CN106023052A

CN106023052A - Image encryption algorithm based on memoristor hyper-chaotic system, cellular automaton and DNA calculation

Info

Publication number: CN106023052A
Application number: CN201610303944.5A
Authority: CN
Inventors: 柴秀丽; 刘鹏飞; 贾培艳; 甘志华; 杨康; 张苗辉
Original assignee: Henan University
Current assignee: Henan University
Priority date: 2016-05-09
Filing date: 2016-05-09
Publication date: 2016-10-12
Anticipated expiration: 2036-05-09
Also published as: CN106023052B

Abstract

The invention relates to an image encryption algorithm based on memoristor hyper-chaotic system, cellular automaton and DNA calculation. First of all, a four-dimensional memoristor hyper-chaotic system based on a Chua circuit is employed, at the same time, a secret key is generated by enabling a plaintext image on an SHA256 function; a pseudo random sequence generated by the chaos system is taken as a basis of DNA dynamic encoding, rules of cellular dynamic evolution are determined according to a DNA matrix after diffusion, and in an encryption process, partitioning processing is performed on the image; and finally, the image is encrypted through a pseudo DNA calculation method, and diffusion operation is carried out while the image is scrambled. According to the invention, on one hand, secret key space is increased and the capability of the algorithm in fending off violent attacks is enhanced; and on the other hand, the secret key is enabled to be generated through close reliance on a plaintext, the capability of the algorithm in fending off plaintext attacks is improved, the capability of fending off exhausive attacks is higher, parallel calculation is facilitated, the operation efficiency is further improved, and the security of the algorithm is improved.

Description

The resume image calculated based on memristor hyperchaotic system, cellular automata and DNA

Technical field

The present invention relates to image encryption field, particularly to one based on memristor hyperchaotic system, cellular automata and DNA The resume image calculated.

Background technology

Now, along with the fast development of intelligent terminal and universal, the most information in our life, such as The picture shared on microblogging, utilize wechat video conversation etc., will be by the transmission of network.Image is raw owing to having image The advantage such as dynamic, simple, directly perceived, has been developed as exchange way indispensable in our life.But, network is pacified by people Full research does not reach a cocksure stage, so the transmission that image is in a network there is also huge safety Leak.The news report that information is divulged a secret is the most of common occurrence, it is ensured that the safety that information is in network transmits has become For researcher must faced by problem.As a rule, image to be transmitted is usually constructed with the feature that some are identical, all exists That data volume is big, neighbor dependency strong, redundancy high.Originally, the research of information security is mainly focused on by people In text message, they are the most all with one-dimensional data stream as design object, as DES, 3-DES and RSA etc., do not consider To the feature of digital picture, if using the cipher mode identical with text message that image is encrypted, its cipher round results Do not reach intended purpose.Put people so finding a kind of safe, reliable, practical image encryption method In front.At present, use chaos system and combine other cryptographic means and image is encrypted has become as information security research One focus, has huge application potential.

Past, most of resume image was all based on the chaos system of low-dimensional, and Low-dimensional Chaotic Systems has structure letter Single, easily operated and calculate fireballing advantage, but Low-dimensional Chaotic Systems is less due to key space, the pseudorandom sequence of generation Row complexity is the highest and is easily subject to shortcoming that phase space reconfiguration method attacks and the safety of image that causes it to encrypt is the highest, with The raising of the computer speed of service and the proposition of New Algorithm, much AES based on Low-dimensional Chaotic Systems is become Merit cracks, and this just promotes more scholar to be encrypted image by the hyperchaotic system using higher-dimension.Hyperchaotic system Attractor has impalpable topological structure, 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 makes hyperchaotic system possess higher at communication encryption and information security field Use value.Start along with the scientist of HP Lab in 2008 successfully develops the memristor of first physics realization, Various hyperchaotic system based on memristor also have become as a focus of academia research.Memristor is a kind of non-linear nothing Source element, has advantage non-linear, non-volatile, that volume is little and low in energy consumption, and this all makes memristor become chaotic sea The ideal chose of circuit.Chaos system based on memristor has following advantage: 1. memristor has nano level chi Very little, when the non-linear timesharing being applied to chaos system can be substantially reduced the physical size of system；2. the resistance of memristor is Produce along with magnetic flux or the change of electric charge, its VA characteristic curve can zero crossing, various non-linear song can be obtained Line, this provides for improved the complexity of chaos system and the randomness of signal；The most most of memristor materials can be held concurrently with CMOS technology Holding, this allows for memristor system and has lower energy expenditure, and due to these advantages, memristor chaos system adds in communication and information Close field has broad application prospects.

In recent years, along with deepening continuously of cellular automata research, cellular automata is applied to image encryption increasingly Favored by researcher.Cellular automata belongs to a kind of discrete dynamical system, has in time, state and the most all Discrete characteristic, in addition, structure cell is simple, concurrency good, each cellular by simple with or etc. logical operations group Becoming, computing is simple, and being especially suitable for the realization of image encryption, especially two dimensional cellular automaton has in terms of parallel encryption especially Natural advantage, so being combined with cellular automata by chaos system, to be used for image encryption be also one new direction of image encryption. But, current image encryption technology and relevant theory are the most perfect, and a lot of algorithms only rely only on cellular automata or list Pure chaotic maps carries out figure encryption, safety or not high enough, it is therefore necessary to the image finding a kind of compound structure adds Close system.

Currently, another uses more image encryption method to utilize pseudo-DNA to calculate exactly and is encrypted image, DNA encryption is mainly with the limitation of biology techniques for safety foundation, unrelated with computing capability, even therefore quantum calculation Machine also cannot break through the cryptographic protection of DNA, thus has higher safety.Simultaneously as DNA calculate have many other Characteristic not available for calculation, such as superelevation concurrency, super low energy consumption etc., has again superpower storage capacity, and this makes DNA count Calculate and there is in cryptography inborn advantage.But existing AES biotic experiment to be depended on based on DNA enters Row operation, the shortcomings such as due to biotic experiment apparatus expensive, experimental situation is difficult to control to, and experiment susceptiveness is high, cause counting based on DNA The encryption method calculated or theory, more than practice, can avoid biotic experiment by using pseudo-DNA calculating to be encrypted image. In addition, DNA encoding rule has 8 kinds, and great majority AES based on DNA is all to use a certain coding rule therein Then, it is strong to the resistivity of exhaustive attack that this has resulted in algorithm, the safety storage of serious threat information and transmission.

Summary of the invention

For overcoming deficiency of the prior art, the present invention propose a kind of based on memristor hyperchaotic system, cellular automata and The resume image that DNA calculates, overcomes that Low-dimensional Chaotic Systems key space is little, safety is the highest and algorithm lacks with bright The shortcoming of system of Federation of Literary and Art Circles, also eliminates the DNA regular coding anti-exhaustive attack ability of rule more weak raw by complexity with DNA encryption simultaneously Thing operation realizes the drawback that difficulty is big, has higher anti-exhaustive attack ability, and during encryption, does image Piecemeal processes, it is simple to parallel computation, improves efficiency；By pseudo-DNA computational methods, image is encrypted, has broken away from the life of complexity Thing experimental implementation, and this algorithm is encryption based on bit-level, has been also carried out diffusion behaviour while image is carried out scramble Make, improve the safety of algorithm.

According to design provided by the present invention, a kind of based on memristor hyperchaotic system, cellular automata and DNA calculating Resume image, comprise the steps of:

Step 1. utilizes SHA256 function to calculate the plaintext image P that size is M × N, obtains the Kazakhstan of a group 256 Wish value and using it as image key Key, image key Key of 256 is scaled 32 decimal number k₁, k₂..., k₃₂, Calculate the initial state value of four-dimensional memristor hyperchaotic system based on Chua circuit；

Step 2. is brought the initial state value obtained into memristor hyperchaotic system 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], state value matrix X, Y, Z are modified obtaining matrix X1= [x₁'_,1,x₁'_,2,...,x₁'_,4MN], Y1=[y₁'_,1,y₁'_,2,...,y₁'_,4MN], Z1=[z₁'_,1,z₁'_,2,...,z₁'_,4MN], make Obtain x₁'_,h、y₁'_,h、z₁'_,h∈ [1,8], is modified obtaining matrix W 1=[w to state value matrix W₁'_,1,w₁'_,2,...,w₁'_,4MN], Make w₁'_,h∈ [0,1], h ∈ [Isosorbide-5-Nitrae MN], be reassembled as, by row, the matrix X_1, Y_ that size is M × 4N respectively by X1, Y1, Z1, W1 1, Z_1, W_1；

Matrix X_1, Y_1, Z_1 after restructuring is grouped by step 3., note A1=[X_1, Y_1], A2=[X_1, Z_ 1], A3=[Y_1, Z_1], utilize first pixel in plain text to choose the regular matrix number will being used for needed for DNA dynamic coding R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3；

Step 4. will be launched in plain text in image P step-by-step, for the matrix U of M × 8N sized by obtaining eight bit planes and recombinating,

(i, j)=[U (i, 2*j-1), U (i, 2*j)], is one group by each two element in matrix U, as in D to make 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 also by row respectively It is designated as D_1, R_1, R_2, wherein represents the piecemeal square of kth block in D_1, R_1, R_2 with D_1 [k], R_1 [k], R_2 [k] respectively Battle array, k=1,2 ..., p × q；

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

Step 7. is to initial configuration C⁰Develop, wherein C^kRepresent the configuration obtained after kth time develops, carry out kth time During differentiation, the DNA matrix-block that evolution rules is obtained for-1 time by kth after diffusion determines, k=1,2 ..., p × q；

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

Step 9. is diffused operation to the encoder matrix DNA (D_1 [k]) obtained；

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

Encrypted all piecemeal DNA matrixes are reassembled as the matrix of M × 4N and according in rule matrix number R1 by step 11. Corresponding regular number carries out DNA decoding operation, obtains the binary matrix Q1 that size is M × 8N, then enters matrix Q1 The conversion operation of row decimal scale, obtains the decimal scale ciphertext matrix Q2 that size is M × N, is the ciphertext graph picture after encryption.

Above-mentioned, in described step 1, the expression formula of four-dimensional memristor hyperchaotic system based on Chua circuit is:

Wherein, h (x)=m₁x+0.5(m₀-m₁) × (| x+1 |-| x-1 |), X, y, z, w represent the state variable of chaos system, a, b, c, d, e, m₀、m₁It is the control parameter of chaos system, and works 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 pass through formula:

Calculate the initial state value x of the state variable of four-dimensional memristor hyperchaotic system based on Chua circuit₀, y₀, z₀With w₀, wherein, sum (k₂₁,k₂₂,...,k₃₂) represent k₂₁,k₂₂,...,k₃₂Sue for peace, max (k₂₁,k₂₂,...,k₃₂) represent Seek k₂₁,k₂₂,...,k₃₂Maximum,Represent the XOR taking x and y.

Above-mentioned, described step 2 specifically comprises the steps of:

Step 2.1, will be by step 1 calculated initial state value x₀, y₀, z₀And w₀Bring into based on Chua circuit Four-dimensional memristor hyperchaotic system iteration N0 time, whereinObtain 4 sizes to be respectively The state value matrix X=[x of 1 × 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, to state value matrix X, Y, Z, W respectively by revise Formula is modified obtaining matrix X1, Y1, Z1, W1, and 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,hRepresent the h value in state value matrix X, Y, Z, W, h ∈ [Isosorbide-5-Nitrae MN] respectively； X is taken absolute value by abs (x) expression, and floor (x) represents the maximum integer taking no more than x, and (a b) represents a delivery to b to mod Computing；

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

Above-mentioned, step 7 specifically comprises the steps of:

Step 7.1, equation below of passing through:

Determine cellular automata evolution rules, set the state space of cellular as 0,1}, wherein,Represent when t+1 Be in quarter position (i, j) state value of the center cellular at place,Represent and be in position (i, j) the center cellular at place at moment t State value,It is illustrated respectively in moment t and is in upper, the neighbours unit of left, down, right of center cellular The state value of born of the same parents, L, VM, VT, VL, VD, VR be value be the variable of 0 or 1；If L=1, represent that rule is Non-linear programming, no Being exactly then linear programming, VM, VT, VL, VD, VR control middle, upper, five cellulars of left, down, right respectively and whether participate in cellular and develop Process, if value corresponding in VM, VT, VL, VD, VR is 0, then it represents that the cellular of its correspondence 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, pass through formula:

Determining cellular automata evolution rules number, wherein, rule (k) represents that cellular carries out regular number when kth time develops, DNA (E (k-1)) represents the previous DNA matrix-block obtained after diffusion, and sum (DNA (E (k))) represents kth diffusion After DNA matrix 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, rule (k) calculated in step 7.2 is changed into binary system, i.e. try to achieve L, VM, VT, VL, VD, The value of VR, simultaneously according to step 7.1) determine the function that cellular develops.

Above-mentioned, in described step 9, dispersion operation specifically comprises: pass through formula:

The encoder matrix DNA (D_1 [k]) obtained is diffused operation.

Beneficial effects of the present invention:

The present invention overcomes in prior art that Low-dimensional Chaotic Systems key space is little, safety is the highest and algorithm lacks with bright The shortcoming of system of Federation of Literary and Art Circles, also eliminates the DNA regular coding anti-exhaustive attack ability of rule more weak raw by complexity with DNA encryption simultaneously Thing operation realizes the drawback that difficulty is big；Using four-dimensional memristor hyperchaotic system based on Chua circuit, image passes through the most in plain text Act on SHA256 function to produce key, increase key space, strengthen the ability of algorithm opposing brute force attack, the most again The generation making key depends in plain text tightly, improves the ability of algorithm opposing chosen-plain attact；Chaos system is produced Pseudo-random sequence as DNA dynamic coding according to and according to diffusion after DNA matrix determine cellular dynamic evolution Rule, much combines DNA compared to current other and calculates the fixed dna coding rule used in the AES with cellular automata Then evolution rules single with cellular, this algorithm has higher anti-exhaustive attack ability, and during encryption, to image Do piecemeal process, it is simple to parallel computation, improve efficiency；By pseudo-DNA computational methods, image is encrypted, breaks away from complexity Biological experiment operating, and this algorithm is encryption based on bit-level, has been also carried out expanding while image is carried out scramble Dissipate operation, improve the safety of algorithm.

Accompanying drawing illustrates:

Fig. 1 is the schematic flow sheet of the present invention；

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

Fig. 2 (b) is image after the encryption used by embodiment three；

Fig. 2 (c) be the key used by embodiment three correct time decrypted image；

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

Fig. 2 (e) is two of the decrypted image during use false key used by embodiment three；

Fig. 2 (f) is three of the decrypted image during use false key used by embodiment three；

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

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

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

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

Fig. 5 (a) is original image used by embodiment four；

Fig. 5 (b) is image after the encryption used by embodiment four；

Fig. 5 (c) be the key used by embodiment four correct time decrypted image；

Fig. 5 (d) is one of decrypted image during the use false key used by embodiment four；

Fig. 5 (e) is two of the decrypted image during use false key used by embodiment four；

Fig. 5 (f) is three of the decrypted image during use false key used by embodiment four；

Fig. 6 (a) is the rectangular histogram of the original image used by embodiment four；

Fig. 6 (b) is the rectangular histogram of the encrypted image used by embodiment four；

Fig. 7 (a) is the correlation analysis figure of neighbor in the original image horizontal direction used by embodiment four；

Fig. 7 (b) is the correlation analysis figure of neighbor in the encrypted image horizontal direction used by embodiment four；

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

Fig. 8 (b) is image after the encryption used by embodiment five；

Fig. 8 (c) be the key used by embodiment five correct time decrypted image；

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

Fig. 8 (e) is two of the decrypted image during use false key used by embodiment five；

Fig. 8 (f) is three of the decrypted image during use false key used by embodiment five；

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

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

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

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

Detailed description of the invention:

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, shown in Figure 1, a kind of image calculated based on memristor hyperchaotic system, cellular automata and DNA AES, comprises the steps of:

Step 7. is to initial configuration C⁰Develop, wherein C^kRepresent the configuration obtained after kth time develops, carry out kth time During differentiation, the DNA image block that evolution rules is obtained for-1 time by kth after diffusion determines, k=1,2 ..., p × q；

Step 9. is diffused operation to the encoder matrix DNA (D_1 [k]) obtained；

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

Step 1. utilizes SHA256 function to calculate the plaintext image P that size is M × N, obtains the Kazakhstan of a group 256 Wish value and using it as image key Key, image key Key of 256 is scaled 32 decimal number k₁, k₂..., k₃₂, Calculating the initial state value of four-dimensional memristor hyperchaotic system based on Chua circuit, the four-dimensional memristor being specifically based on Chua circuit surpasses The expression formula of chaos system is:

,

Wherein, h (x)=m₁x+0.5(m₀-m₁) × (x+1 |-| x-1),X, Y, z, w represent the state variable of chaos system, a, b, c, d, e, m₀、m₁It is the control parameter of chaos system, and works 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 Pass through formula:

,

Calculate the initial state value x of the state variable of four-dimensional memristor hyperchaotic system based on Chua circuit₀, y₀, z₀With w₀, wherein, sum (k₂₁,k₂₂,...,k₃₂) represent k₂₁,k₂₂,...,k₃₂Sue for peace, max (k₂₁,k₂₂,...,k₃₂) represent Seek k₂₁,k₂₂,...,k₃₂Maximum,Represent the XOR taking x and y；

Step 2. is brought the initial state value obtained into memristor hyperchaotic system 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], state value matrix X, Y, Z are modified obtaining matrix X1= [x₁'_,1,x₁'_,2,...,x₁'_,4MN], Y1=[y₁'_,1,y₁'_,2,...,y₁'_,4MN], Z1=[z₁'_,1,z₁'_,2,...,z₁'_,4MN], make Obtain x₁'_,h、y₁'_,h、z₁'_,h∈ [1,8], is modified obtaining matrix W 1=[w to state value matrix W₁'_,1,w₁'_,2,...,w₁'_,4MN], Make w₁'_,h∈ [0,1], h ∈ [Isosorbide-5-Nitrae MN], be reassembled as, by row, the matrix X_1, Y_ that size is M × 4N respectively by X1, Y1, Z1, W1 1, Z_1, W_1, specifically comprise the steps of:

Step 2.1, will be by step 1 calculated initial state value x₀, y₀, z₀And w₀Bring into based on Chua circuit Four-dimensional memristor hyperchaotic system iteration N0 time, whereinObtain 4 sizes to be respectively The state value matrix X=[x of 1 × 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 modified obtaining matrix X1, Y1, Z1, W1 by correction formula respectively, 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),

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

The rule 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 revising restructuring, P (1) represents first pixel value of image in plain text, and (a b) represents that a is to b delivery, i ∈ [1,3] to mod；

Step 4. will be launched in plain text in image P step-by-step, for the matrix U of M × 8N, order sized by obtaining eight bit planes and recombinating (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 ∈ to D [1, M], j ∈ [Isosorbide-5-Nitrae N]；

Step 7. is to initial configuration C⁰Develop, wherein C^kRepresent the configuration obtained after kth time develops, carry out kth time During differentiation, the DNA matrix-block that evolution rules is obtained for-1 time by kth after diffusion determines, k=1,2 ..., p × q, specifically wraps Containing following steps:

Step 7.1, equation below of passing through:

Determine cellular automata evolution rules, set the state space of cellular as 0,1}, wherein,Represent when t+1 Be in quarter position (i, j) state value of the center cellular at place,Represent and be in position (i, j) the center cellular at place at moment t State value, It is illustrated respectively in moment t and is in upper, the neighbours unit of left, down, right of center cellular The state value of born of the same parents, L, VM, VT, VL, VD, VR be value be the variable of 0 or 1；If L=1, represent that rule is Non-linear programming, no Being exactly then linear programming, VM, VT, VL, VD, VR control middle, upper, five cellulars of left, down, right respectively and whether participate in cellular and develop Process, if value corresponding in VM, VT, VL, VD, VR is 0, then it represents that the cellular of its correspondence 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, pass through formula:

Determining cellular automata evolution rules number, wherein, rule (k) represents that cellular carries out regular number when kth time develops, DNA (E (k-1)) represents the previous DNA matrix in block form obtained after diffusion, and sum (DNA (E (k))) represents kth expansion The ASCII character value summation of each element of the DNA matrix after Saning, as k=1, E (0)=C⁰, C⁰Represent the initial configuration of cellular, K=1,2 ..., p × q；

Step 7.3, rule (k) calculated in step 7.2 is changed into binary system, i.e. try to achieve L, VM, VT, VL, VD, The value of VR, simultaneously according to step 7.1) determine the function that cellular develops；

Step 9. is diffused operation to the encoder matrix DNA (D_1 [k]) obtained, and passes through formula:

It is diffused operation；

Embodiment three, sees shown in Fig. 2 (a)～4 (b), and in the present embodiment, the programming software of employing is Matlab R2014a, choosing the Lena gray level image that size is 256 × 256 is experimental subject, and concrete ciphering process is as follows:

Step 1. inputs the Lena gray level image that original size is 256 × 256, reads with P=imread (' lena.bmp') Take image information, utilize SHA256 function that plaintext image P is calculated, 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, it is used for calculating four-dimensional memristor and surpasses Specifically comprising the following steps that of the initial state value of chaos system

1.1) four-dimensional memristor hyperchaotic system based on Chua circuit is used to produce the pseudorandom sequence needed for AES Row, its expression formula is as follows:

,

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, m₁When=-0.1, system is in hyperchaos State.

1.2) utilizing SHA256 function to calculate plaintext image, (16 enter can to obtain the cryptographic Hash of a group 256 Tabulation is shown as [2 62 88 f e 13 e e e e 0 c 6 b a a f 8 d a 1c 8 c 25 f 5 a c 36 9 a 0994656 d 59 e 4605 e 3 d 0476723 e 9]), and using it as image Key, is then converted to 32 decimal numbers (38 40 143 225 62 238 224 198 186 by the cryptographic Hash of 256 175141 161 200 194 95 90 195 105 160 153 70 86 213 158 70 5 227 208 71 103 35 , and be defined as k 233)₁,k₂,...,k₃₂, followed by the initial state value of equation below calculating memristor hyperchaotic system:

,

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

Step 2. is brought the initial state value obtained into memristor hyperchaotic system and is iterated, and can obtain 4 sizes and divide It is not the state value matrix X=[x of 1 × 262144_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, the Z obtained is repaiied Just obtaining matrix X1=[x₁'_,1,x₁'_,2,...,x₁'_,262144], Y1=[y₁'_,1,y₁'_,2,...,y₁'_,262144], Z1=[z₁'_,1, z₁'_,2,...,z₁'_,262144] so that x₁'_,h、y₁'_,h、z₁'_,h∈ [1,8], is modified obtaining matrix W 1=to state value matrix W [w₁'_,1,w₁'_,2,...,w₁'_,262144] so that w₁'_,h∈ [0,1], h ∈ [1,262144], and then again X1, Y1, Z1, W1 are pressed row Being reassembled as matrix X_1, Y_1, Z_1, W_1 that size is 256 × 1024, it specifically comprises the following steps that

2.1) in order to avoid adverse effect, we first will be by the calculated (x of step 1₀,y₀,z₀,w₀) bring chaos into System iteration N0 time, whereinAnd then again chaos system is iterated Three sizes can be obtained and be respectively state value matrix X, Y, Z, W of 256 × 1024.

2.2) respectively state value matrix X, Y, Z, the W obtained is modified by correction formula, 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 the h value in state value matrix X, Y, Z, W respectively, h ∈ [1,256 × 1024]；X is taken absolute value by abs (x) expression, and floor (x) represents the maximum integer taking no more than x, and (a b) represents that a is to b to mod Modulo operation.

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

Its whole process is as follows:

Matrix X_1, Y_1, Z_1 after revising restructuring is grouped by step 3., note A1=[X_1, Y_1], A2=[X_1, Z_1], A3=[Y_1, Z_1], chooses, followed by first pixel in plain text, the rule will being used for needed for DNA dynamic coding Then matrix number R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3；

The rule of selection rule matrix number R1 and R2 is 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 revising restructuring, P (1) represents first pixel value of image in plain text, and (a b) represents that a is to b delivery, i ∈ [1,3] to mod.

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

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

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

Wherein, P represents in plain text image, P0～P7 represents 8 bit planes of image P in plain text, and U represents and pressed by 8 bit planes The matrix that obtains after row restructuring, D represents the matrix that will obtain after each two element is seen as a group in U,Represent image P in plain text (i, the t bit value after j) individual element is converted to binary system, t ∈ [0,7].

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

Matrix D is carried out piecemeal:

By going the D_1 [k] that recombinates to obtain

In like manner, with reference to the method obtaining D_1 [k], it is also possible to obtain the matrix in block form that R_1 [k], R_2 [k] are corresponding, wherein p ∈[1,4],q∈[1,16]。

Step 6. starts to choose 2mn=2 × 64 × 64=8192 unit successively by row from the first of matrix W _ 1 element Element, reformulating size is the matrix of 64 × 128, and initial configuration C developed as cellular automata by this matrix⁰, wherein, Cellular automata (Cellular Automata is called for short CA) is the most discrete a kind of dynamical system, has The advantages such as simple in construction, concurrency are good.Each cellular by simply with or etc. logical operations form, computing is simple.Cellular is automatic Machine can use the four-tuple of formula CA=(C, S, V, F) to represent, wherein: C represents cellular space, and S represents cellular state space, V Representing the neighborhood combination of cellular, 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 formulaRepresent,It is three input variables, respectively Represent cellular in t cellular state at position i-1, i and i+1,Represent cellular in t+1 moment unit at the i of position Born of the same parents' 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 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 that t+1 moment cellular is in position (i, j) state at place.

The evolution properties of cellular automata is determined by rule, here rule be otherwise known as local state transfer letter Number.For the one-dimensional cellular automatic machine of radius of neighbourhood r=1, its state valueValue can only be 0 or 1, because of 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: table 1 radius of neighbourhood is the one-dimensional cellular automatic machine 80 of 1 Rule truth table

The rule number that cellular develops can represent with 8 bits, as above shown in No. 80 regular truth tables of table, turns to Binary system is (01010000)₂=(80)₁₀, rule number is expressed as the decimal form such as formula simplifiedInstitute Show.In like manner, the Else Rule of one-dimensional cellular automatic machine also can determine after the same method.

Obtain cellular initial configuration C⁰Whole process as follows:

Start to choose 8192 elements (shown in dotted line) as row from the first of W_1 element, then it is reassembled as 64 × The matrix of 128, is C⁰:

Step 7. is to initial configuration C⁰Develop, wherein C^kRepresent the configuration obtained after kth time develops, specifically exist When carrying out kth time differentiation, the DNA matrix-block that evolution rules is obtained for-1 time by kth after diffusion determines, k=1,2 ..., 64, wherein, the two dimensional cellular automaton of improvement is as one-dimensional cellular automatic machine, and the size of two dimensional cellular automaton neighborhood also may be used To represent with radius r, but define the complex and quantity of evolution rule and complexity can be along with cellular number in neighborhood Increasing and form exponential increase, this enhances the safety 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 develops is determined by this formula, wherein,Represent and be in position (i, j) place in t+1 moment The state value of center cellular,Represent moment t be in position (i, j) state value of the center cellular at place,Represent the state value of neighbours' cellular of upper, left, down, right being in center cellular at moment t, L, VM, VT, VL, VD, VR be value be the variable of 0 and 1.If L=1, represent that rule is Non-linear programming, be exactly otherwise linear Rule.VM, VT, VL, VD, VR represent middle, upper, five cellulars of left, down, right respectively, and which unit is the value of these five variablees determine Born of the same parents participate in the renewal of middle cellular state value.We just determine every kind of possible rule by the value of these 6 variablees.Such as (L, VM, VT, VL, VD, VR)=(001110)₂=(14)₁₀, this rule is known as rule 14, carries out state transition function by above-mentioned The simplified formula that amendment obtains is formula:Owing to there being six variablees, so one has 2⁶=64 Plant rule, on the premise of ensureing safety, greatly reduce amount of calculation, improve encryption efficiency.Wherein, L, VM, VT, The value of VL, VD, VR variable can be tried to achieve by previous DNA matrix in block form, is equivalent to determine that cellular updates by cryptographic block Rule, rule number obtained by equation below:

,

Wherein, rule (k) represents that cellular carries out regular number when kth time develops, and DNA (E (k-1)) represents previous process The DNA matrix-block obtained after diffusion, sum (DNA (E (k))) represents each element of the DNA matrix after spreading kth ASCII character value is sued for peace, as k=1, and E (0)=C⁰, k=1,2 ..., p × q.

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

One specific example is as follows:

Assuming 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 develops and become:According to this rule, cellular is entered Row develops for the first timeAssuming that the DNA matrix obtained after diffusion for the first time is represented by

So

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 develops:

Cellular then carries out second time develop and can obtain:

And then the cellular configuration of arbitrarily time differentiation can also be tried to achieve.

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

The specific example that D_1 [k] (now k is assumed to 5) carries out DNA encoding is as follows:

Assuming thatSo according in D_1 [5] The coding rule corresponding in R_1 [5] of element can obtainIn like manner, arbitrary D_1 [k], R_1 [k] can also try to achieve.

Step 9. is diffused operation to the encoder matrix DNA (D_1 [k]) obtained, and it specifically comprises the following steps that

It is diffused operating to the DNA matrix obtained by following,

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

Step 10. makes k=k+1, circulation perform step 7-10, until all of piecemeal all completes DNA encryption.

Encrypted all piecemeal DNA matrixes are reassembled as the matrix of 256 × 1024 and according to coding rule square by step 11. Battle array regular number corresponding to R1 carries out DNA decoding operation, can obtain the binary matrix Q1 that size is 256 × 2048, so Afterwards matrix Q1 is carried out decimal scale conversion operation, the decimal scale ciphertext matrix Q2 that size is 256 × 256 can be obtained, i.e. For the ciphertext graph picture after encryption.

One specific example is as follows:

Assuming that the DNA matrix after encrypted has two, it is respectively Decoding rule in corresponding R1 is respectivelyWith Through decoded matrix it isWithThen it is converted into Decimal scale is respectivelyWith

One good AES should be able to resist various attack, and key space is sufficiently large, and the sensitivity of key is enough High.Below the resume image of the present invention is carried out safety analysis.

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

Chaos system is to initial condition and controls parameter sensitivity extremely, and any small initial deviation all can be exponential Amplifying, therefore the safety of chaos encryption algorithm and key space have much relations.In general, key space is the biggest, and it supports The ability of anti-exhaustive attack is the strongest.Key specifically includes herein: 1) 256 cryptographic Hash produced by SHA256 function.2) Number N0 of the memristor chaos sequence given up.3) for choosing pixel value P (1) (note: the P of DNA encoding regular matrix R1 and R2 (1) first pixel value of image in plain text is represented).If arranging precision is 10^-14, then key space is at least 2¹²⁸, it is seen that key Space is sufficiently large, it is possible to effectively resist exhaustive attack.

2. key sensitivity is high

The safety of chaos encryption, is its sensitivity to key, say, that when assailant with one with key very Close data carry out image when cracking, and can not recover original image.Accompanying drawing 2 (d), 2 (e), 2 (f) are that key is sensitive Property experiment, wherein memristor Chaotic system control parameter a=30, b=36, c=0.1, d=2.5, e=3.5, m₀=-0.5, m₁=- 0.1, choose the pixel value P (1)=162 of encryption required matrix R1, R2 and correct 256 cryptographic Hash key (decimal scale tables Show) Key=38 40 143 225 62 238 224 198 186 175 141 161 200 194 9,590 195 105 160 153 70 86 213 158 70 5 227 208 71 103 35 233.Accompanying drawing 2 (d) is when remaining initial value is constant, order system Decrypted image during system parameter e=3.50000000001.Fig. 2 (e) and 2 (f) are when remaining initial value is constant, respectively by key Decrypted image after Key first (changing 39 into by 38) and last position (changing 234 into by 233) change.Design sketch from deciphering From the point of view of sheet, this AES is high to the sensitivity of key, and cryptographic security is more preferable.

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

Rectangular histogram describes the frequency that the pixel of all gray levels in digital picture occurs.One good resume image After being encrypted image, the grey level histogram of the ciphertext graph picture obtained should be smooth and uniform, is so possible to prevent The person of stealing secret information cracks image by histogrammic leak.Accompanying drawing 3 (a) represents the rectangular histogram of image in plain text；Fig. 3 (b) represents encryption The rectangular 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], it is possible to effectively resisting the attack of statistical analysis.

4. original image neighbor height correlation, after encryption, image neighbor correlation coefficient is close to 0, the most not phase Close.

As the dependency of neighbor, the correlation coefficient of neighbor is introduced in order to analyze image and ciphertext graph in plain text.Phase Close coefficient the biggest, illustrate that the dependency of neighbor is the biggest；Otherwise, the dependency of neighbor is the least.From image respectively with Machine is chosen 10000 to level, vertical and diagonally opposed neighbor pair, with the phase relation of equation below quantitative Analysis neighbor Number:

In formula, x, y represent the pixel value of adjacent two pixels in image respectively, and D (x) represents the mean square deviation of pixel value, E X () is the meansigma methods of pixel value, (x y) is correlation function, R to cov_x,yIt it is the correlation coefficient of adjacent two pixels.

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

In plain text, the contrast of ciphertext dependency see table:

Adjacent direction	Original image	Encrypted image
			Horizontal direction	0.9588	-0.0016
Vertical direction	0.9260	-0.0033
			Diagonally opposed	0.9025	0.0130

Can be seen that image neighbor is height correlation in plain text, correlation coefficient is close to 1.And the adjacent phase of encrypted image Pass coefficient is close to 0, and between neighbor, dependency is obviously reduced, and now statistical property in plain text has been diffused into random ciphertext In, can effectively resist statistical attack.

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

Algorithm is the strongest to sensitivity in plain text, and the ability of opposing differential attack is the strongest, 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) the tolerance AES sensitivity to plaintext.Computing formula is as follows:

In formula, M and N represents line number and the columns of image, C₁Represent original ciphertext graph picture, C₂Represent and obtain after changing in plain text The ciphertext graph picture arrived, C₁(i j) represents that image is at coordinate (i, j) pixel value at place, C in plain text₂(i j) represents that ciphertext graph picture is being sat Mark (i, j) pixel value at place.D represents with ciphertext graph as equirotal matrix, and (i, value j) is by C for D₁(i, j) and C₂(i, j) certainly 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, Change into first pixel value of original plaintext image after 223, obtaining a new plaintext image, then the two image is used Same key encryption forms corresponding ciphertext graph as C₁And C₂.NPCR and the UACI value calculating ciphertext graph picture is as shown in the table, can To see that the value of NPCR is more than 99%, the value of UACI is more than 33%.This shows, even if original image does small change, logical Crossing after this algorithm is encrypted, ciphertext graph picture also has obvious difference.Therefore, this algorithm can be effective against differential attack, NPCR and the UACI value 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 safety 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 occurred, 2ⁿIt it is total status number of information source m.After information encryption, information The expected value of entropy is 8.If encrypted image comentropy closely 8, then show that this ciphertext graph picture is close to random distribution.

Being encrypted the Lena image inventive algorithm of standard 256 × 256, the comentropy of ciphertext graph picture is 7.9971, closely ideal value 8, this shows that the AES that the present invention provides has good safety.

Embodiment four: seeing shown in Fig. 5 (a)～7 (b), in the present embodiment, the programming software of employing is Matlab R2014a, choosing the Baboon image that size is 512 × 512 is experimental subject, and the process of image encryption is as follows:

Step 1. utilizes SHA256 function to calculate the Baboon gray level image P that size is 512 × 512, obtains one (hexadecimal representation is [8 e 49 f b 5 c c d 0 a 5 a a c 680505 e to organize the cryptographic Hash of 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 6c db d e e 4 7 c 2 5 4 a 6 5]), and using it as image key Key, then the Key of 256 is 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), it is used for calculating the initial state value of four-dimensional memristor hyperchaotic system.

Initial state value (the x that step 2. will obtain₀=0.5664, y₀=1.0664, z₀=1.0430, w₀=0.2008) Bring memristor hyperchaotic system into be iterated, 4 sizes can be obtained and be respectively the state value matrix X=of 1 × 1048576 [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], then state matrix X, Y, the Z obtained is modified obtaining matrix X1=[x₁'_,1,x₁ '_,2,...,x₁'_,1048576], Y1=[y₁'_,1,y₁'_,2,...,y₁'_,1048576], Z1=[z₁'_,1,z₁'_,2,...,z₁'_,1048576], make Obtain x₁'_,h、y₁'_,h、z₁'_,h∈ [1,8], is modified obtaining matrix W 1=[w to state value matrix W₁'_,1,w₁'_,2,..., w₁'_,1048576] so that w₁'_,h∈ [0,1], h ∈ [1,1048576], and then again X1, Y1, Z1, W1 are reassembled as size by row are The matrix X_1 of 512 × 2048, Y_1, Z_1, W_1.

Matrix X_1, Y_1, Z_1 after revising restructuring is grouped by step 3., note A1=[X_1, Y_1], A2=[X_1, Z_1], A3=[Y_1, Z_1], chooses, followed by first pixel in plain text, the rule will being used for needed for DNA dynamic coding Then matrix number R1 and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3.

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

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

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

Step 7. is to initial configuration C⁰Develop, wherein C^kRepresent the configuration obtained after kth time develops, specifically exist When carrying out kth time differentiation, the DNA matrix that evolution rules is obtained for-1 time by kth after diffusion determines, k=1,2 ..., 256。

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

Step 9. is diffused operation to the encoder matrix DNA (D_1 [k]) obtained.

Encrypted all piecemeal DNA matrixes are reassembled as the matrix of 512 × 2048 and according to coding rule square by step 11. Battle array regular number corresponding to R1 carries out DNA decoding operation, can obtain the binary matrix Q1 that size is 512 × 4096, so Afterwards matrix Q1 is carried out decimal scale conversion operation, the decimal scale ciphertext matrix Q2 that size is 512 × 512 can be obtained, i.e. For the ciphertext graph picture after encryption.

Concrete steps refer to described in embodiment two.Resume image to the present invention carries out safety and divides below Analysis.

2. key sensitivity is high

Accompanying drawing 5 (d), 5 (e), 5 (f) are initial value sensitivity experiments, wherein 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)=147 of encryption required matrix R1, R2 And 256 correct cryptographic Hash key (decimal representation) Key=142 73 251 92 205 10 90 172 104 55 228 192 25 146 206 228 158 95 200 65 114 69 104 108 219 222228 124 37 74 101。 Accompanying drawing 5 (d) is when remaining initial value is constant, makes initial value m₀Decrypted image when=-0.500000000001.Fig. 5 (e) and 5 F () is when remaining initial value is constant, (changed into 101 in first (changing 143 into by 142) and last position of key Key respectively 102) decrypted image after changing.From the point of view of the effect picture of deciphering, AES is to key extreme sensitivity, and algorithm security is also More preferably.

Accompanying drawing 6 (a) represents the rectangular histogram of image in plain text；Fig. 6 (b) represents the rectangular histogram of encrypted image.Can from figure Going out, before encryption, the pixel value distributed pole of image is uneven, and the pixel value after encrypting is smooth and is evenly distributed in [0,255] In, it is possible to effectively resist the attack of statistical analysis.

(x, y) place's test result such as accompanying drawing 7 (a) and 7 (b) are shown for point.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 neighbor in encrypted image horizontal direction.In plain text, ciphertext Dependency contrast see table:

Adjacent direction	Original image	Encrypted image
			Horizontal direction	0.7569	-0.0042
Vertical direction	0.8587	0.0076
			Diagonally opposed	0.7184	-0.0010

Can be seen that image neighbor is height correlation in plain text, correlation coefficient is close to 1.And the adjacent picture of encrypted image Element correlation coefficient is close to 0, and between neighbor, dependency is obviously reduced, and now statistical property in plain text has been diffused into random In ciphertext, can effectively resist statistical attack.

In the present invention, change into first pixel value of original plaintext image obtaining a new plaintext image after 148, so After the two image is formed corresponding ciphertext graph as C with same key encryption₁And C₂.Calculate ciphertext graph picture NPCR and UACI value is as shown in the table, it can be seen that the value of NPCR is more than 99%, and the value of 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 and the UACI value of ciphertext graph picture:

	Ciphertext graph picture
		NPCR	0.9961
UACI	0.3353

Being encrypted the Baboon image inventive algorithm of standard 512 × 512, ciphertext image information entropy is 7.9992, closely ideal value 8, this shows that the AES that the present invention provides has good safety.

Embodiment five: seeing shown in Fig. 8 (a)～10 (b), in the present embodiment, the programming software of employing is Matlab R2014a, choosing the City image that size is 256 × 320 is experimental subject, as follows to the process of City image encryption:

Step 1. utilizes SHA256 function to calculate the City gray level image P that size is 256 × 320, obtains one group (hexadecimal representation is [c b 90 e 3 c 14 f b b 1 c e c e c 1 b a e 2 c 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 1a c 9 9 c 8 1 0 f d F]), and using it as image key Key, then the Key of 256 is scaled 32 decimal number k₁, k₂..., k₃₂ (203144 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), it is used for calculating the initial state value of memristor hyperchaotic system.

Initial state value (the x that step 2. will obtain₀=0.4883, y₀=1.2656, z₀=0.6055, w₀=0.2166) Bring memristor hyperchaotic system into be iterated, 4 sizes can be obtained and be respectively the state value matrix X=[x of 1 × 327680_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], then matrix X, Y, the Z obtained is modified obtaining matrix X1=[x₁'_,1,x₁'_,2,..., x₁'_,327680], Y1=[y₁'_,1,y₁'_,2,...,y₁'_,327680], Z1=[z₁'_,1,z₁'_,2,...,z₁'_,327680] so that x₁'_,h、 y₁'_,h、z₁'_,h∈ [1,8], is modified obtaining matrix W 1=[w to state value matrix W₁'_,1,w₁'_,2,...,w₁'_,327680] so that w₁'_,h∈ [0,1], h ∈ [1,327680], and then again X1, Y1, Z1, W1 are reassembled as, by row, the matrix that size is 256 × 1280 X_1、Y_1、Z_1、W_1。

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

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

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

Step 7. is to initial configuration C⁰Develop, wherein C^kRepresent the configuration obtained after kth time develops, specifically exist When carrying out kth time differentiation, the DNA matrix-block that evolution rules is obtained for-1 time by kth after diffusion determines, k=1,2 ..., 80。

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

Step 9. is diffused operation to the encoder matrix DNA (D_1 [k]) obtained.

Encrypted all piecemeal DNA matrixes are reassembled as the matrix of 256 × 1280 and according to coding rule square by step 11. Battle array regular number corresponding to R1 carries out DNA decoding operation, can obtain the binary matrix Q1 that size is 256 × 2560, so Afterwards matrix Q1 is carried out decimal scale conversion operation, the decimal scale ciphertext matrix Q2 that size is 256 × 320 can be obtained, i.e. For the ciphertext graph picture after encryption.

Concrete steps refer to described in embodiment two.Resume image to the present invention carries out safety and divides below Analysis:

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

2. key sensitivity is high, and accompanying drawing 8 (d), 8 (e), 8 (f) are initial value sensitivity experiments, wherein memristor chaos system Control parameter a=30, b=36, c=0.1, d=2.5, e=3.5, m₀=-0.5, m₁=-0.1, choose the required matrix R1 of encryption, The pixel value P (1)=102 of R2 and correct 256 cryptographic Hash key Key (decimal representation)= 20314422719379187282362362717444105232114603428175144941922102148332620115612 915223.Accompanying drawing 8 (d) is when remaining initial value is constant, makes decrypted image during initial value e=3.500000000001.Fig. 8 E () and 8 (f) is when remaining initial value is constant, respectively (will by first (changing 204 into by 203) and last position of key Key 223 change 224 into) change after decrypted image.From the point of view of the effect picture of deciphering, this AES is extremely sensitive to key, calculates Method safety is 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 rectangular histogram of texts and pictures picture；Fig. 9 (b) represents the rectangular histogram of encrypted image.It can be seen that the pixel value of image divides before encryption Cloth is the most uneven, and the pixel value after encrypting is smooth and is evenly distributed in [0,255], it is possible to effectively resist statistical analysis Attack；

4. original image neighbor height correlation, after encryption, image neighbor correlation coefficient is close to 0, the most not phase Closing, (x, y) place's test result such as accompanying drawing 10 (a) and 10 (b) are shown for point.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 neighbor in encrypted image horizontal direction.In plain text, ciphertext Dependency contrast see table:

Adjacent direction	Original image	Encrypted image
			Horizontal direction	0.7789	0.0025
Vertical direction	0.6197	0.0036
			Diagonally opposed	0.5907	-0.0090

Can be seen that image neighbor is height correlation in plain text, and the correlation coefficient of the neighbor of encrypted image connects Being bordering on 0, between neighbor, dependency is obviously reduced, and now statistical property in plain text has been diffused in random ciphertext, permissible Effectively resist statistical attack；

5.NPCR is more than 99%, and UACI is more than 33%, and resisting differential attacking ability is strong, in the present invention, by original plaintext image First pixel value change into after 148, obtaining a new plaintext image, then by the two image with same key encryption Form corresponding ciphertext graph as C₁And C₂.NPCR and the UACI value calculating ciphertext graph picture is as shown in the table, it can be seen that the value of NPCR More than 99%, the value of UACI is more than 33%.This shows, even if original image does small change, 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 value:

	Ciphertext graph picture
		NPCR	0.9960
UACI	0.3345

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

From above-described embodiment, the AES that the present invention provides 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 detailed description of the invention, those skilled in the art also can make multiple change accordingly, But any with the present invention equivalent or similar change all should contain within the scope of the claims.

Claims

1. the resume image calculated based on memristor hyperchaotic system, cellular automata and DNA, it is characterised in that: bag Containing following steps:

Step 1. utilizes SHA256 function to calculate the plaintext image P that size is M × N, obtains the cryptographic Hash of a group 256 And using it as image key Key, image key Key of 256 is scaled 32 decimal number k₁, k₂..., k₃₂, calculate The initial state value of four-dimensional memristor hyperchaotic system based on Chua circuit；

Step 2. is brought the initial state value obtained into memristor hyperchaotic system 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], state value matrix X, Y, Z are modified obtaining matrix X1=[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] so that x '_1,h、 y′_1,h、z′_1,h∈ [1,8], is modified obtaining 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], be reassembled as the matrix X_1 that size is M × 4N, Y_1, Z_ by row respectively by X1, Y1, Z1, W1 1, W_1；

Matrix X_1, Y_1, Z_1 after restructuring is grouped by step 3., note A1=[X_1, Y_1], A2=[X_1, Z_1], A3 =[Y_1, Z_1], utilize first pixel in plain text choose will be used for regular matrix number R1 needed for DNA dynamic coding and R2, and make R1=Ai (1), R2=Ai (2), i=1,2,3；

Step 4. will be launched in plain text in image P step-by-step, be the matrix U of M × 8N sized by obtaining eight bit planes and recombinating, 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 full Foot m × p=M, n × q=4N, and the matrix after segmentation by row, is reassembled as one-dimensional matrix that size is 1 × pq respectively and is designated as D_1, R_1, R_2, wherein represent the matrix in block form of kth block, k in D_1, R_1, R_2 respectively with D_1 [k], R_1 [k], R_2 [k] =1,2 ..., p × q；

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

Step 7. is to initial configuration C⁰Develop, wherein C^kRepresent the configuration obtained after kth time develops, develop carrying out kth time Time, the DNA image block that evolution rules is obtained for-1 time by kth after diffusion determines, k=1,2 ..., p × q；

Step 8. 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 Carry out DNA encoding, and the matrix after coding is designated as DNA (D_1 [k])；The cellular configuration C that differentiation is obtained^kAccording in R_2 Coding rule corresponding in k block matrix in block form R_2 [k] carries out DNA encoding, and the matrix after coding is designated as DNA (C^k), k= 1,2,...,p×q；

Step 9. is diffused operation to the encoder matrix DNA (D_1 [k]) obtained；

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

The image encryption calculated based on memristor hyperchaotic system, cellular automata and DNA the most according to claim 1 is calculated Method, it is characterised in that: in described step 1, the expression formula of four-dimensional memristor hyperchaotic system based on Chua circuit is:

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

, calculate four-dimensional memristor based on Chua circuit super mixed The initial state value x of the state variable of ignorant system₀, y₀, z₀And w₀, wherein, sum (k₂₁,k₂₂,...,k₃₂) represent k₂₁, k₂₂,...,k₃₂Sue for peace, max (k₂₁,k₂₂,...,k₃₂) represent and seek k₂₁,k₂₂,...,k₃₂Maximum,Representative takes The XOR of x and y.

The image encryption calculated based on memristor hyperchaotic system, cellular automata and DNA the most according to claim 2 is calculated Method, it is characterised in that:

Described step 2 specifically comprises the steps of:

Step 2.1, will be by step 1 calculated initial state value x₀, y₀, z₀And w₀Bring the four-dimension based on Chua circuit into recall Resistance hyperchaotic system iteration N0 time, whereinObtain size and be respectively 1 × 4MN's State 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]；

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,hRepresent the h value in state value matrix X, Y, Z, W, h ∈ [1, M × 4N] respectively；abs X x is taken absolute value by () expression, floor (x) represents the maximum integer taking no more than x, and (a b) represents that the delivery of b is transported by a to mod Calculate；

The image encryption calculated based on memristor hyperchaotic system, cellular automata and DNA the most according to claim 3 is calculated Method, it is characterised in that:

Step 7 specifically comprises the steps of:

Step 7.1, equation below of passing through:

Decision cellular automata evolution rules, wherein,Represent and be in position (i, j) shape of the center cellular at place in the t+1 moment State value,Represent moment t be in position (i, j) state value of the center cellular at place,Point Not representing the state value of neighbours' cellular of upper, left, down, right being in center cellular at moment t, L, VM, VT, VL, VD, VR are values It it is the variable of 0 or 1；If L=1, representing that rule is Non-linear programming, be exactly otherwise linear programming, VM, VT, VL, VD, VR divide Do not control middle, upper, five cellulars of left, down, right and whether participate in cellular evolution process, if corresponding in VM, VT, VL, VD, VR Value is 0, then it represents that the cellular of its correspondence 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) determines；

Step 7.2, pass through formula:

Determining cellular automata evolution rules number, wherein, rule (k) represents that cellular carries out regular number when kth time develops, DNA (E (k-1)) represents the previous DNA matrix in block form obtained after diffusion, after sum (DNA (E (k))) represents kth diffusion DNA matrix 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, rule (k) calculated in step 7.2 is changed into binary system, i.e. tries to achieve L, VM, VT, VL, VD, VR Value, simultaneously according to step 7.1) determine the function that cellular develops.

The image encryption calculated based on memristor hyperchaotic system, cellular automata and DNA the most according to claim 4 is calculated Method, it is characterised in that:

In described step 9, dispersion operation specifically comprises: pass through formula:

, to the encoder matrix DNA (D_1 obtained [k]) it is diffused operation.