image, is added by this algorithm After close, ciphertext graph picture also has obvious difference.Therefore, this algorithm can be effective against differential attack.The NPCR of ciphertext graph picture With UACI values：

	Ciphertext graph picture
		NPCR	0.9960
UACI	0.3345

6. the comentropy of ciphertext graph picture closely ideal value 8, AES security is good, to standard 256 × 320 City gray level images are encrypted with inventive algorithm, and ciphertext image information entropy is 7.9976, closely ideal value 8, this table The AES that the bright present invention is provided has good security.

From above-described embodiment, the AES that the present invention is provided can carry out Gao An to the gray level image of M=N or M ≠ N Full encryption, has broad application prospects in field of information encryption.

The invention is not limited in above-mentioned specific embodiment, those skilled in the art can also accordingly make various changes, But it is any all to cover within the scope of the claims with equivalent or similar change of the invention.

Claims (5)

1. it is a kind of based on memristor hyperchaotic system, cellular automata and DNA calculate image encryption method, it is characterised in that：Bag Containing following steps：

Step 1., for the plaintext image P of M × N is calculated, obtains the cryptographic Hash of a group 256 using SHA256 function pairs size And the image key Key of 256 is scaled 32 decimal number k by it as image key Key₁, k₂..., k₃₂, calculate The initial state value of the memristor hyperchaotic system based on Chua circuits；

The initial state value that step 2. will be obtained is brought memristor hyperchaotic system into and is iterated, obtain 4 sizes be respectively 1 × The state value matrix X=[x of 4MN_1,1,x_1,2,...,x_1,4MN], Y=[y_1,1,y_1,2,...,y_1,4MN], Z=[z_1,1,z_1,2,..., z_1,4MN], W=[w_1,1,w_1,2,...,w_1,4MN], matrix X1=[x ' are modified to obtain to state value matrix X, Y, Z_1,1,x ′_1,2,...,x′_1,4MN], Y1=[y '_1,1,y′_1,2,...,y′_1,4MN], Z1=[z '_1,1,z′_1,2,...,z′_1,4MN] so that x '_1,h、 y′_1,h、z′_1,h∈ [1,8], is modified to obtain matrix W 1=[w ' to state value matrix W_1,1,w′_1,2,...,w′_1,4MN] so that w′_1,h∈ [0,1], h ∈ [Isosorbide-5-Nitrae MN], the matrix X_1, Y_1, Z_ that size is M × 4N are reassembled as by X1, Y1, Z1, W1 by row respectively 1, W_1；

Matrix X_1, Y_1, Z_1 after step 3. pair restructuring are grouped, note A1=[X_1, Y_1], A2=[X_1, Z_1], A3 =[Y_1, Z_1], using plaintext first pixel choose will be used for DNA dynamic codings needed for regular matrix number R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3, wherein, the rule for choosing R1 and R2 is as follows：

Index=mod (P (1), 3)+1；

If index=1, then i=1, Ai=A1, now R1=X_1, R2=Y_1；

If index=2, then i=2, Ai=A2, now R1=X_1, R2=Z_1；

If index=3, then i=3, Ai=A3, now R1=Y_1, R2=Z_1；

Wherein, index is a variable of setting, and X_1, Y_1, Z_1 represent the state value matrix after amendment restructuring, and P (1) is represented First pixel value of plaintext image, mod (a, b) represents a to b modulus, i ∈ [1,3]；

Step 4. by plaintext image P step-by-steps launch, obtain eight bit planes and be reassembled as size be M × 8N matrix U, make D (i, J)=[U (i, 2*j-1), U (i, 2*j)], is one group by each two element in matrix U, as an element in D, i ∈ [1, M], j ∈ [Isosorbide-5-Nitrae N]；

Matrix D, R1, R2 are divided into p × q matrix in block form by step 5. respectively, and the size of each matrix in block form is m × n, and completely Sufficient m × p=M, n × q=4N, and the matrix after segmentation is reassembled as size for the one-dimensional matrix of 1 × pq by row respectively and is designated as D_1, R_1, R_2, wherein representing the matrix in block form of kth block in D_1, R_1, R_2, k respectively with D_1 [k], R_1 [k], R_2 [k] =1,2 ..., p × q；

Step 6. chooses 2mn element successively since first element of matrix W _ 1 by row, and reformulation size is m × 2n Matrix, and the initial configuration C that the matrix is developed as cellular automata⁰；

Step 7. is to initial configuration C⁰Developed, wherein C^kThe configuration obtained after kth time is developed is represented, is developed kth time is carried out When, evolution rules are determined for -1 time by kth by the DNA image block obtained after diffusion, k=1,2 ..., p × q；

Step 8. is by kth block matrix in block form D_1 [k] in D_1 according to the coding rule in kth block matrix in block form R_1 [k] in R_1 DNA encoding is carried out, and the matrix after coding is designated as DNA (D_1 [k])；The cellular configuration C obtained to differentiation^kAccording in R_2 Corresponding coding rule carries out DNA encoding in k block matrixs in block form R_2 [k], and the matrix after coding is designated as into DNA (C^k), k= 1,2,...,p×q；

The encoder matrix DNA (D_1 [k]) that step 9. pair is obtained is diffused operation；

Step 10. makes k=k+1, and circulation performs step 7-10, until all of piecemeal all completes DNA encryptions；

Encrypted all piecemeal DNA matrixes are reassembled as the matrix of M × 4N and according to correspondence in regular matrix number R1 by step 11. Regular number carry out DNA decoding operates, obtain a size be M × 8N binary matrix Q1, ten then are carried out to matrix Q1 System conversion operation, obtains the decimal system ciphertext matrix Q2 that a size is M × N, the ciphertext graph picture after as encrypting.

2. it is according to claim 1 based on memristor hyperchaotic system, cellular automata and DNA calculate image encryption side Method, it is characterised in that：The expression formula of the memristor hyperchaotic system based on Chua circuits is in the step 1：

$\left\{\begin{array}{c}\stackrel{\·}{x}=a\[W\left(w\right)(y-x)-h\left(x\right)\]\\ \stackrel{\·}{y}=W\left(w\right)(x-y)+z\\ \stackrel{\·}{z}=-by-cz\\ \stackrel{\·}{w}=y-x\end{array}\right.$ ,

Wherein, h (x)=m₁x+0.5(m₀-m₁) × (| x+1 |-| x-1 |),X, y, Z, w represent the state variable of memristor hyperchaotic system, a, b, c, d, e, m₀、m₁It is the control parameter of memristor hyperchaotic system, and Work as a=30, b=36, d=2.5, e=3.5, m₀=-0.5, m₁During=- 0.1 and c ∈ [0.073,0.162], system is in super mixed Ignorant state；And by formula：

$\left\{\begin{array}{c}{x}_0=\frac{1}{256}(k_1\⊕k_2\⊕k_3\⊕k_4+k_5\⊕k_6\⊕k_7\⊕k_8)\\ y_0=\frac{1}{256}(k_9\⊕k_{10}\⊕k_{11}\⊕k_{12}+k_{13}\⊕k_{14}\⊕k_{15}\⊕k_{16})\\ z_0=\frac{1}{256}(k_{17}\⊕k_{18}\⊕k_{19}\⊕k_{20}+k_{21}\⊕k_{22}\⊕k_{23}\⊕k_{24})\\ w_0=\frac{1}{32}\×\frac{sum(k_{21},k_{22},...,k_{32})}{\max (k_{21},k_{22},...,k_{32})}\end{array}\right.$ ,

Calculate the initial state value x of the state variable of the memristor hyperchaotic system based on Chua circuits₀, y₀, z₀And w₀, wherein, sum (k₂₁,k₂₂,...,k₃₂) represent to k₂₁,k₂₂,...,k₃₂Sued for peace, max (k₂₁,k₂₂,...,k₃₂) represent and seek k₂₁, k₂₂,...,k₃₂Maximum,Representative takes the XOR of x and y.

3. it is according to claim 2 based on memristor hyperchaotic system, cellular automata and DNA calculate image encryption side Method, it is characterised in that：The step 2 is specifically comprised the following steps：

Step 2.1, the initial state value x that will be calculated by step 1₀, y₀, z₀And w₀The memristor based on Chua circuits is brought into surpass Chaos system iteration N0 times, whereinObtain the state that size is respectively 1 × 4MN Value matrix X=[x_1,1,x_1,2,...,x_1,4MN], Y=[y_1,1,y_1,2,...,y_1,4MN], Z=[z_1,1,z_1,2,...,z_1,4MN], W= [w_1,1,w_1,2,...,w_1,4MN]；

Step 2.2, matrix X1, Y1, Z1, W1 are modified to obtain by correction formula respectively to state value matrix X, Y, Z, W, wherein Correction formula is as follows：

X1=mod ((abs (x_1,h)-floor(x_1,h))×10¹⁴, 8) and+1,

Y1=mod ((abs (y_1,h)-floor(y_1,h))×10¹⁴), 8)+1,

Z1=mod ((abs (z_1,h)-floor(z_1,h))×10¹⁴, 8) and+1,

W1=mod ((abs (w_1,h)-floor(w_1,h))×10¹⁴, 2),

Wherein, x_1,h, y_1,h, z_1,h, w_1,hH-th value in state value matrix X, Y, Z, W, h ∈ [1, M × 4N] are represented respectively；abs X () represents and x is taken absolute value, floor (x) is represented and taken the no more than maximum integer of x, and mod (a, b) represents modulus fortune of a to b Calculate；

Step 2.3, by X1, Y1, Z1, W1 respectively by row be reassembled as size be M × 4N matrix X_1, Y_1, Z_1, W_1.

4. it is according to claim 3 based on memristor hyperchaotic system, cellular automata and DNA calculate image encryption side Method, it is characterised in that：

Step 7 is specifically comprised the following steps：

Step 7.1, by equation below：

$S_{i,j}^{t+1}=L\⊕(VM\×S_{i,j}^t)\⊕(VT\×S_{i-1,j}^t)\⊕(VL\×S_{i,j-1}^t)\⊕(VD\×S_{i+1,j}^t)\⊕(VR\×S_{i,j+1}^t)$

Cellular automata evolution rules are determined, wherein,Represent and be in the shape of the center cellular at position (i, j) place at the t+1 moment State value,The state value that the center cellular at position (i, j) place is in moment t is represented,Point The state value that upper, left, down, right neighbours' cellular of center cellular is in moment t is not represented, and L, VM, VT, VL, VD, VR are values It is 0 or 1 variable；If L=1, represent that rule is Non―linear programming, be otherwise exactly linear programming, VM, VT, VL, VD, VR point Do not control whether middle, upper, five cellulars of left, down, right participate in cellular evolution process, if corresponding in VM, VT, VL, VD, VR Be worth is 0, then it represents that its corresponding cellular is not involved in developing；The value of L, VM, VT, VL, VD, VR is by the evolution rules in step 7.2 Rule (k) is determined；

Step 7.2, by formula：

$\begin{array}{c}rule\left(k\right)=L\×2^5+VM\×2^4+VT\×2^3+VL\×2^2+VD\×2^1+VR\×2^0\\ =\left\{\begin{array}{cc}\mathrm{mod}\left(sum\left(DNA\left(E\left(k-1\right)\right)\right),64\right);& k\≠1\\ \mathrm{mod}\left(sum\left(E\left(0\right)\right),64\right);& k=1\end{array}\right.\end{array}$

Determine cellular automata evolution rules number, wherein, rule (k) represents that cellular carries out regular number when kth time is developed, DNA (E (k-1)) represents the previous DNA matrixs in block form by being obtained after diffusion, and sum (DNA (E (k))) is represented after being spread to k-th DNA matrixes each element ASCII character value summation, as k=1, E (0)=C⁰, C⁰Represent the initial configuration of cellular, k= 1,2,...,p×q；

Step 7.3, the rule (k) that will be calculated in step 7.2 are changed into binary system, that is, try to achieve L, VM, VT, VL, VD, VR Value, while according to step 7.1) determine the function that cellular is developed.

5. it is according to claim 4 based on memristor hyperchaotic system, cellular automata and DNA calculate image encryption side Method, it is characterised in that：

Dispersion operation is specifically included in the step 9：By formula：

$\left\{\begin{array}{c}DNA(E\[1\])=DNA\left(C^1\right)\⊕DNA(D\_1\[1\])\⊕DNA(D\_1\[p\×q\]),k=1\\ DNA(E\[k\])=DNA\left(C^k\right)\⊕DNA(D\_1\[k\])\⊕DNA(E\[k-1\]),k\≠1\end{array}\right.$ ,

Encoder matrix DNA (D_1 [k]) to obtaining is diffused operation.