CN104240177A - Colored image encryption method based on chaotic system and fractional order Fourier transform - Google Patents

Abstract

The invention discloses a colored image encryption method based on a chaotic system and the fractional order Fourier transform and relates to the field of the image encryption systems. The method comprises the steps that the Logistic chaotic system is utilized for generating a chaotic sequence at first, and global pixel scrambling is carried out on a regrouped colored image matrix; then the fractional order Fourier transform is carried out on the result obtained in the last step; finally, the Logistic chaotic system is utilized again for generating a chaotic sequence, global pixel scrambling is carried out on the regrouped matrix with the module length and phase angle extracted in the last step, and therefore image encryption is achieved. According to the colored image encryption method based on the chaotic system and the fractional order Fourier transform, one image is introduced for building a complex matrix, algorithm space occupation caused when two images are adopted for building a complex matrix is reduced, global pixel scrambling and the fractional order Fourier transform are introduced for pixel value encryption, the image pixel point relevancy is lowered, algorithm anti-interference performance and anti-attacking performance are improved, the encryption effect is good, and safety is high.

Description

A kind of color image encrypting method based on chaos system and fraction Fourier conversion

Technical field

The invention belongs to image procossing and information security field, particularly relate to a kind of color image encrypting method based on chaos system and fraction Fourier conversion adopting single image cipher mode.

Background technology

Along with developing rapidly of computer networking technology, information security has become the serious problems of information transmission and storage, and image information transmission and image encryption technology all attract wide attention.It is large that image information itself has data volume, degree of correlation high between data, traditional encryption method for plain text information, as data encryption standards (DES), IDEA, rivest, shamir, adelman RSA etc., and is not exclusively applicable to image encryption.The features such as to have key space large due to chaos system, initial value sensitivity, aperiodicity, non-linear and unpredictability, the image encryption method based on chaos has advantage in security, adaptability, obtains in recent years and studies widely.

At present, New chaotic image encryption method can be divided into two classes by the method for encrypted image: image pixel values transformation and pixel coordinate conversion.Image pixel values transformation carrys out encrypted image by change image intensity value, and pixel coordinate conversion changes encryption picture by change image pixel coordinates.But all with expressly image is irrelevant for the encryption key of these traditional two kinds of encryption methods, so be difficult to resist known plain text attack.

In addition, the conventional at present encryption method based on chaos image uses dual image encryption.Although dual image is encrypted in image encryption to use have the high advantage of encryption complexity, there is algorithm and take the shortcomings such as the large and practical application of storage space is inconvenient.Use single image is encrypted, and cryptographic algorithm takes up room little and practical application convenient, and relative dual image is encrypted in the aspects such as image encryption efficiency and security and has certain advantage.

Summary of the invention

The object of this invention is to provide that a kind of cipher round results is good, security is high based on the color image encrypting method of chaos system and fraction Fourier conversion.

The present invention is achieved by the following technical solutions:

Based on a color image encrypting method for chaos system and fraction Fourier conversion, comprise following step:

Step one: input is of a size of the plaintext colour element image I of M × N _in, extract three chrominance channel matrix R of expressly colour element image, G, B connect into the matrix I of a 3M × N in turn _irgb;

Step 2: by initial parameter λ ₁with primary iteration value x ₀substitute into Logistic chaos system iteration m+3MN time, ignore front m iteration result, obtain chaos sequence x={x _m+1, x _m+2..., x _m+3MN, all values of chaos sequence x is sorted, obtains new sequence and obtain sequence in the position T of each element value in former chaos sequence x ₁={ t ₁, t ₂..., t _3MN, namely $x_i={\stackrel{\‾}{x}}_{t_i}(i=\mathrm{1,2},...,3\mathrm{MN});$

Step 3: to matrix I _irgbcarry out overall pixel permutation, by matrix I _irgbbe transformed into the matrix I of 3MN × 1 _t, by I _tall row according to T ₁rearrange, by I _tt ₁row moves to the first row, by I _tt ₂row moves to the second row, by that analogy, until by I _tt _3MNrow moves to last column, obtains matrix I ₁;

Step 4: by matrix I ₁be divided into two matrix I ₁₁and I ₁₂, allow matrix I ₁₁as mould, matrix I ₁₂a complex matrix is formed as phase angle $I_e=I_{11}{e}^{\mathrm{j\π}{I}_{12}};$

Step 5: by complex matrix I _ecarry out the fraction Fourier conversion that rotation angle is α, obtain complex matrix I ₂;

Step 6: extract complex matrix I ₂mould and phase angle, obtain matrix I ₂₁and I ₂₂, by matrix I ₂₁and I ₂₂be merged into the matrix I of 3MN × 1 ₃;

Step 7: substitute into initial parameter λ ₂with primary iteration value y ₀, repeat step 2 to step 3, obtain matrix I _orgb;

Step 8: by I _orgbbe divided into the matrix of 3 isometric MN × 1 and rearrange, obtaining the matrix I of M × N _or, I _og, I _ob, and three matrix compounds are finally obtained ciphertext graph as I _out.

Beneficial effect of the present invention is:

1, adopt single image encryption, algorithm takes up room little, and cryptographic algorithm travelling speed is fast.Namely dual image cryptographic algorithm encryption times is 2.367s, and decryption time is 2.376s; Encryption times of the present invention is 0.674s, and decryption time is 0.688s.

2, make use of two chaos system and have more complicated dynamics and the advantage of greater security, overcoming single chaos system, to carry out the key space of image encryption little, the shortcoming that security is low.Namely adopt two chaos system (cipher key number is 6), precision is 10 ^-15key space is 10 ⁹⁰, much larger than 2 ¹²⁸, key space enough resists known various attack.

3, utilize overall pixel permutation and fraction Fourier conversion encrypted pixel gray-scale value, greatly reduce the correlativity between ciphertext pixel value.Namely between original image pixel, correlativity is more than 99%, and the present invention encrypts rear image slices vegetarian refreshments correlativity and reduces to less than 2%.

Accompanying drawing explanation

Fig. 1 is the inventive method process flow diagram;

Fig. 2 a is Lena original image;

Fig. 2 b is the R channel image of Fig. 2 a;

Fig. 2 c is the G channel image of Fig. 2 a;

Fig. 2 d is the channel B image of Fig. 2 a;

Fig. 3 a is the encrypted image of Fig. 2 a;

Fig. 3 b is the R channel image of Fig. 3 a;

Fig. 3 c is the G channel image of Fig. 3 a;

Fig. 3 d is the channel B image of Fig. 3 a;

Fig. 4 a is the correct decrypted image of Fig. 3 a;

Fig. 4 b is the wrong parameter x of Fig. 4 a ₀decrypted image;

Fig. 4 c is the wrong parameter y of Fig. 4 a ₀decrypted image;

Fig. 4 d is the wrong parameter λ of Fig. 4 a ₁decrypted image;

Fig. 4 e is the wrong parameter λ of Fig. 4 a ₂decrypted image;

Fig. 5 a is that Fig. 3 a hides 20% image;

Fig. 5 b is Fig. 3 a interpolation mean square deviation is 0.05 Gaussian noise image;

Fig. 5 c is the decrypted image of Fig. 5 a;

Fig. 5 d is the decrypted image of Fig. 5 b;

Fig. 6 a is original image and encrypted image R, G, B each passage pixel interdependence table;

Fig. 6 b is R, G, same position pixel interdependence table between channel B;

Fig. 6 c is R, G, pixel interdependence table in adjacent position between channel B.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further details.

As shown in Figure 1 based on a color image encrypting method for chaos system and fraction Fourier conversion, comprise the steps:

S1: known-plaintext colour element image I _in(.bmp form), picture size is M × N, and extract three chrominance channel matrix R of image, G, B connect and compose the matrix I of a 3M × N in turn _irgb.

S2: initial parameter λ is set ₁with primary iteration value x ₀, substitute into Logistic chaos system iteration m+3MN time.Ignore front m iteration result to avoid deleterious effect, obtain chaos sequence x={x _m+1, x _m+2..., x _m+3MN.

S3: sorted by all values of chaos sequence x, obtains new sequence and obtain sequence in the position T of each element value in former sequence x ₁={ t ₁, t ₂..., t _3MN, namely

S4: to I _irgbcarry out overall pixel permutation, that is, by I _irgbbe transformed into the matrix I of 3MN × 1 _t, by I _tall row according to T ₁rearrange, by I _tt ₁row moves to the first row, just I _tt ₂row moves to the second row, by that analogy, until by I _tt _3MNrow moves to last column, and now we obtain matrix I ₁.

S5: by I ₁be divided into two parts I ₁₁and I ₁₂, allow I ₁₁the I as mould ₁₂a complex matrix is formed, namely as phase angle now we obtain matrix I _e.

S6: by I _ecarry out the fraction Fourier conversion (DFrFT that rotation angle is α ^α), now we obtain matrix I ₂.

S7: extract complex matrix I ₂mould and phase angle, obtain matrix I respectively ₂₁and I ₂₂, by I ₂₁and I ₂₂be merged into the matrix of 3MN × 1, now we obtain matrix I ₃.

S8: initial parameter λ is set ₂with primary iteration value y ₀, repeat step S2-S4, now we obtain matrix I _orgb.

S9: by I _orgbbe divided into the matrix of 3 isometric MN × 1 and rearrange, obtaining the matrix I of M × N _or, I _og, I _ob, their compound is finally obtained ciphertext graph as I _out(.bmp form).

MATLAB software is used to emulate the image encryption method that the present invention proposes, expressly image selection standard test coloured image Lena, picture size 256 × 256) as shown in Figure 2 a, the encryption based on chaos system and fraction Fourier conversion is carried out to it, key parameter is x ₀=0.8927, y ₀=0.7035, m=300, n=349, α=0.5000, λ ₁=3.9735, λ ₂the encryption of=3.9824, and analytical performance.Fig. 2 b is the R channel image of Fig. 2 a, and Fig. 2 c is the G channel image of Fig. 2 a, and Fig. 2 d is the channel B image of Fig. 2 a.

First by expressly image is according to step S1-S9, obtain encrypted image as shown in Figure 3 a, Fig. 3 b is the R channel image of Fig. 3 a, and Fig. 3 c is the G channel image of Fig. 3 a, and Fig. 3 d is the channel B image of Fig. 3 a.

Key sensitivity analysis is tested: use correct key x ₀=0.8927, y ₀=0.7035, m=300, n=349, α=0.5000, λ ₁=3.9735, λ ₂=3.9824 deciphering, obtain decrypted image as Fig. 4 a, respectively mistake in key x ₀=0.8927+10 ^-15, y ₀=0.7035+10 ^-15, λ ₁=3.9735+10 ^-15, λ ₂=3.9824+10 ^-15obtain decrypted result image as Fig. 4 b, Fig. 4 c, Fig. 4 d, Fig. 4 e.As can be seen from decrypted result, key susceptibility is high, and key space is large, can keep out cipher key attacks.

Encryption method attack tolerant analytical test: hide 20% as Fig. 5 a to encrypted result image graph 3a, it is decrypted, obtains decrypted result figure as Fig. 5 c; To encrypted result image graph 3a add mean square deviation be the Gaussian noise of 0.05 as Fig. 5 b, it is decrypted, obtains decrypted result figure as Fig. 5 d.As can be seen from decrypted result, encrypted image still can effectively be deciphered after receiving certain attack, and show that encryption method robustness is good, attack tolerant is high.

Pixel interdependence analytical test: the correlativity of neighbor can reflect the diffusion of image pixel, and in original plaintext image, the correlativity of adjacent two pixels is usually very large, allows the relative coefficient of encrypted image neighbor close to zero as far as possible.Table 1 is original image and encrypted image R, each passage pixel interdependence of G, B, and table 2 is R, G, same position pixel interdependence between channel B, and table 3 is R, G, adjacent position pixel interdependence between channel B.As can be seen from above form, original image correlativity is comparatively strong, and encrypted image correlativity is more weak, and security is high.

Decrypting process:

Image decryption process is the inverse process of image encryption process.

In the present invention, decrypting process can use key x ₀=0.8927, y ₀=0.7035, m=300, n=349, α=0.5000, λ ₁=3.9735, λ ₂=3.9824, by completing deciphering with the process of ciphering process contrary.

Such as, image to be encrypted is standard testing color Lena image, picture size 256 × 256, and the key carried out based on chaos system and fraction Fourier conversion it is x ₀, y ₀, m, n, α, λ ₁, λ ₂color image encryption, then deciphering time also can use key parameter x ₀, y ₀, m, n, α, λ ₁, λ ₂the process participating in ciphering process contrary is decrypted.

A kind of encryption method based on chaos system and fraction Fourier conversion provided by the invention, security is high, and antidecoding capability is strong, for image encryption provides a new solution, using image to carry out the occasion communicated, this encryption method has very high use value.

Claims (1)

1., based on a color image encrypting method for chaos system and fraction Fourier conversion, it is characterized in that, comprise following step:

Step one: input is of a size of the plaintext colour element image I of M × N _in, extract three chrominance channel matrix R of expressly colour element image, G, B connect into the matrix I of a 3M × N in turn _irgb;

Step 2: by initial parameter λ ₁with primary iteration value x ₀substitute into Logistic chaos system iteration m+3MN time, ignore front m iteration result, obtain chaos sequence x={x _m+1, x _m+2..., x _m+3MN, all values of chaos sequence x is sorted, obtains new sequence and obtain sequence in the position T of each element value in former chaos sequence x ₁={ t ₁, t ₂..., t _3MN, namely $x_i={\stackrel{\‾}{x}}_{t_i}(i=\mathrm{1,2},...,3\mathrm{MN});$

Step 3: to matrix I _irgbcarry out overall pixel permutation, by matrix I _irgbbe transformed into the matrix I of 3MN × 1 _t, by I _tall row according to T ₁rearrange, by I _tt ₁row moves to the first row, by I _tt ₂row moves to the second row, by that analogy, until by I _tt _3MNrow moves to last column, obtains matrix I ₁;

Step 4: by matrix I ₁be divided into two matrix I ₁₁and I ₁₂, allow matrix I ₁₁as mould, matrix I ₁₂a complex matrix is formed as phase angle $I_e=I_{11}{e}^{\mathrm{j\π}{I}_{12}};$

Step 5: by complex matrix I _ecarry out the fraction Fourier conversion that rotation angle is α, obtain complex matrix I ₂;

Step 6: extract complex matrix I ₂mould and phase angle, obtain matrix I ₂₁and I ₂₂, by matrix I ₂₁and I ₂₂be merged into the matrix I of 3MN × 1 ₃;

Step 7: substitute into initial parameter λ ₂with primary iteration value y ₀, repeat step 2 to step 3, obtain matrix I _orgb;

Step 8: by I _orgbbe divided into the matrix of 3 isometric MN × 1 and rearrange, obtaining the matrix I of M × N _or, I _og, I _ob, and three matrix compounds are finally obtained ciphertext graph as I _out.