CN105118017A - Gray image encryption method based on two-dimension Henon mapping - Google Patents

Abstract

The invention discloses a gray image encryption method based on two-dimension Henon mapping. The method comprises two processes of scrambling and diffusion. During a scrambling process, the two-dimension Henon mapping is used to realize changes of a pixel position so that correlation of the position and a gray level is eliminated. During a diffusion process, the two-dimension Henon mapping is used to change a gray value of the pixel so that a ciphertext is sensitive to a plaintext. The method of the invention has the following advantage that during two processes of the scrambling and the diffusion of gray image encryption, the two-dimension Henon mapping is used so that the gray image encryption can be high-efficiently and conveniently completed and simultaneously high safety is possessed.

Description

A kind of gray level image encryption method mapped based on two-dimentional Henon

Technical field

The present invention relates to a kind of gray level image encryption method mapped based on two-dimentional Henon, belong to the image security technology in information security field.

Background technology

Image is the important means of mankind's obtaining informations, expressing information and transmission of information.Along with the fast development of internet and multimedia technology, more and more image can be issued quickly and easily and transmit on network.Some images relating to individual privacy, trade secret or state secret are just easy to be browsed easily by malicious attacker, steal, alter, bootlegging and propagation; if do not take necessary safety precautions to these images, the serious consequence brought thus is immeasurable.Thus, the core technology that image encryption is protected as safety of image, its application is more and more extensive, and its requirement is also more and more high.Different from text message, image has that data volume is large, redundance is high, the features such as correlativity is strong between neighbor, as good in although DES, AES possess the obscuring and diffusion property of some traditional symmetric encipherment algorithms, but the efficiency that seems when image data processing is not high, effect is undesirable, these problems propose new challenge to image encryption, and we are in the urgent need to researching and developing out the encryption method of how applicable image own characteristic.

From pertinent literature both domestic and external, the method for digital image encryption can be divided three classes: based on the image encryption method of scramble, based on the image encryption method of diffusion and the image encryption method based on scramble-diffusion.Research shows, the image encryption method based on scramble-diffusion can provide higher security than first two method, but complexity is higher than first two method.

Summary of the invention

Goal of the invention: for problems of the prior art, the invention provides a kind of gray level image encryption method mapped based on two-dimentional Henon, the scramble that the method is encrypted at gray level image all adopts two-dimentional Henon to map with spreading in two processes, efficiently can complete gray level image encryption expediently, there is higher security simultaneously.

Technical scheme: a kind of gray level image encryption method mapped based on two-dimentional Henon, the concrete implementation step of the method comprises scramble and diffusion two processes, as follows:

(1) scrambling process

Step 1, determines whether original-gray image is square-shaped image, if not square-shaped image, then this original-gray image is expanded to square-shaped image, and using the image after expansion as original-gray image, be designated as P, its size is N × N number of pixel; Wherein, N is positive integer;

Step 2, setting image scrambling number of times is the parameter a of L and Henon mapping, the value of b is respectively a ₀, b ₀, the expression formula that Henon maps is as follows:

$\left\{\begin{array}{cc}{x}^{\′}=1-{\mathrm{ax}}^2+y& \mathrm{mod}N\\ y^{\′}=x+b& \mathrm{mod}N\end{array}\right.---\left(1\right)$

Wherein, the span of L is the integer between 2 ~ 10; The span of a is 1 ~ 2 ¹²⁸between integer, and to get rid of be wherein the number of the multiple of N; The span of b is 0 ~ 2 ¹²⁸between integer; (x, y) is the point coordinate in original image P, and x, y ∈ 0,1,2 ..., N-1}; (x', y') is (x, y) point coordinate after Henon mapping transformation, the point coordinate namely in ciphertext graph picture, and x', y' ∈ 0,1,2 ..., N-1};

Step 3, the Henon mapping pair original image P in step 2 is utilized to carry out scramble, the method that scramble is 1 time is: by original image P mid point (x, y) gray-scale value that place's pixel is corresponding moves to the point (x' after Henon mapping transformation, y') place, thus obtain a width scramble once after image;

Step 4, using the image after scramble 1 time as original image repeated execution of steps 3, until scramble number of times reaches the L preset, thus the scramble image after obtaining scramble L time, be designated as P ';

(2) diffusion process

Step 1, extracts the picture element matrix of scramble image P ', and the picture element matrix of two dimension is converted to the pixel sequence A of one dimension according to order from top to bottom from left to right ₁, A ₂..., A _m, M=N ², M is the total number of pixel, and N is the number that original image is extended to horizontal direction after square chart picture or vertical direction pixel;

Step 2, makes x ₀=A ₁, y ₀=A ₂, wherein A ₁for the 1st pixel value of scramble image P ', A ₂for the 2nd pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a ₁, b ₁henon map according to formula (1) iteration t ₁secondary, produce two final states make the 1st pixel value C of ciphertext graph picture ₁for 2nd pixel value C of ciphertext graph picture ₂for

Step 3: make x ₀=(A ₃+ C ₁) mod256, y ₀=(A ₄+ C ₂) mod256, wherein A ₃for the 3rd pixel value of scramble image P ', A ₄for the 4th pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a ₂, b ₂henon map according to formula (1) iteration t ₂secondary, produce two final states make the 3rd pixel value C of ciphertext graph picture ₃for 4th pixel value C of ciphertext graph picture ₄for

Continue by that analogy to perform, until make x ₀=(A _m-1+ C _m-3) mod256, y ₀=(A _m+ C _m-2) mod256, wherein A _m-1for M-1 the pixel value of scramble image P ', A _mfor M the pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a _m/2, b _m/2henon map according to formula (1) iteration t _m/2secondary, produce two final states make M-1 pixel value C of ciphertext graph picture _m-1for m pixel value C of ciphertext graph picture _mfor

The parameter a that above-mentioned Henon maps ₁, b ₁, a ₂, b ₂..., a _m/2, b _m/2, and the iterations t that Henon maps ₁, t ₂..., t _m/2produce by pseudo-random sequence generator, parameter a ₁, b ₁, a ₂, b ₂..., a _m/2, b _m/2span be 1 ~ 2 ¹²⁸between integer, iterations t ₁, t ₂..., t _m/2span 2 ~ 10 between integer;

By the M of ciphertext graph picture pixel value C ₁, C ₂..., C _mjust final ciphertext graph picture is obtained after being converted to the two-dimensional pixel matrix of N × N; If want to obtain scramble and diffusion process that better cipher round results and higher security can carry out many wheels.

The present invention adopts above technical scheme compared with prior art, all adopts two-dimentional Henon to map, efficiently can complete gray level image encryption expediently, have higher security simultaneously in the scramble and diffusion two processes of gray level image encryption.

Accompanying drawing explanation

Fig. 1 is original image;

Fig. 2 is ciphertext graph picture;

Fig. 3 is the histogram of original image;

Fig. 4 is the histogram of ciphertext graph picture.

Embodiment

Below in conjunction with specific embodiment, illustrate the present invention further, these embodiments should be understood only be not used in for illustration of the present invention and limit the scope of the invention, after having read the present invention, the amendment of those skilled in the art to the various equivalent form of value of the present invention has all fallen within the application's claims limited range.

This specific embodiment adopts Mathematica8 software to emulate, original image select size be 256 × 256 standard testing gray level image Lena, each pixel of image is made up of 8 bits, as shown in Figure 1.

Be encrypted Lena gray level image, its detailed process is as follows:

(1) scramble

Step 1, original-gray image Lena is square-shaped image, meets the demands, and is designated as P, wherein N=256;

Step 2, the expression formulas that setting image scrambling number of times is the parameter a of L=3 and Henon mapping, the value of b is respectively 53,170, Henon mappings are as follows:

$\left\{\begin{array}{cc}{x}^{\′}=1-{\mathrm{ax}}^2+y& \mathrm{mod}N\\ y^{\′}=x+b& \mathrm{mod}N\end{array}\right.---\left(1\right)$

Wherein, (x, y) is the point coordinate in original image P, and x, y ∈ 0,1,2 ..., 255}; (x', y') is (x, y) point coordinate after Henon mapping transformation, the point coordinate namely in ciphertext graph picture, and x', y' ∈ 0,1,2 ..., 255};

Step 3, the Henon mapping pair original image P in step 2 is utilized to carry out scramble, the method that scramble is 1 time is: by original image P mid point (x, y) gray-scale value that place's pixel is corresponding moves to the point (x' after Henon mapping transformation, y') place, thus obtain a width scramble once after image;

Step 4, using the image after scramble 1 time as original image repeated execution of steps 3, until scramble number of times reaches the L=3 preset, thus the scramble image after obtaining scramble 3 times, be designated as P ';

(2) spread

Step 1, extracts the picture element matrix of scramble image P ', and the picture element matrix of two dimension is converted to the pixel sequence A of one dimension according to order from top to bottom from left to right ₁, A ₂..., A ₆₅₅₃₆;

Step 2, makes x ₀=A ₁, y ₀=A ₂, wherein A ₁for the 1st pixel value of scramble image P ', A ₂for the 2nd pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a ₁, b ₁henon map according to formula (1) iteration t ₁secondary, produce two final states make the 1st pixel value C of ciphertext graph picture ₁for 2nd pixel value C of ciphertext graph picture ₂for

Step 3: make x ₀=(A ₃+ C ₁) mod256, y ₀=(A ₄+ C ₂) mod256, wherein A ₃for the 3rd pixel value of scramble image P ', A ₄for the 4th pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a ₂, b ₂henon map according to formula (1) iteration t ₂secondary, produce two final states make the 3rd pixel value C of ciphertext graph picture ₃for 4th pixel value C of ciphertext graph picture ₄for

Continue by that analogy to perform, until make x ₀=(A ₆₅₅₃₅+ C ₆₅₅₃₃) mod256, y ₀=(A ₆₅₅₃₆+ C ₆₅₅₃₄) mod256, wherein A ₆₅₅₃₅for the 65535th pixel value of scramble image P ', A ₆₅₅₃₆for the 65536th pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a ₃₂₇₆₈, b ₃₂₇₆₈henon map according to formula (1) iteration t ₃₂₇₆₈secondary, produce two final state x _t32768, y _t32768, make the 65535th pixel value C of ciphertext graph picture ₆₅₅₃₅for x _t32768, the 65536th pixel value C of ciphertext graph picture ₆₅₅₃₆for y _t32768;

The parameter a that above-mentioned Henon maps ₁, b ₁, a ₂, b ₂..., a ₃₂₇₆₈, b ₃₂₇₆₈, and the iterations t that Henon maps ₁, t ₂..., t ₃₂₇₆₈produce by pseudo-random sequence generator, parameter a ₁, b ₁, a ₂, b ₂..., a ₃₂₇₆₈, b ₃₂₇₆₈span be 1 ~ 2 ¹²⁸between integer, iterations t ₁, t ₂..., t ₃₂₇₆₈span 2 ~ 10 between integer;

By 65536 of ciphertext graph picture pixel value C ₁, C ₂..., C ₆₅₅₃₆just ciphertext graph picture is obtained, as shown in Figure 2 after being converted to the two-dimensional pixel matrix of 256 × 256;

Below in conjunction with accompanying drawing, performance evaluation is carried out to embodiment:

1, histogram analysis

Histogram is objectively responding of image information statistical law, and a good resume image should make ciphertext graph picture statistically can not provide any useful information.More satisfactory state is that the uneven distribution of original image pixels value is become being uniformly distributed of pixel value by ciphering process, makes the probability of ciphertext pixel value in whole spatial dimension impartial.Fig. 3 is the histogram of expressly gray level image Fig. 1, Fig. 4 is the histogram of ciphertext graph as Fig. 2, contrast can be found out, the histogram of ciphertext graph picture is from expressly image is completely different, its histogram distribution is smooth and distribute uniformly, and this shows the attack that the inventive method effectively can be resisted Corpus--based Method and analyzed.

2, correlation analysis

In digital picture, the correlativity of neighbor is usually very high, and one of target of image encryption is exactly reduce the correlativity of neighbor.In order to analyze the correlativity of neighbor, first in the horizontal direction, vertical direction and to respectively Stochastic choice 20000 pairs of neighbors on angular direction, then the related coefficient γ on three directions is calculated according to formula (2)-(5) _xy.

$E\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{x}_i---\left(2\right)$

$D\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{(x_i-E(x\left)\right)}^2---\left(3\right)$

$\mathrm{cov}(x,y)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}(x_i-E(x\left)\right)(y_i-E(y\left)\right)---\left(4\right)$

${\mathrm{\γ}}_{xy}=\frac{\mathrm{cov}(x,y)}{\sqrt{D\left(x\right)}\sqrt{D\left(y\right)}}---\left(5\right)$

Wherein, x and y represents the pixel value of adjacent 2 pixels in image respectively.Table 1 is depicted as the related coefficient before and after encryption on three directions, the neighbor height correlation of visible original image, related coefficient is close to 1, and after encryption, neighbor related coefficient is close to 0, and statistical information is expressly diffused into random ciphertext well and has suffered.

Table 1

3, the Analysis of Entropy

Image information entropy is a kind of statistical form of feature, it reflects the number of average information in image.The one dimension entropy of image represents the quantity of information that in image, the aggregation characteristic of intensity profile comprises makes p _irepresent the ratio of gray-scale value shared by the pixel of i in image, then the unitary gray level entropy defining gray level image is:

$H=\underset{i=0}{\overset{255}{\Σ}}{p}_i{\mathrm{logp}}_i---\left(6\right)$

The one dimension entropy of image can represent the aggregation characteristic that gradation of image distributes, and the value of image information entropy, more close to 8, illustrates that cipher round results is better.The information entropy of the present invention being encrypted to rear image is tested, and testing the result obtained is 7.9217, shows that the image encryption method described in the present invention can be good at resisting the Analysis of Entropy.

Claims (2)

1. based on the gray level image encryption method that two-dimentional Henon maps, it is characterized in that, the concrete implementation step of the method comprises scramble and diffusion two processes, as follows:

(1) scramble

Step 1, determines whether original-gray image is square-shaped image, if not square-shaped image, then this original-gray image is expanded to square-shaped image, and using the image after expansion as original-gray image, be designated as P, its size is N × N number of pixel; Wherein, N is positive integer;

Step 2, setting image scrambling number of times is the parameter a of L and Henon mapping, the value of b, and the expression formula that Henon maps is as follows:

$\left\{\begin{array}{cc}{x}^{\′}=1-{\mathrm{ax}}^2+y& \mathrm{mod}N\\ y^{\′}=x+b& \mathrm{mod}N\end{array}\right.---\left(1\right)$

Wherein, the span of L is the integer between 2 ~ 10; The span of a is 1 ~ 2 ¹²⁸between integer, and to get rid of be wherein the number of the multiple of N; The span of b is 0 ~ 2 ¹²⁸between integer; (x, y) is the point coordinate in original image P, and x, y ∈ 0,1,2 ..., N-1}; (x', y') is (x, y) point coordinate after Henon mapping transformation, the point coordinate namely in ciphertext graph picture, and x', y' ∈ 0,1,2 ..., N-1};

Step 3, the Henon mapping pair original image P in step 2 is utilized to carry out scramble, the method that scramble is 1 time is: by original image P mid point (x, y) gray-scale value that place's pixel is corresponding moves to the point (x' after Henon mapping transformation, y') place, thus obtain a width scramble once after image;

Step 4, using the image after scramble 1 time as original image repeated execution of steps 3, until scramble number of times reaches the L preset, thus the scramble image after obtaining scramble L time, be designated as P ';

(2) spread

Step 1, extracts the picture element matrix of scramble image P ', and the picture element matrix of two dimension is converted to the pixel sequence A of one dimension according to order from top to bottom from left to right ₁, A ₂..., A _m, M=N ², M is the total number of pixel, and N is the number that original image is extended to horizontal direction after square chart picture or vertical direction pixel;

Step 2, makes x ₀=A ₁, y ₀=A ₂, wherein A ₁for the 1st pixel value of scramble image P ', A ₂for the 2nd pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a ₁, b ₁henon map according to formula (1) iteration t ₁secondary, produce two final states make the 1st pixel value C of ciphertext graph picture ₁for 2nd pixel value C of ciphertext graph picture ₂for

Step 3: make x ₀=(A ₃+ C ₁) mod256, y ₀=(A ₄+ C ₂) mod256, wherein A ₃for the 3rd pixel value of scramble image P ', A ₄for the 4th pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a ₂, b ₂henon map according to formula (1) iteration t ₂secondary, produce two final states make the 3rd pixel value C of ciphertext graph picture ₃for 4th pixel value C of ciphertext graph picture ₄for

Continue by that analogy to perform, until make x ₀=(A _m-1+ C _m-3) mod256, y ₀=(A _m+ C _m-2) mod256, wherein A _m-1for M-1 the pixel value of scramble image P ', A _mfor M the pixel value of scramble image P ', x ₀and y ₀two original states of Henon mapping respectively, then parameter is a _m/2, b _m/2henon map according to formula (1) iteration t _m/2secondary, produce two final states make M-1 pixel value C of ciphertext graph picture _m-1for m pixel value C of ciphertext graph picture _mfor

The parameter a that above-mentioned Henon maps ₁, b ₁, a ₂, b ₂..., a _m/2, b _m/2, and the iterations t that Henon maps ₁, t ₂..., t _m/2produce by pseudo-random sequence generator, parameter a ₁, b ₁, a ₂, b ₂..., a _m/2, b _m/2span be 1 ~ 2 ¹²⁸between integer, iterations t ₁, t ₂..., t _m/2span 2 ~ 10 between integer;

By the M of ciphertext graph picture pixel value C ₁, C ₂..., C _mjust final ciphertext graph picture is obtained after being converted to the two-dimensional pixel matrix of N × N.

2. a kind of gray level image encryption method mapped based on two-dimentional Henon according to claim 1, if scramble and the diffusion process of wanting to obtain that better cipher round results and higher security can carry out many wheels.