CN106530197A - Image encryption method based on Kent mapping and generalized Gray codes - Google Patents

Abstract

The invention discloses an image encryption method based on Kent mapping and generalized Gray code, which comprises the steps of: scanning the plain text of the image to be encrypted according to the order of row priority, and transforming it into a one-dimensional sequence; obtaining the chaos parameter S of the chaos system and the chaos system The number of iterations c; the parameter S and the initial value x ₁ are substituted into the Kent map, then the Kent map iterates c times, and then iterates a×b times to generate a chaotic sequence L of length a×b, and uses the heap sorting algorithm Arrange the chaotic sequence from small to large, so as to generate a sequence w that records the new position of each element in the sequence sequence in the original sequence L; use the sequence w to scramble the plaintext image I; and use the binary generalized Gray code to pair The image after position scrambling is replaced by pixel value. The key sensitivity of the present invention is stronger, and the image after encryption perfectly hides the plaintext information; the correlation of the encrypted image is worse, and the distribution is more uniform.

Description

An Image Encryption Method Based on Kent Map and Generalized Gray Code

technical field

The invention relates to the field of information security, in particular to an image encryption method based on Kent mapping and generalized Gray code.

Background technique

Encryption usually means that the sender uses a specific encryption function and encryption key to convert plaintext information, and the converted information does not have a directly readable meaning. This converted information is called ciphertext information. The recipient then uses the specified decryption key and decryption function to decrypt the ciphertext information that does not contain the direct intention, and restore it to plaintext information, thereby completing the decryption process. It can be seen from the above that to complete an encryption and decryption process, it must include five parts: plaintext space, encryption function, key space, ciphertext space, and decryption function.

Plaintext space: the collection of all information that needs to be encrypted, and its types are not single, including video information, text information, image information, audio information, etc.

Encryption function: A specific algorithm (mathematical formula, etc.) that converts plaintext into ciphertext.

Keyspace: Contains all keys. The reason why the key child can play a role lies in the prior agreement between the sender and the receiver, such as the generation of the key, the use of the key, the management and distribution of the key, and so on. The traditional DES algorithm has the same encryption key and decryption key, and the later RSA algorithm that the encryption key can be disclosed and the decryption key needs to be kept secret.

Ciphertext space: the content generated after the plaintext information completes the encryption operation

Decryption function: Contrary to the encryption function, it is used to convert ciphertext into plaintext.

However, because image information has the characteristics of high correlation between data, strong data redundancy, and large data volume, traditional cryptographic algorithms for text information such as: asymmetric encryption algorithm RSA, Data Encryption Standard (DES), International Data Encryption algorithms, etc., are not completely suitable for image encryption.

Due to its cryptographic characteristics such as initial value sensitivity, aperiodicity, pseudo-randomness, and ergodicity of chaotic sequences, chaos has been widely used in image encryption to ensure the safe transmission of information. Therefore, a variety of image encryption algorithms based on chaotic systems or combined with them have been proposed in large numbers.

A typical chaotic encryption algorithm with scrambling and substitution structures proposed by Chen Guangrong once became a research hotspot among scholars. The algorithm first uses the three-dimensional Arnold transformation to scramble the position of the completed image, and then uses the intermediate key generated by the Logistic chaotic system to replace the gray value of the pixel. Although this algorithm has a small time cost and low complexity, it cannot resist plaintext attacks.

Contents of the invention

In order to overcome the deficiencies of the prior art, the present invention proposes an image encryption method based on Kent mapping and generalized Gray code.

The technical scheme of the present invention is realized like this, a kind of image encryption method based on Kent mapping and generalized Gray code, comprises steps

S1: The plaintext of the image to be encrypted is scanned in row-first order, and converted into a one-dimensional sequence I={i ₁ , i ₂ , i ₃ ...i _a×b } with a length of a×b;

S2: Calculate the chaotic parameter S of the chaotic system and the number of iterations c of the chaotic system;

S3: Substitute the parameter S and the initial value x ₁ into the Kent map, then the Kent map iterates c times to weaken the adverse effects of transient effects, and then iterates a×b times to generate a chaos with a length of a×b Sequence L={l ₁ , l ₂ , l ₃ ...l _a×b }, and use the heap sorting algorithm to arrange the chaotic sequence from small to large, so as to generate a record order sequence in which each element in the original sequence L The sequence w={w ₁ , w ₂ , w ₃ ....w _a×b } of the new position in

S4: Use the sequence w to scramble the plaintext image I;

S5: Use binary generalized Gray codes to replace the pixel values of the scrambled image.

Further, the calculation formula of the chaotic parameter S in step S2 is The calculation formula of the number of iterations c of the chaotic system is c=mod(a*a+b*b, a+b)+2a+b.

Further, step S5 includes the step

S51: performing an XOR operation on the pixel points of the image after the position of the plaintext is scrambled;

S52: Replace the pixel values of the pixel points obtained after the XOR according to the replacement rule of the generalized Gray code.

The beneficial effect of the present invention is that, compared with the prior art, the key sensitivity of the present invention is stronger, and in the case of extremely small changes, it will cause obvious changes in the image; the encrypted image perfectly hides the plaintext information ; The correlation of the encrypted image is worse and the distribution is more uniform.

Description of drawings

Fig. 1 is the flow chart of the image encryption method based on Kent mapping and generalized Gray code in the present invention.

Figure 2 is a plaintext image.

Fig. 3 is the ciphertext image after the encryption in Fig. 2 is completed.

FIG. 4 is an image histogram of FIG. 2 .

FIG. 5 is an image histogram of FIG. 3 .

Fig. 6 is the correlation of adjacent pixels in Fig. 2 .

Fig. 7 is the correlation of adjacent pixels in Fig. 3 .

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

Kent mapping is a chaotic system with excellent performance, and the mapping relationship is:

Among them, S is the control parameter of the chaotic system. When x∈(0,1), S∈(0,1), the formula (1) has a positive Lyapunov exponent, and the Kent map will be in a chaotic state, so the initial condition The sequence generated by x0 in the Kent map has good pseudo-random properties such as autocorrelation, cross-correlation and balance.

At the same time, the Kent map has strong sensitivity to initial conditions. Even when the initial conditions change slightly, the generated random sequence will be completely different. According to this characteristic, the Kent map can be well used in the encryption of chaotic images.

Generalized Gray code transformation

For a non-negative integer u, its q-ary code is recorded as u=(u _p u _p-1 ... u ₀ ) _q , and the transformation is defined as follows:

Wherein, q≥2 is a positive integer, a _ij is an integer, i,j=0,1,...,p. When and the determinant of the coefficient matrix |a _ij | and q are mutually prime numbers, the transformation conforms to the generalized Gray transformation of u, and g(u)=(g _p g _p-1 ...g ₀ ) _q is called Generalized Gray code.

Please refer to Fig. 1, the present invention comprises steps

S1: Scan the plaintext of the image to be encrypted in line-first order, and convert it into a one-dimensional sequence of length a×b I={i ₁ , i ₂ , i ₃ ...i _a×b };

S2: Calculate the chaotic parameter S of the chaotic system and the number of iterations c of the chaotic system.

First, sum the pixel values sum of the plaintext image.

Next, formula 2 is used to calculate the chaotic parameter S of the chaotic system, and formula 3 is used to calculate the number of iterations c of the chaotic system.

c=mod(a*a+b*b, a+b)+2a+b (3)

S3: Generating a new position sequence and performing position scrambling using subscripts.

Combined with the chaotic parameter S obtained from S2, an initial value x ₁ is set for the chaotic system, and the parameter S and the initial value x ₁ are substituted into formula (1).

The Kent mapping iterates c times to weaken the bad influence of the transient effect.

Next, iterate a×b times to generate a chaotic sequence L={l ₁ , l ₂ , l ₃ . . . l _a×b } whose length is a×b.

Use the heap sorting algorithm to arrange the chaotic sequence from small to large, so as to generate a sequence w={w ₁ , w ₂ , w ₃ ....w that records the new position of each element in the original sequence L. _a×b }.

S4: Use the sequence w to scramble the plaintext image I, and the dependency rule of scrambling is The sequence record after scrambling is:

L'={l' _i , l' _i , l' _i ...l' _a×b }

S5: Pixel value replacement of the image.

In this stage, the binary generalized Gray code is used to replace the pixel value of the image I' after the position scrambling.

The binary code for any non-negative integer u is u=(u _n-1 u _n-2 ...u ₀ ) ₂

make

Generate a new binary code g=(g _n-1 g _n-2 …g ₀ ) ₂ by transformation

S51: Execute an XOR operation on the pixels of the image I′ after the positions of the plaintext are scrambled. The XOR rules are as follows

S52: Replace the pixel values of the pixels obtained after the XOR in step 1 according to the replacement rule of the generalized Gray code.

After the encryption is completed, the ciphertext image is obtained.

experiment analysis

lab environment

The test platform used in this experiment is:

Intel(R) Core(TM) i5 CPU clocked at 2.67GHz, memory 4.0GB.

Win10 operating system.

The picture uses 256×256 grayscale Lena image simulation software MATLAB 2015a.

Experimental content

Algorithm Statistical Characteristic Analysis

First observe the grayscale histogram before and after encryption, compare the plaintext histogram in Figure 2 and the ciphertext histogram in Figure 3, and find that the pixel distribution of the original image without any encryption processing is uneven distribution, while the distribution of the gray histogram of the ciphertext image obtained after encryption is uniform, which hides the image information very well.

Then compare and analyze the horizontal, vertical, and diagonal correlations of pixels before and after encryption of plaintext images. The mathematical formula used for calculation is as follows:

Among them, x and y represent the gray values of two adjacent pixels in the image, and r _{x, y} are the correlation coefficients of two adjacent pixels.

Key Sensitivity Analysis

Sensitivity of the key must have the property that even the slightest change can cause a noticeable change in the image. When the plaintext decryption operation is performed on the ciphertext image, if one of the keys changes slightly, the final decrypted image will be completely different from the plaintext.

Comparing the plaintext image in Figure 2 and the ciphertext image after encryption in Figure 3, it can be found that the plaintext information is perfectly hidden after encryption.

By slightly changing the initial value of the chaotic system, the decrypted image obtained is completely different from the plaintext image, which further verifies the sensitivity of the algorithm to the key.

Comparing the histograms of the plaintext image in Figure 4 and the ciphertext image in Figure 5, it is found that the distribution of pixel values in the ciphertext image after encryption is more uniform, thus covering up the image information very well.

Comparing the adjacent positions of the plaintext image in Figure 6 and the ciphertext image in Figure 7 in the two-dimensional coordinate system, it is found that the correlation of the encrypted image is worse and the distribution is more uniform.

The above description is a preferred embodiment of the present invention, it should be pointed out that for those skilled in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications are also considered Be the protection scope of the present invention.

Claims (3)

1. an image encryption method based on Kent mapping and generalized Gray code, it is characterized in that, comprising steps S1: The plaintext of the image to be encrypted is scanned in row-first order, and converted into a one-dimensional sequence I={i ₁ , i ₂ , i ₃ ...i _a×b } with a length of a×b; S2: Calculate the chaotic parameter S of the chaotic system and the number of iterations c of the chaotic system; S3: Substitute the parameter S and the initial value x ₁ into the Kent map, then the Kent map iterates c times to weaken the adverse effects of transient effects, and then iterates a×b times to generate a chaos with a length of a×b Sequence L={l ₁ , l ₂ , l ₃ ...l _a×b }, and use the heap sorting algorithm to arrange the chaotic sequence from small to large, so as to generate a record order sequence in which each element in the original sequence L The sequence w={w ₁ , w ₂ , w ₃ ....w _a×b } of the new position in S4: Use the sequence w to scramble the plaintext image I; S5: Use binary generalized Gray codes to replace the pixel values of the scrambled image. 2. the image encryption method based on Kent mapping and generalized Gray code as claimed in claim 1, is characterized in that, the computing formula of chaos parameter S among the step S2 is The calculation formula of the number of iterations c of the chaotic system is c=mod(a*a+b*b, a+b)+2a+b. 3. the image encryption method based on Kent mapping and generalized Gray code as claimed in claim 1, is characterized in that, step S5 comprises the step S51: performing an XOR operation on the pixel points of the image after the position of the plaintext is scrambled; S52: Replace the pixel values of the pixel points obtained after the XOR according to the replacement rule of the generalized Gray code.