CN109657484A - The multichannel image decoding method spliced based on gamma function and ciphertext - Google Patents

The multichannel image decoding method spliced based on gamma function and ciphertext Download PDF

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CN109657484A
CN109657484A CN201811514614.6A CN201811514614A CN109657484A CN 109657484 A CN109657484 A CN 109657484A CN 201811514614 A CN201811514614 A CN 201811514614A CN 109657484 A CN109657484 A CN 109657484A
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CN109657484B (en
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蔡达岭
孙文卿
陈宝华
王军
吴泉英
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Suzhou University of Science and Technology
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Abstract

The present invention relates to a kind of color image decoding methods of gyrator transformation and gamma random function, can be used for image encryption.In encryption side, color image is decomposed into three individual color channel component pictures of RGB, then generates three group encryption parameters, then generate three groups of random phase functions, and component image is encrypted respectively in airspace and frequency domain using gyrator transformation, obtains ciphertext.Three random integers are finally generated, by ciphertext data being spliced in a matrix at random.In decryption side, matrix decomposition will be spliced and be decrypted at the ciphertext data of three components, then with each channel image of conjugate phase key pair, recovery synthesizes color image.Ciphertext phase distribution mode can be changed in the method for the present invention, the attack for resisting Phase Retrieve Algorithm is attacked from other algorithms for cracking scheme by splicing to resist at random, improves encryption intensity, this method can encrypt Three Channel Color image, have excellent Social benefit and economic benefit.

Description

The multichannel image decoding method spliced based on gamma function and ciphertext
Technical field
The invention belongs to field of information security technology, and in particular to a kind of image encryption and decryption technology.
Background technique
With the continuous development of internet and multimedia technology, in terms of information security the problem of, be can not be ignored.Digitized map As one of most important information transmitting carrier.In fields such as military affairs, finance, medical treatment, scientific researches, image data will often be carried out It is being transmitted after encryption, for preventing stealing for information, therefore, image encryption technology is also increasingly by the weight of people Depending on.
The purpose of image encryption is to be hidden the expressed information of image itself, makes the user for not grasping key can not The true content of image is obtained, and the user for grasping key can obtain true image information by decipherment algorithm.Optical picture As encryption technology is, using certain algorithm, to carry out certain disturb to original image by electro-optical system or virtual optical system Disorderly operation, realizes the encryption of image data.Earliest optical image encryption system be Refregier and Javidi propose it is double with Machine phase code system, the system is in typical 4f system, respectively on the input plane of optical signal and fourier spectrum face It is respectively put into one piece of random phase mask plate, the purpose is to the amplitudes to input picture to encrypt respectively with phase information, To achieve the purpose that the ciphertext for enabling output becomes a width white noise acoustic image completely.Hereafter the system has been extended to score Fourier again Leaf domain, Fresnel domain etc..There has also been sizable development for the means and application field of encryption, to also further improve The safety of system.
But there is result of study to show through Phase Retrieve Algorithm, it can recover by white noise random phase plate Encrypted image, even if passing through iterative calculation in the case where key is totally unknown, it is also possible to enough recover the letter of image Breath, and the degree of human readable can be reached.Therefore, according to Phase Retrieve Algorithm the characteristics of, improves adding for this kind of system Close mode is to need further to solve the problems, such as.In recent years it has been proposed that the mode that the phase key of structuring is encrypted, this Structuring phase key used in class system is some functions, by inputting random parameter, generates different phase distribution moulds Formula, but the number of parameters in generic function only has 2-3 or so, this will make the space of key be obviously reduced.Especially When cracking the encryption of color image, a part if image of each individual color channel is cracked respectively, but pass through the folded of channel Add, is then easier that image can be distinguished by the mankind.Moreover, we also note that, Phase Retrieve Algorithm can recover Original image, one of particularly significant reason are exactly that the phase distribution of encrypted image has equally distributed statistical property.
The invention proposes codings and solution based on gyrator transformation and the color image of Gamma distribution random phase function Code method, can be used in the encryption to color image.To the component image in each channel, different encryption parameters is used respectively Encrypted, can change the phase distribution statistical law of encrypted image, hinder using Phase Retrieve Algorithm to ciphertext image into Row cracks.Meanwhile method the characteristics of multichannel image is utilized that this patent proposes, by the ciphertext data in each channel carry out with Machine splicing, further enhances the resistivity that this method cracks other scheme, improves the safety of encryption system.The party Method can be also used for other than it can encrypt to color image to other multi-pass such as high spectrum image and multiple image The encryption of road image.
Summary of the invention
In view of the deficiencies of the prior art, the invention proposes based on gyrator transformation and Gamma distribution random phase function Color image encryption and decryption method.The present invention will be further described in detail with reference to the accompanying drawing.To realize above-mentioned mesh , the solution of the present invention includes:
As shown in Figure 1, ciphering process is as follows:
1) image to be encrypted is I (x, y), for the color image of RGB triple channel, can be decomposed into point in three channels Spirogram picture, uses I respectivelyR(x, y), IG(x, y) and IB(x,y).The image in each channel is real number on each pixel, can be with It is seen as an amplitude function, x and y indicate the pixel coordinate of image.The Pixel Dimensions of image are M*N.
2) random phase function R1 (x, y)=exp [i*m is generated1(x, y)], wherein i indicates imaginary unit, m1(x, y) is indicated The random matrix of Gamma distribution by linear transformation, m1(x, y) can be write as
m1(x,y)=a1+b1*g(α1,β1, x, y), (1)
Wherein, a1And b1It is linear transformation parameter, takes real number, according to the definition of gamma function, which is contained Form parameter and scale parameter respectively use α in formula (1)1And β1It indicates.
3) by image I to be encryptedR(x, y) is multiplied with random phase function R1 (x, y), and as the defeated of system Enter, i.e.,
t(x,y)=IR(x,y)*R1(x,y).(2)
4) it is converted with gyrator and input t (x, y) is encrypted, which can use Fast Fourier Transform in a computer Algorithm is realized, can be indicated with following formula,
T(x,y)=FFT[t(x,y)*exp[i*2π*x*y*cot(ξ1)]]*exp[i*2π*x*y*cot(ξ1)], (3)
Wherein, ξ1The angle parameter for indicating gyrator transformation, generally takes 0 < ξ1<2π。
5) it is used in identical method in step 2, but selects another group of linear transformation parameter a1、b1, form parameter α1 With scale parameter β1, generate random phase function R2 (x, y)=exp [i*m2(x, y)], then the output function T that gyrator is converted (x, y) multiplied by R2 (x, y), i.e.,
T´(x,y)=T(x,y)*R2(x,y).(4)
6) gyrator transformation is carried out again, obtains encrypted image cR(x, y) can be indicated with following formula,
cR(x,y)=FFT[T´(x,y)*exp[i*2π*x*y*cot(ξ2)]]*exp[i*2π*x*y*cot(ξ2)], (5)
Wherein, ξ2It is also the angle parameter for indicating gyrator transformation, ξ1And ξ2Different values can be taken, encryption can be improved in this way Intensity, the encrypted image c of outputR(x, y) is that complex function contains amplitude and phase two parts.
7) to the image I in green and blue channelG(x, y) and IB(x, y) repeats step 2 and is added respectively to step 6) It is close, obtain ciphertext cG(x, y) and cB(x,y)。
8) selection generates three integers between 1~N, k1, k2 and k3.By cRThe column of kth 1 of (x, y) are put into new matrix c In 1 column of (x, y), then by cGThe k2 column of (x, y) are put into the 2nd column of matrix c (x, y), finally by cBThe k3 column of (x, y) are put into In the 3rd column of matrix c (x, y), after completing this circulation, k1, k2 and k3 are added 1 respectively, if k1, k2 or k3 are greater than N, then will It is set as 1.It repeats cR(x,y)、cG(x, y) and cBCiphertext data in (x, y) are put into line by line in c (x, y), Zhi Daosuo Until some data are stuffed entirely with c (x, y).
9) by spliced ciphertext c (x, y) by common signal channel, and three groups of random phase function R2 (x, y) and angle of transformation Spend parameter ξ1And ξ2And k1, k2, k3 are transferred to recipient by cryptochannel, can be decrypted.
As shown in Fig. 2, decrypting process comprises the following steps:
1) according to the value of k1, k2, k3, the 1st column of c (x, y) are put into cRIn the column of (x, y) kth 1, the 2nd column of c (x, y) are put into cGIn the column of (x, y) kth 2, the 3rd column of c (x, y) are put into cBIn the column of (x, y) kth 3, after completing this circulation, by k1, k2 and k3 Respectively plus 1, if k1, k2 or k3 are greater than N, then it is set to 1.Above-mentioned steps are repeated, by data all in c (x, y) Column are all restored to cR(x,y)、cG(x,y)、cBIn (x, y).
2) it is obtained being distributed R3 (x, y) for the conjugate function of decryption by R2 (x, y), i.e.,
R3(x,y)=exp[-i*m2(x,y)].(6)
3) decrypted image is calculated according to the following formula,
rT(x,y)=FFT[cR(x,y)*exp[i*2π*x*y*cot(-ξ2)]]*exp[i*2π*x*y*cot(-ξ2)], (7)
RT ' (x, y)=rT (x, y) * R3 (x, y), (8)
rt(x,y)=FFT[rT´(x,y)*exp[i*2π*x*y*cot(-ξ1)]]*exp[i*2π*x*y*cot(-ξ1)].(9)
4) amplitude components for taking decrypted result are exactly original plaintext image,
rIR(x, y)=Abs [rt (x, y)], (10)
Wherein, Abs [-] indicates to take the amplitude components of plural number.
5) decryption step 1 is repeated) to 3), respectively to the ciphertext c in green and blue channelG(x, y) and cB(x, y) is solved It is close.
6) by the image combined color image in three channels.
Compared with prior art, the present invention beneficial effect is: the invention proposes based on gyrator transformation and gamma point The color image encoding and coding/decoding method of cloth random phase function, can be used for the encryption to color image, to each channel Component image is encrypted using different encryption parameters respectively, can change the phase distribution statistical law of encrypted image, resistance Hinder and ciphertext image is cracked using Phase Retrieve Algorithm.Meanwhile multichannel image is utilized in the method that this patent proposes Feature is spliced the ciphertext data in each channel at random, is further enhanced this method and is cracked supporting for scheme for other Anti- ability improves the safety of encryption system.This method can be also used for pair other than it can encrypt to color image The encryption of other multichannel images such as high spectrum image and multiple image has excellent Social benefit and economic benefit.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples.
Fig. 1 is the color image encryption stream of the present invention using gyrator transformation and Gamma distribution random phase function Cheng Tu.
Fig. 2 is that the color image of the present invention using gyrator transformation and Gamma distribution random phase function decrypts stream Cheng Tu.
Fig. 3 is three channels of red, green and blue of color image to be encrypted used in the embodiment of the present invention.
Fig. 4 is the three channel Gamma distribution random phase encryption function R1 generated in the embodiment of the present invention.
Fig. 5 is the three channel Gamma distribution random phase encryption function R2 generated in the embodiment of the present invention.
Fig. 6 is the distribution of amplitudes in three channels of encrypted image in the embodiment of the present invention.
Fig. 7 is the phase distribution in three channels of encrypted image in the embodiment of the present invention.
Fig. 8 is the distribution of amplitudes of three random stitching images in channel of encrypted image in the embodiment of the present invention.
Fig. 9 is the phase distribution of three random stitching images in channel of encrypted image in the embodiment of the present invention.
Figure 10 is the three channel Gamma distribution random phase decryption function R3 generated in the embodiment of the present invention.
Figure 11 is the three channel decrypted images obtained in the embodiment of the present invention.
Specific embodiment
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real Applying mode, invention is further described in detail.
Embodiment:
Image encryption process: as shown in figure 3, logical to RGB three of the image " pepper " that pixel resolution is 512*512 Road is encrypted respectively.
According to encrypting step 2), set the form parameter α of red channel1=2, scale parameter β1=1, linear transformation parameter a1= 1, b1=1, and generate random phase function R1 (x, y)；Set the form parameter α of green channel1=2, scale parameter β1=2, linearly Transformation parameter a1=2, b1=1, and generate random phase function R1 (x, y)；Set the form parameter α of blue channel1=1, scale ginseng Number β1=1, linear transformation parameter a1=1, b1=1, and random phase function R1 (x, y) is generated, as shown in Figure 4.
According to encrypting step 3), by image IR(x, y), IG(x, y) and IB(x, y), respectively with respective random phase function R1 (x, y) is multiplied.
According to encrypting step 4), the parameter in three channels, red component ξ is set separately1=π/4, green component ξ1The He of=π/5 Blue component ξ1=π/2.And gyrator transformation is carried out to the input picture of component.
According to encrypting step 5), the form parameter in three channels, scale parameter and linear transformation parameter is set separately.It is right In red channel α2=2, β2=1, a2=2, b2=0；For green channel α2=2, β2=1, a2=3, b2=2；For blue channel α2=2, β2=2, a2=3, b2=3.To each channel, random phase function R2 (x, y) is generated respectively.Again by encrypting step 4) in output letter Number is respectively multiplied by R2 (x, y), as shown in Figure 5.
According to encrypting step 6) -7), the gyrator transformation parameter in three channels, red component ξ is set separately2=π/3, it is green Colouring component ξ2=π/4, blue component ξ2=π/4 carry out a gyrator transformation to the output of step 5) again, obtain ciphertext image, Phase and distribution of amplitudes difference are as shown in Figure 6 and Figure 7.
According to encrypting step 8), set k1=10, k2=30, k3=40, by the ciphertext of triple channel be spliced into a matrix c (x, Y), phase and distribution of amplitudes difference are as shown in Figure 8 and Figure 9.
According to encrypting step 9), by the corresponding R1 (x, y) in each channel, R2 (x, y), ξ1And ξ2It is transmitted by cryptochannel Recipient is transferred to by common signal channel to recipient, and by ciphertext c (x, y).
Image decryption process:
According to decryption step 1), according to the value of k1, k2, k3, the component in three channels is isolated from c (x, y).
According to decryption step 2), the conjugate function R3 (x, y) of each channel R2 (x, y) is obtained, as shown in Figure 10.
According to decryption step 3) and each channel parameter ξ1, ξ2With R3 (x, y), calculated from formula (7)-(9) Decrypted result.
According to decryption step 4), the amplitude components of each channel decryption function in result are taken out, are exactly plaintext image.
According to decryption step 5), the plaintext image in three channels is calculated, as shown in figure 11.
According to decryption step 6), the decrypted image in three channels is synthesized to original color image.

Claims (1)

  1. The color image encryption and decryption method of 1.gyrator transformation and Gamma distribution random phase function, which is characterized in that packet Include following steps:
    As shown in Figure 1, ciphering process is as follows:
    1) image to be encrypted is I (x, y), for the color image of RGB triple channel, can be decomposed into point in three channels Spirogram picture, uses I respectivelyR(x, y), IG(x, y) and IB(x, y), the image in each channel are real number on each pixel, can be with It is seen as an amplitude function, x and y indicate the pixel coordinate of image, and the Pixel Dimensions of image are M*N；
    2) random phase function R1 (x, y)=exp [i*m is generated1(x, y)], wherein i indicates imaginary unit, m1(x, y) indicates to pass through The random matrix of the Gamma distribution of linear transformation, m1(x, y) can be write as
    m1(x,y)=a1+b1*g(α1,β1, x, y), (1)
    Wherein, a1And b1It is linear transformation parameter, takes real number, according to the definition of gamma function, which contains shape Shape parameter and scale parameter respectively use α in formula (1)1And β1It indicates；
    3) by image I to be encryptedR(x, y) is multiplied with random phase function R1 (x, y), and as the input of system, i.e.,
    t(x,y)=IR(x,y)*R1(x,y)；(2)
    4) it is converted with gyrator and input t (x, y) is encrypted, which can use Fast Fourier Transform in a computer Algorithm is realized, can be indicated with following formula,
    T(x,y)=FFT[t(x,y)*exp[i*2π*x*y*cot(ξ1)]]*exp[i*2π*x*y*cot(ξ1)], (3)
    Wherein, ξ1The angle parameter for indicating gyrator transformation, generally takes 0 < ξ1<2π；
    5) it is used in identical method in step 2, but selects another group of linear transformation parameter a1、b1, form parameter α1And ruler Spend parameter beta1, generate random phase function R2 (x, y)=exp [i*m2(x, y)], then by gyrator transformation output function T (x, Y) multiplied by R2 (x, y), i.e.,
    T´(x,y)=T(x,y)*R2(x,y)；(4)
    6) gyrator transformation is carried out again, obtains encrypted image cR(x, y) can be indicated with following formula,
    cR(x,y)=FFT[T´(x,y)*exp[i*2π*x*y*cot(ξ2)]]*exp[i*2π*x*y*cot(ξ2)], (5)
    Wherein, ξ2It is also the angle parameter for indicating gyrator transformation, ξ1And ξ2Different values can be taken, encryption can be improved in this way Intensity, the encrypted image c of outputR(x, y) is that complex function contains amplitude and phase two parts；
    7) to the image I in green and blue channelG(x, y) and IB(x, y) repeats step 2 and is encrypted respectively to step 6), obtained To ciphertext cG(x, y) and cB(x,y)；
    8) selection generates three integers between 1~N, k1, k2 and k3, by cRThe column of kth 1 of (x, y) are put into new matrix c (x, y) In 1 column, then by cGThe k2 column of (x, y) are put into the 2nd column of matrix c (x, y), finally by cB(x, y) k3 column be put into matrix c (x, Y) in the 3rd column, after completing this circulation, k1, k2 and k3 are added 1 respectively, if k1, k2 or k3 are greater than N, are then set to 1, it repeats cR(x,y)、cG(x, y) and cBCiphertext data in (x, y) are put into line by line in c (x, y), until all data Until being stuffed entirely with c (x, y)；
    9) by spliced ciphertext c (x, y) by common signal channel, and three groups of random phase function R2 (x, y) and transformation angle are joined Number ξ1And ξ2And k1, k2, k3 are transferred to recipient by cryptochannel, can be decrypted；
    As shown in Fig. 2, decrypting process comprises the following steps:
    1) according to the value of k1, k2, k3, the 1st column of c (x, y) are put into cRIn the column of (x, y) kth 1, the 2nd column of c (x, y) are put into cGIn the column of (x, y) kth 2, the 3rd column of c (x, y) are put into cBIn the column of (x, y) kth 3, after completing this circulation, by k1, k2 and k3 Respectively plus 1, if k1, k2 or k3 are greater than N, then it is set to 1, repeats above-mentioned steps, by data all in c (x, y) Column are all restored to cR(x,y)、cG(x,y)、cBIn (x, y)；
    2) it is obtained being distributed R3 (x, y) for the conjugate function of decryption by R2 (x, y), i.e.,
    R3(x,y)=exp[-i*m2(x,y)]；(6)
    3) decrypted image is calculated according to the following formula,
    rT(x,y)=FFT[cR(x,y)*exp[i*2π*x*y*cot(-ξ2)]]*exp[i*2π*x*y*cot(-ξ2)], (7)
    RT ' (x, y)=rT (x, y) * R3 (x, y), (8)
    rt(x,y)=FFT[rT´(x,y)*exp[i*2π*x*y*cot(-ξ1)]]*exp[i*2π*x*y*cot(-ξ1)]；(9)
    4) amplitude components for taking decrypted result are exactly original plaintext image,
    rIR(x, y)=Abs [rt (x, y)], (10)
    Wherein, Abs [-] indicates to take the amplitude components of plural number；
    5) decryption step 1 is repeated) to 3), respectively to the ciphertext c in green and blue channelG(x, y) and cB(x, y) is decrypted；
    6) by the image combined color image in three channels.
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CN110232285A (en) * 2019-06-19 2019-09-13 首都师范大学 A kind of method and device of image encryption
CN110532793A (en) * 2019-08-30 2019-12-03 首都师范大学 Image encryption method, image encrypting apparatus, electronic equipment and readable storage medium storing program for executing

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CN103295185A (en) * 2013-06-28 2013-09-11 浙江农林大学 Asymmetrical image encryption method based on random amplitude plate and Fourier transformation
CN103761703A (en) * 2014-01-15 2014-04-30 西安理工大学 Single channel color image encryption method based on GT conversion and chaos
CN106504175A (en) * 2016-09-30 2017-03-15 天津大学 Nonlinear optics image encryption method in Gyrator transform domains

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CN102567943A (en) * 2012-01-09 2012-07-11 浙江农林大学 Asymmetric double image encryption method based on joint of fourier transformation and phase cutting
CN103295185A (en) * 2013-06-28 2013-09-11 浙江农林大学 Asymmetrical image encryption method based on random amplitude plate and Fourier transformation
CN103761703A (en) * 2014-01-15 2014-04-30 西安理工大学 Single channel color image encryption method based on GT conversion and chaos
CN106504175A (en) * 2016-09-30 2017-03-15 天津大学 Nonlinear optics image encryption method in Gyrator transform domains

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Publication number Priority date Publication date Assignee Title
CN110232285A (en) * 2019-06-19 2019-09-13 首都师范大学 A kind of method and device of image encryption
CN110232285B (en) * 2019-06-19 2021-02-26 首都师范大学 Image encryption method and device
CN110532793A (en) * 2019-08-30 2019-12-03 首都师范大学 Image encryption method, image encrypting apparatus, electronic equipment and readable storage medium storing program for executing
CN110532793B (en) * 2019-08-30 2021-06-11 首都师范大学 Image encryption method, image encryption device, electronic equipment and readable storage medium

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