CN106570814A - Novel hyper-chaotic image encryption method - Google Patents

Abstract

The invention puts forward a novel hyper-chaotic image encryption method which is mainly used in the field of gray image encryption. The algorithm mainly comprises the following steps: first, a plain image of which the size is N*M is segmented into M column vector groups, the pixels in the obtained vector groups are converted into bits to get 8*M vector groups, and scrambling operation is carried out; then, the obtained scrambled pixel values are re-mapped to an interval [0, 255] to get an intermediate cipher text; and finally, diffusion operation is carried out on a chaotic sequence generated by a Hyperhenon chaotic system and the intermediate cipher text to get a final cipher text. Experimental simulation shows that the algorithm not only can improve the disadvantages of a low-dimensional chaotic system and resist statistical characteristic attack and differential attack, but also can effectively resist four classic attacks, well hide plaintext information and achieve a good encryption effect.

Description

A kind of new hyperchaos image encryption method

Technical field

The invention belongs to gray level image encryption method, more particularly to a kind of new hyperchaos image encryption method.

Background technology

With the fast development of computer network, the quantity that picture is transmitted in a network is more and more, causes people to figure The concern that piece safe transmission is asked, nowadays Chinese scholars the encryption that picture how is carried out in image transmitting is given height Pay attention to.

The features such as due to the strong correlation of image itself pixel, highly redundant and big data volume, determine that traditional text adds Decryption method is difficult to be applied in the middle of image encryption.In recent years, expert points out that chaos system has to the extremely sensitive of primary condition Property, positive Lyapunov indexes, point shape with point dimension property the features such as, can apply with the middle of image encryption, gradually propose some chaos Image encryption method：Such as one-time pad, bit encryption, Mathematical Modeling encryption and DNA sequence dna encryption

But there is clearly disadvantageous part in method indicated above：

As one time key has very big difficulty in transmission and distribution；Bit encryption method need when being encrypted by Pixel value is wholly converted into binary system and carries out image encryption, and such encryption efficiency is very time-consuming than relatively low；Mathematical Modeling encryption method The factor that need to be considered compares, and is unfavorable for the realization of AES；And the pixel coefficient correlation in DNA sequence dna encryption method is compared with Gao Rong It is subject to attacker's decryption.

The content of the invention

For the weak point that above-mentioned encryption method is present, the present invention proposes a kind of new hyperchaos image encryption side Method.The present invention is directly encrypted and generates key according to plaintext pixel value, can solve well the efficiency of image encryption with The problem of cipher key delivery, in addition also introduces Hyperhenon hyperchaotic systems and is encrypted, and not only simplifies encryption system Realize, and reduce the correlation of ciphertext image pixel.Except, the present invention can effectively resist classical four kinds of attack methods, reach Good cipher round results.

The hyperchaos image encryption method of the present invention, it is characterised in that including procedure for cipher key initialization, scramble transformation mistake Journey, Hyperhenon hyperchaotic map diffusion processes.

(1) procedure for cipher key initialization

Encryption key K is mainly that 400 binary systems aid in close K by length₁, it is input into key X₀, Y₀Three parts constitute.

Step 1：It is that 400 binary systems aid in close K first by length₁It is cut into the binary system list that ten parts of length is 40 Unit, respectively K₁₀, K₁₁..., K₁₉。

Step 2：Will input key X₀, Y₀As the initial key of Hyperhenon mappings, as shown in formula (1), wherein making c =1.76, d=0.1, and X₀, Y₀(0,1) between value, producing one group of Hyperchaotic Sequence is used to spread computing.

K=0,1,2 ... (1)

(2) scramble transformation process

Step 1：First N × M plaintext images are divided into into M Column vector groups, and by the pixel of each Vector Groups with 8 two System is represented, therefore can obtain 8 × M Column vector groups.

Step 2：According to auxiliary key matrix K₁₀, K₁₁..., K₁₉Value, calculate two control parameters v in Cat maps And w, such as shown in formula (2)：

Step 3：The v tried to achieve with reference to step 2 and w, and become with being designated as input under each column vector, substitute into Arnold mappings and work as In, such as shown in formula (3), s and t, wherein r=0 being tried to achieve, 1,2 ..., 8 × M is expressed as the position scalar of each Column vector groups；s =0,1,2 ..., 8 × M represent column vector after Arnold conversion, new position scalar；T be expressed as column vector bit group to The digit of upper swing offset.

Step 4：According to step 3 gained s, the Column vector groups that r is represented are moved in the Column vector groups represented by s.According to The t of step 3 gained, each element that will be moved into the Column vector groups of s positions is circulated up moving t.

Step 5：Repeat step 3,4 is carried out 8 × M time, obtains intermediate ciphertext B.

(3) Hyperhenon hyperchaotic maps diffusion process

Step 1：By the binary system intermediate ciphertext B for obtaining, become decimal system ciphertext P, size is N × M.

Step 2：If initial value X₀For x₁, Y₀For y₁, in substituting into Hyperhenon hyperchaotic map systems, give up first 200 times Iteration result, then N × M iteration is carried out, obtain the chaos sequence L={ l that length is N × M₁, l₂..., l_N×M, it is mixed by what is obtained Ignorant sequence L is updated in formula (4), makes element value range conversion between [0,255], obtaining new chaos sequence Q={ q₁, q₂..., q_N×M}。

q_i=mod (l_i×10⁵, 256) 1≤i≤N × M (4)

Step 3：To intermediate ciphertext P, each pixel carries out formula (5) operation, makes c₀For intermediate ciphertext P pixel value it is flat Average, so increases plaintext and ciphertext correlation, to reach pixel diffusion effect, obtains final ciphertext C={ c₁, c₂..., c_N×M}。

Beneficial effect of the present invention：

The present invention increases key by constituting encryption key with input key by the auxiliary key that length is 400 bits Length with combine, allow exhaustive attack become it is impossible.Then by auxiliary key information, plaintext shuffle operation, Neng Gouyou are carried out Effect is resisted in plain text (ciphertext only attack).The intermediate ciphertext for obtaining and hyper-henon hyperchaotic maps are produced into chaos sequence is carried out Xor operation, improves the undesirable features such as the period windows that low-dimensional chaos conversion is present.The present invention can effectively resist classical attack, Ensure the security in transmission, have wide application prospects in digital medium information security fields.

Description of the drawings

Fig. 1 is the encryption flow figure of the present invention

Fig. 2 is key K₁Composition figure

Fig. 3 is intermediate ciphertext bit composition figure

Fig. 4 (a) is 256 × 256 gray scales Lena figure

Fig. 4 (b) is final encrypted image

Fig. 5 (a) plaintext grey level histograms

Fig. 5 (b) ciphertext image grey level histograms

Fig. 6 (a) plaintext graphs of a relation

Fig. 6 (b) ciphertext graphs of a relation

Fig. 7 (a) K₂Decryption figure

Fig. 7 (b) K₃Decryption figure

Fig. 7 (c) K₄Decryption figure

Specific embodiment

Specific implementation step is as shown in the encryption flow figure of Fig. 1.

The present invention will realize image encryption, first have to realize the initialization procedure of key, as shown in Figure 2.

Encryption key K is mainly that 400 binary systems aid in close K by length₁, it is input into key X₀, Y₀Three parts constitute.

Step 1：It is that 400 binary systems aid in close K first by length₁It is cut into the binary system list that ten parts of length is 40 Unit, respectively K₁₀, K₁₁..., K₁₉。

Step 2：Will input key X₀, Y₀As the initial key of Hyperhenon mappings, as shown in formula (1), wherein making c =1.76, d=0.1, and X₀, Y₀(0,1) between value, producing one group of Hyperchaotic Sequence is used to spread computing.

K=0,1,2 ... (1)

After Fig. 2 procedure for cipher key initialization is completed, then the image encryption process of Fig. 1 is carried out, period can also produce middle ratio Special ciphertext matrix, as shown in Figure 3.

Step 1：First N × M plaintext images are divided into into M Column vector groups, and by the pixel of each Vector Groups with 8 two System is represented, therefore can obtain 8 × M Column vector groups.

Step 2：According to auxiliary key matrix K₁₀, K₁₁..., K₁₉Value, calculate two control parameters v in Cat maps And w, such as shown in formula (2)：

Step 3：The v tried to achieve with reference to step 2 and w, and become with being designated as input under each column vector, substitute into Arnold mappings and work as In, such as shown in formula (3), s and t, wherein r=0 being tried to achieve, 1,2 ..., 8 × M is expressed as the position scalar of each Column vector groups；s =0,1,2 ..., 8 × M represent column vector after Arnold conversion, new position scalar；T be expressed as column vector bit group to The digit of upper swing offset.

Step 4：According to step 3 gained s, the Column vector groups that r is represented are moved in the Column vector groups represented by s.According to The t of step 3 gained, each element that will be moved into the Column vector groups of s positions is circulated up moving t.

Step 5：Repeat step 3,4 is carried out 8 × M time, obtains intermediate ciphertext B.

Step 6：By the binary system intermediate ciphertext B for obtaining, become decimal system ciphertext P, size is N × M.

Step 7：If initial value X₀For x₁, Y₀For y₁, in substituting into Hyperhenon hyperchaotic map systems, give up first 200 times Iteration result, then N × M iteration is carried out, obtain the chaos sequence L={ l that length is N × M₁, l₂..., l_N×M, it is mixed by what is obtained Ignorant sequence L is updated in formula (4), makes element value range conversion between [0,255], obtaining new chaos sequence Q={ q₁, q₂..., q_N×M}。

q_i=mod (l_i×10⁵, 256) 1≤i≤N × M (4)

Step 8：To intermediate ciphertext P, each pixel carries out formula (5) operation, makes c₀For intermediate ciphertext P pixel value it is flat Average, so increases plaintext and ciphertext correlation, to reach pixel diffusion effect, obtains final ciphertext C={ c₁, c₂..., c_N×M}。

Experiment simulation, plaintext image such as Fig. 4 are carried out for 256 × 256 gray scale Lena figure to size using matlab 2014 A shown in (), wherein system input key is respectively：X₀=0.314 852 2456, Y₀=0.425 852 7320.Finally can obtain Shown in encrypted image such as Fig. 4 (b).

Carry out the analysis of secure context to the image encryption method of the present invention below.

1st, histogram analysis

Fig. 5 (a) (b) is respectively plaintext and ciphertext histogram.It can be seen that plaintext histogram pixel value point Cloth is quite uneven, and attacker can obtain image information according to pixel distribution information.It is close and image is after present invention encryption Texts and pictures are quite uniform as histogram distribution, and pixel value information is hidden well, reach cipher round results.

2nd, statistical analysis

It is random to choose two groups of adjacent horizontal directions, vertical direction and diagonal pictures in plaintext and ciphertext graph picture respectively Vegetarian refreshments, draws to obtain the related figure of pixel.As Fig. 7 (a) show plaintext graph of a relation, Fig. 7 (b) show ciphertext graph of a relation, and according to public affairs Formula (6)-(9) calculate the coefficient correlation between pixel.

In formula, x and y represents respectively the gray value of image sets of adjacent pixels, E (.) expression mathematic expectaion, cov (.) represent association Variance, γ_xyIt is expressed as the coefficient of relationship of neighbor.As shown in table 1, coefficient correlation represents correlation to result of calculation closer to 1 It is stronger, it is less to represent more uncorrelated.

The neighbor correlation coefficient charts of table 1

3rd, the sensitivity analysis of initial value

The decruption key K of the present invention consists of K=[K₁, X₀, Y₀], wherein correct decruption key K₂=[K₁, X₀, Y₀], its Middle K₁For 400 groups of binary bits for giving, X₀=0.314 852 2456, Y₀=0.425 8527320, when input key X₀, Y₀It is to obtain decruption key K respectively that minor variations occur respectively₃, K₄, wherein K₃Middle X₀=0.314 852 2457, other values are not Become a solution, K₄Middle Y₀=0.425 852 7321, other values do not become another solution.As seen from Figure 6, if decruption key occurs 10^-10Minor variations also cannot successful decryption, it is seen that invention is extremely strong to initial value sensitivity, and it is poor to be effective against Divide and attack.

4th, classical type flaw attack

According to Kerckhoff principles, following four type is defined as into classical attack：

(1) attack with known plaintext (Ciphertext only attack)：In attacker's hand in addition to the ciphertext intercepted and captured, do not have Other any auxiliary informations.

(2) known plain text attack (Known plaintext attack)：Attacker has also grasped portion except grasping ciphertext The corresponding relation of clearly demarcated text and ciphertext.

(3) chosen -plain attact (Chosen plaintext attack)：Attacker knows AES, while can Select in plain text and obtain the ciphertext corresponding to corresponding plaintext.

(4) chosen ciphertext attacks (Chosen ciphertext attack)：Attacker knows AES, while can be with Select ciphertext and obtain corresponding plaintext.

Obviously chosen -plain attact is maximally effective attack method, adds AES effectively to resist this method excessively Attack, also just can effectively resist attacking for additive method.

But chosen -plain attact is invalid to the present invention, mainly there are following 2 reasons：First, the present invention is to key Sensitiveness is high, as long as input key has minor variations, cannot all be normally carried out decryption；Second, when computing is diffused, draw Cleartext information is entered, has allowed and want to carry out cracking by the two-dimensional matrix of full 0 to become impossible.In sum, the present invention can be supported effectively The classical attack of system.

5th, plaintext sensitivity analysis

The sensitiveness of plaintext is referred to when the pixel value in image occurs minor variations, can all obtain completely different close Texts and pictures picture.Typically it is analyzed using NPCR (change ratio of pixel) and UACI (normalization pixel mean change) the two parameters.

Input same key, obtains two width identical ciphertexts.Wherein one secondary ciphertext graph picture is taken, will (438, pixel 337) Value 174 changes over 173, and according to formula (10), (11) can obtain, NPCR=99.64%, UACI=33.78%.As a result show, this Invention is very strong to plaintext sensitiveness, can effectively resist differential attack.

6th, key space analysis

The input key of the present invention is all that significance bit reaches 16, therefore key space reaches using double-precision floating point type To 10³²If 400 groups of binary bits in auxiliary key are considered into key space length, key space of the present invention will become Obtain and more increase, want to obtain plaintext image information by exhaustive attack, almost become impossible.As can be seen here, the present invention's is close Key space can effectively resist exhaustive attack, reach the effect of safe transmission, it is ensured that image information is not compromised.

Claims (1)

1. a kind of hyperchaos image encryption method, successively including procedure for cipher key initialization, scramble transformation process, Hyperhenon surpass Chaotic maps diffusion process, it is characterised in that

(1) procedure for cipher key initialization

Encryption key K is that 400 binary systems aid in close K by length₁, it is input into key X₀, Y₀Three parts constitute；

Step 1：It is that 400 binary systems aid in close K first by length₁The binary cell that ten parts of length is 40 is cut into, is obtained final product To auxiliary key matrix K₁₀, K₁₁..., K₁₉；

Step 2：Will input key X₀, Y₀As the initial key of Hyperhenon mappings, such as shown in following formula (1), wherein making c= 1.76, d=0.1, and X₀, Y₀(0,1) between value, producing one group of Hyperchaotic Sequence is used to spread computing；

$\begin{array}{c}\left\{\begin{array}{c}{X}_{K+1}=c-{Y^2}_{k+1}-d*Z_{k+1}\\ Y_{k+1}=X_k\\ Z_{k+1}=Y_k\end{array}\right.\\ k=0,1,2,\mathrm{...}\end{array}---\left(1\right)$

(2) scramble transformation process

Step 1：N × M plaintext images are divided into into M Column vector groups, and by the pixel of each Vector Groups with 8 binary forms Show, obtain 8 × M Column vector groups；

Step 2：According to auxiliary key matrix K₁₀, K₁₁..., K₁₉Value, calculate two control parameters v and the w in Cat maps, As shown in following formula (2)：

$\begin{array}{c}v=bin2dec(K_{10}\⊕K_{11}\⊕K_{12}\⊕K_{13}\⊕K_{14})\mathrm{mod}(8\×M)\\ w=bin2dec(K_{15}\⊕K_{16}\⊕K_{17}\⊕K_{18}\⊕K_{19})\mathrm{mod}(8\×M)\end{array}---\left(2\right)$

Step 3：The v tried to achieve with reference to step 2 and w, and to be designated as input variable under each column vector, substitute into Arnold mappings and work as In, such as shown in following formula (3), s and t, wherein r=0 being tried to achieve, 1,2 ..., 8 × M is expressed as the position scalar of each Column vector groups；s =0,1,2 ..., 8 × M represent the new position scalar after Arnold conversion of column vector；T be expressed as column vector bit group to The digit of upper swing offset；

$\left[\begin{array}{c}s\\ t\end{array}\right]=A\left[\begin{array}{c}r\\ r\end{array}\right]\mathrm{mod}(8\×M)=\left[\begin{array}{cc}1& v\\ w& vw\end{array}\right]\left[\begin{array}{c}r\\ r\end{array}\right]\mathrm{mod}(8\×M)---\left(3\right)$

Step 4：According to step 3 gained s, the Column vector groups that r is represented are moved in the Column vector groups represented by s, according to step 3 The t of gained, each element that will be moved into the Column vector groups of s positions is circulated up moving t；

Step 5：Repeat step 3,4 is carried out 8 × M time, obtains intermediate ciphertext B；

(3) Hyperhenon hyperchaotic maps diffusion process

Step 1：By the binary system intermediate ciphertext B for obtaining, it is changed into decimal system ciphertext P, size is N × M；

Step 2：If initial value X₀For x₁, Y₀For y₁, in substituting into Hyperhenon hyperchaotic map systems, give up front 200 iteration As a result, then N × M iteration is carried out, obtains the chaos sequence L={ l that length is N × M₁, l₂..., l_N×M, by the chaos sequence for obtaining Row L is updated in following formula (4), makes element value range conversion between [0,255], obtains new chaos sequence

Q={ q₁, q₂..., q_N×M}

q_i=mod (l_i×10⁵, 256) 1≤i≤N × M (4)

Step 3：To intermediate ciphertext P, each pixel carries out following formula (5) operation, makes c₀For the mean value of the pixel value of intermediate ciphertext P, Plaintext and ciphertext correlation are so increased, to reach pixel diffusion effect, final ciphertext C={ c is obtained₁, c₂..., c_N×M}。

$c_i=\mathrm{mod}(q_i+p_i,256)\⊕c_{i-1},1\≤i\≤N\×M---\left(5\right).$