CN103971320A - Image scrambling and restoring method based on Henon mapping - Google Patents

Abstract

The invention discloses an image scrambling and restoring method based on Henon mapping. The method includes the image scrambling process and the image restoring process, image scrambling is achieved through iteration of Henon mapping, and image restoration is achieved through iteration of inverse transformation of Henon mapping. According to the method, original images are iterated at least twice through Henon mapping and then can reach the satisfactory scrambling degree, and fast image scrambling is achieved; meanwhile, the original images can be fast restored through the steps with the number same as iteration of inverse iteration from the scrambling state. Besides, the method is high in attack resistance, resistant to a certain degree of attack of shearing and noise, and readability of the restored images are not influenced.

Description

A kind of image scrambling and restoration methods based on Henon mapping

Technical field

The present invention relates to a kind of image scrambling and restoration methods based on Henon mapping, belong to the image security technology in information security field.

Background technology

Digital Image Scrambling refers to image is confused, and eliminates position or Gray Correlation, thereby makes the mankind or computer system cannot understand the expressed real meaning of original image.The Chaotic Technology of digital picture, can regard a kind of approach of digital image encryption as, also can be used as digital image hidden, digital watermarking image is implanted and digital picture is secret shared pre-service and last handling process.

Common image scrambling method has Arnold conversion, Fibonacci-Q conversion, Magic Square Transformation, knight cruise conversion, Hilbert curve, Conway game, image encryption method etc.Wherein, the Image Scrambling Algorithm that the Arnold of take conversion, Fibonacci-Q conversion and Magic Square Transformation are representative is most widely used in image encryption, Information hiding and digital watermarking field, they have transformation matrix simple structure, scramble is realized the features such as easy, and can resist the normal images such as shearing, interpolation noise and attack.But shortcoming is repeatedly to repeat scramble, just can reach satisfied scramble effect, and utilizes periodically and come Recovery image consuming time long, be unfavorable for the fast quick-recovery after image scrambling.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of image scrambling and restoration methods based on Henon mapping, the method only needs less scramble number of times just can obtain satisfied scramble effect, and utilize the inverse transformation of Henon mapping to recover comparatively simple and direct to image, reduced calculated amount, improved scramble efficiency.

The present invention is for solving the problems of the technologies described above by the following technical solutions:

The invention provides a kind of image scrambling and restoration methods based on Henon mapping, realized the quick scramble of image, from the identical step number of the reverse iteration of scramble state, just can recover very soon original image simultaneously.

First, the invention provides a kind of image scrambling method based on Henon mapping, concrete implementation step is as follows:

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

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

$\left\{\begin{array}{cc}{x}^{\′}=1-{\mathrm{ax}}^2+y& \mathrm{mod}N\\ y^{\′}=x+b& \mathrm{mod}N\end{array}\right.---\left(3\right)$

Wherein, the span of L is the integer between 2～10; The span of a is 1～2 ¹²⁸between integer, and get rid of the number of the multiple be wherein 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, i.e. point coordinate in ciphertext graph picture, and x', y' ∈ 0,1,2 ..., N-1};

Step 3, utilizes the Henon mapping in step 2 to carry out scramble to original image P, and the method that scramble is 1 time is as follows:

Original image P mid point (x, y) is located to the point (x', y') that gray-scale value corresponding to pixel or RGB color value move to after Henon mapping transformation and locate, thereby obtain the image of a width scramble after once;

Step 4, using the image after scramble 1 time as original image repeated execution of steps 3, until scramble number of times reaches predefined L, thereby obtains the ciphertext graph picture after scramble L time.

Secondly, the invention provides and a kind of the image that adopts a kind of image scrambling method based on Henon mapping to carry out after scramble is carried out to restoration methods, concrete implementation step is as follows:

Step 1, the expression formula of inverse transformation of being derived Henon mapping by formula (3) is as follows:

$\left\{\begin{array}{cc}y=x^{\′}-1+{\mathrm{ax}}^2& \mathrm{mod}N\\ x=y^{\′}-b& \mathrm{mod}N\end{array}\right.---\left(4\right)$

Wherein, parameter a, the b of inverse transformation of Henon mapping are, the setting of N is consistent with relevant parameter in image scrambling; The setting of the random number of times of image inverted is identical with image scrambling number of times L;

Step 2, the inverse transformation that utilizes the mapping of Henon in step 1 to the ciphertext graph after scramble L time look like to carry out image recover be inverted disorderly, the method that inverted unrest is 1 time is as follows:

Ciphertext graph is located to the point (x, y) that gray-scale value corresponding to pixel or RGB color value move to after Henon mapping inverse transformation as mid point (x', y') and locate, thereby obtain the disorderly image after 1 time of a width inverted;

Step 3, using inverted disorderly the image after 1 time as ciphertext graph as repeated execution of steps 2, until the random number of times of inverted reaches predefined value, thus the original image being restored.

The present invention adopts above technical scheme compared with prior art, original image shines upon minimum iteration by Henon just can reach satisfied scramble degree 2 times, realized the quick scramble of image, from the identical step number of the reverse iteration of scramble state, just can recover very soon original image simultaneously.In addition, this method anti-attack ability is strong, can resist certain shearing, the attack of noise, and the readability of Recovery image is unaffected.

Accompanying drawing explanation

Fig. 1 is FB(flow block) of the present invention.

Fig. 2 is original image.

Fig. 3 is the ciphertext graph picture after scramble, wherein, (a) is the ciphertext graph picture of scramble after once; (b) be the ciphertext graph picture after twice of scramble; (c) be the ciphertext graph picture after scramble three times.

Fig. 4 is the restoration result that adds the ciphertext graph picture after salt-pepper noise, wherein, and (a) for adding the ciphertext graph picture after salt-pepper noise; (b) be image restoration result.

Fig. 5 is the restoration result that adds the ciphertext graph picture after Gaussian noise, wherein, and (a) for adding the ciphertext graph picture after Gaussian noise; (b) be image restoration result.

Fig. 6 is the restoration result of shearing the image of ciphertext graph after as partial data, wherein, and (a) for shearing the image of ciphertext graph after as partial data; (b) be image restoration result.

Embodiment

Describe embodiments of the present invention below in detail, the example of described embodiment is shown in the drawings, and wherein same or similar label represents same or similar element or has the element of identical or similar functions from start to finish.Below by the embodiment being described with reference to the drawings, be exemplary, only for explaining the present invention, and can not be interpreted as limitation of the present invention.

Those skilled in the art of the present technique are understandable that, unless specially statement, singulative used herein " ", " one ", " described " and " being somebody's turn to do " also can comprise plural form.Should be further understood that, the wording of using in instructions of the present invention " comprises " and refers to and have described feature, integer, step, operation, element and/or assembly, but do not get rid of, do not exist or adds one or more other features, integer, step, operation, element, assembly and/or their group.Should be appreciated that, when we claim element to be " connected " or " coupling " when another element, it can be directly connected or coupled to other elements, or also can have intermediary element.In addition, " connection " used herein or " coupling " can comprise wireless connections or couple.Wording "and/or" used herein comprises arbitrary unit of listing item and all combinations that one or more is associated.

Those skilled in the art of the present technique are understandable that, unless otherwise defined, all terms used herein (comprising technical term and scientific terminology) have with the present invention under the identical meaning of the general understanding of those of ordinary skill in field.Should also be understood that such as those terms that define in general dictionary and should be understood to have the consistent meaning of meaning in the context with prior art, unless and definition as here, can not explain by idealized or too formal implication.

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

The present invention designs a kind of image scrambling and restoration methods based on Henon mapping, as shown in Figure 1, the method only needs less scramble number of times just can obtain satisfied scramble effect, and utilize the inverse transformation of Henon mapping to recover comparatively simple and direct to image, reduced calculated amount, improved scramble efficiency.

A kind of image scrambling method based on Henon mapping in the present invention, concrete implementation step is as follows:

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

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

$\left\{\begin{array}{cc}{x}^{\′}=1-{\mathrm{ax}}^2+y& \mathrm{mod}N\\ y^{\′}=x+b& \mathrm{mod}N\end{array}\right.---\left(5\right)$

Wherein, the span of L is the integer between 2～10; The span of a is 1～2 ¹²⁸between integer, and get rid of the number of the multiple be wherein 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, i.e. point coordinate in ciphertext graph picture, and x', y' ∈ 0,1,2 ..., N-1};

Step 3, utilizes the Henon mapping in step 2 to carry out scramble to original image P, and the method that scramble is 1 time is as follows:

Original image P mid point (x, y) is located to the point (x', y') that gray-scale value corresponding to pixel or RGB color value move to after Henon mapping transformation and locate, thereby obtain the image of a width scramble after once;

Step 4, using the image after scramble 1 time as original image repeated execution of steps 3, until scramble number of times reaches predefined L, thereby obtains the ciphertext graph picture after scramble L time.

A kind of in the present invention the image that adopts a kind of image scrambling method based on Henon mapping to carry out after scramble is carried out to restoration methods, concrete implementation step is as follows:

Step 1, the expression formula of inverse transformation of being derived Henon mapping by formula (5) is as follows:

$\left\{\begin{array}{cc}y=x^{\′}-1+{\mathrm{ax}}^2& \mathrm{mod}N\\ x=y^{\′}-b& \mathrm{mod}N\end{array}\right.---\left(6\right)$

Wherein, parameter a, the b of inverse transformation of Henon mapping are, the setting of N is consistent with relevant parameter in image scrambling; The setting of the random number of times of image inverted is identical with image scrambling number of times L;

Step 2, the inverse transformation that utilizes Henon mapping to the ciphertext graph after scramble L time look like to carry out image recover be inverted disorderly, the method that inverted unrest is 1 time is as follows:

Ciphertext graph is located to the point (x, y) that gray-scale value corresponding to pixel or RGB color value move to after Henon mapping inverse transformation as mid point (x', y') and locate, thereby obtain the disorderly image after 1 time of a width inverted;

Step 3, using inverted disorderly the image after 1 time as ciphertext graph as repeated execution of steps 2, until the random number of times of inverted reaches predefined value, thus the original image being restored.

According to specific embodiment, technical scheme of the present invention is further elaborated below:

This specific embodiment adopts Mathematica8 software to carry out emulation, and it is 256 * 256 standard testing gray level image Lena that original image is selected size, and each pixel of image is comprised of 8 bits, as shown in Figure 2.

Lena image is carried out to scramble 3 times, and its detailed process is as follows:

Step 1, is square-shaped image by the image of scramble, meets the demands, wherein N=256;

Step 2, sets parameter value a=53, b=170 that image scrambling number of times L=3, Henon shine upon, and the expression formula of this Henon mapping is as follows:

$\left\{\begin{array}{cc}{x}^{\′}=1-{53x}^2+y& \mathrm{mod}256\\ y^{\′}=x+170& \mathrm{mod}256\end{array}\right.---\left(7\right)$

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, i.e. point coordinate in ciphertext graph picture, and x', y' ∈ 0,1,2 ..., 255}

Step 3, utilize above-mentioned Henon mapping to carry out scramble to Lena image, wherein scramble method is once: by original image P mid point (x, y) locate gray-scale value corresponding to pixel or RGB color value and move to the point (x' after Henon mapping transformation, y') locate, thereby obtain the image after a width scramble 1 time, as shown in (a) in Fig. 3;

Step 4, using the image after scramble 1 time as original image repeated execution of steps 3, until scramble number of times reaches predefined L=3, thereby obtains the ciphertext graph picture after scramble 3 times, as shown in (c) in Fig. 3.

In Fig. 3, (a), (b), (c) are respectively the ciphertext graph picture obtaining after scramble 1 time, 2 times, 3 times, and Lena image just can not be identified for 2 times afterwards completely at scramble, and the image scrambling method in significantly visible the present invention has good scramble effect.

Ciphertext graph after above-mentioned scramble 3 times is looked like to recover, and its detailed process is as follows:

Step 1, arranges the random number of times of image inverted, and its value is identical with image scrambling number of times, i.e. L=3; Recovery image adopts the inverse transformation of Henon mapping, and the expression formula of inverse transformation of being derived Henon mapping by formula (7) is as follows:

$\left\{\begin{array}{cc}y=x^{\′}-1+{53x}^2& \mathrm{mod}256\\ x=y^{\′}-170& \mathrm{mod}256\end{array}\right.---\left(8\right)$

Make parameter a, b, N and the image scrambling stage relevant parameter of inverse transformation of Henon mapping in full accord, i.e. a=53, b=170, N=256;

Step 2, utilize formula (2) to look like to recover to the ciphertext graph after scramble 3 times and inverted disorderly, inverted disorderly method is once: by ciphertext graph as mid point (x', y') locate gray-scale value corresponding to pixel or RGB color value and move to the point (x after Henon mapping inverse transformation, y) locate, thereby obtain the disorderly image after 1 time of a width inverted;

Step 3, using inverted disorderly the image after 1 time as ciphertext graph as repeated execution of steps 2, until the random number of times of inverted reaches predefined value L=3, thus the original image being restored.

Image scrambling method of the present invention is carried out to safety analysis below.

One, key space analysis

Key space refers to all possible key in cryptographic system.The non-adequate condition of necessity of a cryptographic system safety is to have enough large key space to resist exhaustive search to attack.

In image scrambling method of the present invention, parameter a, the b of Henon mapping are key, and wherein, the span of a is 1～2 ¹²⁸between integer, and get rid of the number that those are multiples of N; The span of b is 0～2 ¹²⁸between integer.Comply with therefore, disorder method of the present invention has enough large key space opposing exhaustive attack.

Two, anti-interference capability analysis

Image often can be subject to the interference of noise in the process of transmission, preservation and processing, and a good cryptographic algorithm should have stronger antijamming capability.

By experiment, the ciphertext graph picture after image scrambling method scramble in employing the present invention is added respectively to salt-pepper noise and Gaussian noise, as shown in Figure 4 and Figure 5.Wherein, in Fig. 4, (a) is the ciphertext graph picture adding after the salt-pepper noise that density is 0.02, and the image in employing the present invention after image recovery method recovery is as shown in (b) in Fig. 4; In Fig. 5, (a) is the ciphertext graph picture adding after the Gaussian noise that variance is 0.05, and the image after this ciphertext graph picture recovers is as shown in (b) in Fig. 5.

Simultaneously, experiment is also to adopting the ciphertext graph after image scrambling method scramble in the present invention to look like to carry out shear transformation, as shown in Figure 6, in Fig. 6, (a) shears the image after partial data in ciphertext graph picture, and the image after this image recovers is as shown in (b) in Fig. 6.

From above experimental result, can see, ciphertext graph picture, after noise interpolation and shear transformation, still can recover to a certain extent, and visible Image Scrambling Algorithm of the present invention has good antijamming capability.

The above; it is only the embodiment in the present invention; but protection scope of the present invention is not limited to this; any people who is familiar with this technology is in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprise scope within, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (2)

1. the image scrambling method based on Henon mapping, is characterized in that, the concrete implementation step of the method is as follows:

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

Step 2, sets the parameter a of image scrambling number of times L and Henon mapping, the value of b, and the expression formula of Henon mapping 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 get rid of the number of the multiple be wherein 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, i.e. point coordinate in ciphertext graph picture, and x', y' ∈ 0,1,2 ..., N-1};

Step 3, utilizes the Henon mapping in step 2 to carry out scramble to original image P, and the method that scramble is 1 time is as follows:

Original image P mid point (x, y) is located to the point (x', y') that gray-scale value corresponding to pixel or RGB color value move to after Henon mapping transformation and locate, thereby obtain the image of a width scramble after once;

Step 4, using the image after scramble 1 time as original image repeated execution of steps 3, until scramble number of times reaches predefined L, thereby obtains the ciphertext graph picture after scramble L time.

2. the image that adopts a kind of image scrambling method based on Henon mapping as claimed in claim 1 to carry out after scramble is carried out to a restoration methods, it is characterized in that, the concrete implementation step of the method is as follows:

Step 1, the expression formula of inverse transformation of being derived Henon mapping by formula (1) is as follows:

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

Wherein, parameter a, the b of inverse transformation of Henon mapping are, the setting of N is consistent with relevant parameter in image scrambling; The setting of the random number of times of image inverted is identical with image scrambling number of times L;

Step 2, the inverse transformation that utilizes the mapping of Henon in step 1 to the ciphertext graph after scramble L time look like to carry out image recover be inverted disorderly, the method that inverted unrest is 1 time is as follows:

Ciphertext graph is located to the point (x, y) that gray-scale value corresponding to pixel or RGB color value move to after Henon mapping inverse transformation as mid point (x', y') and locate, thereby obtain the disorderly image after 1 time of a width inverted;

Step 3, using inverted disorderly the image after 1 time as ciphertext graph as repeated execution of steps 2, until the random number of times of inverted reaches predefined value, thus the original image being restored.