CN106447589A - Double random phase optical image encryption method based on Fourier transform - Google Patents
Double random phase optical image encryption method based on Fourier transform Download PDFInfo
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- G—PHYSICS
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T1/00—General purpose image data processing
- G06T1/0021—Image watermarking
Abstract
The invention relates to the technical field of information safety and optical information processing, solves a problem that a first random phase mask cannot serve as a secret key in a classic double random phase optical image encryption method, and solves secret key management and transmission problems in secret key generation. The technical scheme adopted by the invention is that the double random phase optical image encryption method based on Fourier transform comprises the following steps of 1) secret key generation: a first random phase mask and a second random phase mask serve as main secret keys, and the two random phase masks are generated by one-dimensional Logistic chaos systems controlled by different chaos parameters; 2) image encryption: by modulation of a first chaos random phase mask and a second chaos random phase mask, a modulated image is subjected to optical inverse Fourier transform to obtain an encrypted image; 3) image decryption: optical inverse Fourier transform is carried out to obtain a decrypted image. The invention is mainly applied to design manufacturing occasions.
Description
Technical field
The present invention relates to information security and optical information processing technical field, more particularly, to a kind of improved based on Fourier's change
The double random phase optical image encryption method changed.
Background technology
Digital picture, as currently one of most popular multimedia form, has in fields such as politics, economic, military, education
And be widely applied.In Internet technology highly developed today, how to protect digital picture exempt from distort, bootlegging and biography
Broadcast and there is important practical significance.Research to image encryption technology has become one of the focus in current information security field.
Because optical information processing technique has high processing rate, high degree of parallelism, can quickly realize convolution and related operation
The advantages of, in recent years, carry out, using optical meanss, the great interest (see document [1]) that digital image encryption causes people.?
In optical image encryption technology, most representational is that the double random phase based on Optical processing system of the propositions such as Javidi is compiled
Code method (see document [2]).This technology opens the frontier of optical image encryption, has been born large quantities of optics based on this technology
New Method for Encryption and new technique (see Review literature [3]).
However, the Double random phase method based on Optical processing system there are the following problems：
1) key in encryption process is the random phase mask of picture size, and therefore, key management and transmission are inconvenient
(see document [4])；
2) when image to be encrypted be real-valued image when, be placed in input plane first piece of random phase masks can not do close
Key, therefore, key space relatively small (see document [5]).
List of references：
[1]O.Matoba,T.Nomura,E.Perez-Cabre,M.Millan,and B.Javidi,Optical
techniques forinformation security,Proceedings of IEEE 2009,97:1128-1148
[2]P.Réfrégier and B.Javidi,Optical image encryption based on input
planeand Fourier plane random encoding,Opt.Lett.,1995,20:767-769
[3]S.Liu,C.Guo,and J.T.Sheridan,A review of optical image encryption
techniques,Optics &Laser Technology,2014,57:327-342
[4]L.Sui,K.Duan and J.Liang,Double-image encryption based on discrete
multiple-parameter fractional angular transform and two-coupled logistic
maps,Opt.Commun.,2015,343:140-149
[5]W.Chen,B.Javidiand X.Chen,Advances in optical security systems,
Advances in Optics and Photonics,2014,6:120-155.
Content of the invention
For overcoming the deficiencies in the prior art, present invention seek to address that the in classical double random phase optical image encryption method
One piece of random phase masks can not do the problem of key, and solves the problems, such as key management and transmission from key generates, this
Invention employed technical scheme comprise that, based on the double random phase optical image encryption method of Fourier transformation, step is as follows：
1) key production portion：First piece and second piece of random phase mask all play master key effect, two pieces of random phases
Mask respectively by different chaos state modulator dimensional Logistic chaos system generate, the initial value of Logistic chaos system and
Control parameter is in encryption process as main key；
2) image encryption part：Before the encryption specific image of one width, firstly for dimensional Logistic chaos system, if
Fixed suitable initial value and control parameter；The light wave selecting suitable wavelength is as incident light wave；Set suitable Fresnel diffraction away from
From image to be encrypted carries out fresnel transform under the irradiation of incident illumination, and the image after fresnel transform is placed in input
First piece of chaos random phase masks modulation in plane, the image after modulation is placed in Fu after optical Fourier transform again
Second piece of chaos random phase masks modulation in leaf transformation plane, the image after modulation obtains after optical Fourier inverse transformation again
Image to after encryption；
3) image decryption part：Using the image after encryption as decrypting process input picture, input picture carries out optics
Modulated by the complex conjugate of second piece of chaos random phase masks after Fourier transformation, then carry out optical Fourier inverse transformation, then
Carry out Fresnel inverse transformation, the image after being deciphered after being modulated by the complex conjugate of first piece of chaos random phase masks.
In an example, step is as follows：
(1) key production portion：
In encryption method, two pieces of chaos random phase masks play master key effect, the wavelength of Object light wave and fresnel transform away from
Act on from playing auxiliary key, the mathematic(al) representation of the discrete form of dimensional Logistic chaos system is：
xn+1=μ xn(1-xn) (1)
Wherein, the span of control parameter be μ ∈ (3.56..., 4]；xnInitial value for chaos system；xn+1For chaos
The iteration output valve of system；
The size of hypothesis image to be encrypted is M × N number of pixel, then the size of two pieces of chaos random phase masks is also M
× N number of pixel.For the dimensional Logistic chaos by two groups of different chaos state modulator so as to after iteration M × n times, obtain
Two random number sequences X1={ x1′,x2′,...,x′M×NAnd X2={ x1″,x2″,...,x″M×N, wherein x1′,x2′,...,
x′M×NAnd x1″,x2″,...,x″M×NIteration output valve for one-dimensional chaos system.This two random number sequences are integrated into two
Form Z of two-dimensional matrix1={ z 'i,j| i=1,2 ..., M；J=1,2 ..., N } and Z2=z "i,j| i=1,2 ..., M；J=
1,2 ..., N }, wherein z 'i,jWith z "i,jFor the element of two-dimensional matrix, subscript i, j is the coordinate of matrix element；Then can obtain
Two pieces of chaos random phase masks, its mathematic(al) representation is respectively C1(x1,y1)=exp (j2 π z 'i,j) and C2(x2,y2)=exp
(j2πz″i,j), wherein (x1,y1) and (x2,y2) be respectively two pieces of chaos random phase masks position coordinateses, j be imaginary number list
Position, π is pi.Because chaos random phase mask is to be controlled by the initial value of chaos system and control parameter, therefore, mix
The initial value of ignorant system and control parameter are as the master key of encryption system；
(2) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then through distance for the Fresnel diffraction of z after, its mathematic(al) representation is：
Wherein, λ is the wavelength of Object light wave, and π is pi, and j is imaginary unit；U1(x1,y1) cover for first piece of random phase
The Object light wave of image information, (x is carried before film1,y1) be first piece of chaos random phase mask position coordinateses, (x0,y0) it is defeated
Enter the position coordinateses of image；For convenience, above formula is rewritten as following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)] (3)
Wherein, FrTλ,z[] represents fresnel transform；
Image after fresnel transform is placed in first piece of chaos random phase masks modulation on input plane, modulation
Second piece of chaos random phase masks that image afterwards is placed on Fourier transform plane after optical Fourier transform again are adjusted
System, the image after modulation encrypted after optical Fourier inverse transformation again after image U2(x2′,y2′)：
U2(x2′,y2')=IFT { FT { U1(x1,y1)C1(x1,y1)}C2(x2,y2)} (4)
Wherein, FT { } represents optical Fourier transform,Represent optical Fourier inverse transformation；(x2′,y2') for exporting
Position coordinateses at face；
(3) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carries out after optical Fourier transform by the
The complex conjugate modulation of two pieces of chaos random phase masks, then carries out optical Fourier inverse transformation, more random by first piece of chaos
Carry out Fresnel inverse transformation it is possible to image after being deciphered after the complex conjugate modulation of phase mask
Wherein, * is complex conjugate operator.
The feature of the present invention and beneficial effect are：
In the image encryption method that the present invention provides, the introducing of fresnel transform makes two pieces of random phase masks can play
Master key acts on；The initial value of dimensional Logistic chaos system and control parameter, the wavelength of Object light wave and fresnel transform distance
As the key of encryption system, therefore, key management and transmission become more convenient.
Brief description：
The process index path of the image Encrypt and Decrypt method that Fig. 1 invention provides.In figure：
The ciphering process index path of a image encryption method that () provides for the present invention；
The decrypting process index path of b image encryption method that () provides for the present invention；
Fig. 2 encryption and decryption image comparison figure.In figure：
A () is original image to be encrypted；
B image that () encrypts for the system；
C () is decrypted image when all keys are all correct；
Fig. 3 various situation decrypted image comparison diagram.Wherein：
A () is the initial value x of the dimensional Logistic chaos system controlling first piece of random phase masks1Mistake, Qi Tami
Decrypted image when key is all correct；
B () is control parameter μ of the dimensional Logistic chaos system controlling first piece of random phase masks1Mistake, its
Decrypted image when its key is all correct；
C () is the initial value x of the dimensional Logistic chaos system controlling second piece of random phase masks2Mistake, Qi Tami
Decrypted image when key is all correct；
D () is control parameter μ of the dimensional Logistic chaos system controlling second piece of random phase masks2Mistake, its
Decrypted image when its key is all correct；
E () is wavelength X mistake, decrypted image when other keys are all correct；
F () is the decrypted image apart from Z mistake, when other keys are all correct for the Fresnel diffraction；
Fig. 4 various noise encryption and decryption image comparison figure.In figure,
A () is the image obtaining from the deciphering of the encryption in figure containing 10% Gaussian noise；
B () is the image obtaining from the deciphering of the encryption in figure containing 10% salt-pepper noise；
C () is the image obtaining from the deciphering of the encryption in figure containing 10% speckle noise；
Decrypted image comparison diagram in the case of Fig. 5 shearing.In figure：
A () is to decipher, from the encryption in figure cutting off 12.5%, the image obtaining；
B () is to decipher, from the encryption in figure cutting off 25%, the image obtaining；
C () is to decipher, from the encryption in figure cutting off 50%, the image obtaining.
In accompanying drawing, the list of parts representated by each label is as follows：
L1：Lens；L2：Lens；Z：Fresnel diffraction distance.
Specific embodiment
The invention provides a kind of improved double random phase optical image encryption method based on Fourier transformation, this
Bright by introduce fresnel transform, solve first piece of random phase masks in classical double random phase optical image encryption method
The problem of key can not be done, and solve the problems, such as key management and transmission from key generates, described below：
1) key production portion：Different from classical double random phase optical image encryption method, the encryption that the present invention provides
In method, first piece and second piece of random phase mask all play master key effect.Two pieces of random phase masks are respectively by different blended
The dimensional Logistic chaos system of ignorant state modulator generates.The initial value of Logistic chaos system and control parameter are in encryption and decryption
During as main key.It is used in optical system irradiating the wavelength of incident light wave and the Fresnel diffraction distance of input picture
Auxiliary key as encryption process.Therefore, key management and transmission are more convenient.
2) image encryption part：Before the encryption specific image of one width, firstly for dimensional Logistic chaos system, if
Fixed suitable initial value and control parameter；The light wave selecting suitable wavelength is as incident light wave；Set suitable Fresnel diffraction away from
From.Image to be encrypted carries out fresnel transform under the irradiation of incident illumination, and the image after fresnel transform is placed in input
First piece of chaos random phase masks modulation in plane, the image after modulation is placed in Fu after optical Fourier transform again
Second piece of chaos random phase masks modulation in leaf transformation plane, the image after modulation again after optical Fourier inverse transformation just
Image after being encrypted.
3) image decryption part：Using the image after encryption as decrypting process input picture, input picture carries out optics
Modulated by the complex conjugate of second piece of chaos random phase masks after Fourier transformation, then carry out optical Fourier inverse transformation, then
Carried out Fresnel inverse transformation after the complex conjugate modulation of first piece of chaos random phase masks it is possible to figure after being deciphered
Picture.
For making the object, technical solutions and advantages of the present invention clearer, below embodiment of the present invention is made further
Ground describes in detail.
Embodiment 1
A kind of improved double random phase optical image encryption method based on Fourier transformation, its encryption process corresponds to
Index path as shown in figure 1, encryption method is made up of three parts：Key production portion, image encryption part and image decryption portion
Point.
Referring to Fig. 1, two pieces of chaos that wherein key production portion includes being generated by dimensional Logistic chaos system are random
Phase mask CRPM1 and CRPM2；Image encryption part and image decryption part include：Lens L1, L2.
(1) key production portion：
In the encryption method that the present invention provides, two pieces of random phase masks keys are respectively by the one of different chaos state modulator
Dimension Logistic chaos system generates.The initial value of Logistic chaos system and control parameter can substitute two pieces of random phases and cover
Mould is as the master key in encryption process.Additionally, the wavelength of Object light wave and fresnel transform distance can be used as encryption and decryption mistakes
Auxiliary key in journey.
(2) image encryption part：
Before the encryption specific image of one width, first to dimensional Logistic chaos system, set suitable initial value and control
Parameter processed；The light wave selecting suitable wavelength is as Object light wave；Set suitable fresnel transform distance.Then, figure to be encrypted
As carrying out fresnel transform under the irradiation of incident illumination, the image after fresnel transform is placed in first piece on input plane
Chaos random phase masks are modulated, and the image after modulation is placed on Fourier transform plane after optical Fourier transform again
Second piece of chaos random phase masks modulation, after the image after modulation can be obtained by encryption again after optical Fourier inverse transformation
Image.
(3) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carries out after optical Fourier transform by the
The complex conjugate modulation of two pieces of chaos random phase masks, then carries out optical Fourier inverse transformation, more random by first piece of chaos
Carry out Fresnel inverse transformation it is possible to image after being deciphered after the complex conjugate modulation of phase mask.
In sum, the present invention passes through to introduce fresnel transform, solves classical double random phase optical image encryption side
In method, first piece of random phase masks can not do the problem of key, and solves key management and transmission from key generates
Problem.
Embodiment 2
With reference to Fig. 1, design principle, the scheme in embodiment 1 is introduced in detail, described below：
A kind of improved double random phase optical image encryption method based on Fourier transformation, its encryption process corresponds to
Index path as shown in figure 1, encryption method is made up of three parts：Key production portion, image encryption part and image decryption portion
Point.Specific embodiment with regard to this three part is described in detail respectively below.
(1) key production portion：
In encryption method, two pieces of chaos random phase masks play master key effect, the wavelength of Object light wave and fresnel transform away from
Act on from playing auxiliary key.Below with regard to how to generate this two pieces of chaos random phase masks using dimensional Logistic chaos system
Describe in detail.
The mathematic(al) representation of the discrete form of dimensional Logistic chaos system is：
xn+1=μ xn(1-xn) (1)
Wherein, the span of control parameter be μ ∈ (3.56..., 4]；xnInitial value for chaos system；xn+1For chaos
The iteration output valve of system.
The size of hypothesis image to be encrypted is M × N number of pixel, then the size of two pieces of chaos random phase masks is also M
× N number of pixel.For the dimensional Logistic chaos by two groups of different chaos state modulator so as to after iteration M × n times, obtain
Two random number sequences X1={ x1′,x2′,...,x′M×NAnd X2={ x1″,x2″,...,x″M×N, wherein x1′,x2′,...,
x′M×NAnd x1″,x2″,...,x″M×NIteration output valve for one-dimensional chaos system.This two random number sequences are integrated into two
Form Z of two-dimensional matrix1={ z 'i,j| i=1,2 ..., M；J=1,2 ..., N } and Z2=z "i,j| i=1,2 ..., M；j
=1,2 ..., N }, wherein z 'i,jWith z "i,jFor the element of two-dimensional matrix, i, j are the coordinate of matrix element；Two then can be obtained
Block chaos random phase mask, its mathematic(al) representation is respectively C1(x1,y1)=exp (j2 π z 'i,j) and C2(x2,y2)=exp (j2
πz″i,j), wherein (x1,y1) and (x2,y2) be respectively two pieces of chaos random phase masks position coordinateses, j be imaginary unit, π
For pi.Because chaos random phase mask is to be controlled by the initial value of chaos system and control parameter, therefore, chaos system
System initial value and control parameter as encryption system master key.Because master key and auxiliary key are all some numerals, therefore,
Managing and transmitting these numerals to become very convenient.
(2) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then through distance for the Fresnel diffraction of z after, its mathematic(al) representation is：
Wherein, λ is the wavelength of Object light wave, and π is pi, and j is imaginary unit；U1(x1,y1) cover for first piece of random phase
The Object light wave of image information, (x is carried before film1,y1) be first piece of chaos random phase mask position coordinateses, (x0,y0) it is defeated
Enter the position coordinateses of image.
For convenience, above formula is rewritten as following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)]. (3)
Wherein, FrTλ,z[] represents fresnel transform.
Image after fresnel transform is placed in first piece of chaos random phase masks modulation on input plane, modulation
Second piece of chaos random phase masks that image afterwards is placed on Fourier transform plane after optical Fourier transform again are adjusted
System, the image after modulation encrypted after optical Fourier inverse transformation again after image U2(x2′,y2′)：
U2(x2′,y2')=IFT { FT { U1(x1,y1)C1(x1,y1)}C2(x2,y2)} (4)
Wherein,Represent optical Fourier transform,Represent optical Fourier inverse transformation；(x2′,y2') it is defeated
Appear locate position coordinateses.
(3) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carries out after optical Fourier transform by the
The complex conjugate modulation of two pieces of chaos random phase masks, then carries out optical Fourier inverse transformation, more random by first piece of chaos
Carry out Fresnel inverse transformation it is possible to image after being deciphered after the complex conjugate modulation of phase mask
Wherein, * is complex conjugate operator.
In sum, the present invention passes through to introduce fresnel transform, solves classical double random phase optical image encryption side
In method, first piece of random phase masks can not do the problem of key, and solves key management and transmission from key generates
Problem.
Embodiment 3
With reference to specific accompanying drawing, feasibility checking is carried out to the scheme in embodiment 1 and 2, described below：
After piece image (as shown in Fig. 2 (a)) being encrypted using the encryption method that the present invention implements to provide, obtain
Shown in encrypted image such as Fig. 2 (b).
By Fig. 2 (b) as can be seen that any information of original image is all hidden.When all keys are all correct, decrypt
Image such as Fig. 2 (c) shown in.By Fig. 2 (c) as can be seen that original image can be reduced completely.Illustrate using the system to ash
The encryption of degree image and deciphering are successful.
Additionally, when other keys of some wrong cipher key are correct, shown in decrypted result such as Fig. 3 (a) -3 (f).Thus
It can be seen that, the safety of the system is can be guaranteed.
Fig. 4 (a) -4 (c) is encryption figure containing the deciphering figure in the case of 10% Gaussian noise, salt-pepper noise and speckle noise
Picture.Fig. 5 (a) -5 (c) is respectively the decrypted image in the case of encryption figure disappearance 12.5%, 25% and 50%.As can be seen here, even if
To a certain extent by sound pollution or lack part information, the embodiment of the present invention remains able to decrypt certain matter encrypted image
The original image of amount, demonstrates the feasibility of the system, meets the multiple needs in practical application.
To the model of each device in addition to doing specified otherwise, the model of other devices is not limited the embodiment of the present invention,
As long as the device of above-mentioned functions can be completed.
It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
Sequence number is for illustration only, does not represent the quality of embodiment.
The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all spirit in the present invention and
Within principle, any modification, equivalent substitution and improvement made etc., should be included within the scope of the present invention.
Claims (2)
1. a kind of double random phase optical image encryption method based on Fourier transformation, is characterized in that, step is as follows：
1) key production portion：First piece and second piece of random phase mask all play master key effect, two pieces of random phase masks
Respectively by the generation of dimensional Logistic chaos system, the initial value of Logistic chaos system and the control of different chaos state modulator
Parameter is in encryption process as main key；
2) image encryption part：Before the encryption specific image of one width, firstly for dimensional Logistic chaos system, set and close
Suitable initial value and control parameter；The light wave selecting suitable wavelength is as incident light wave；Set suitable Fresnel diffraction distance, treat
The image of encryption carries out fresnel transform under the irradiation of incident illumination, and the image after fresnel transform is placed on input plane
The modulation of first piece of chaos random phase masks, the image after modulation is placed in Fourier transformation after optical Fourier transform again
Second piece of chaos random phase masks modulation in plane, the image after modulation is encrypted after optical Fourier inverse transformation again
Image afterwards；
3) image decryption part：Using the image after encryption as decrypting process input picture, input picture carries out in optics Fu
Modulated by the complex conjugate of second piece of chaos random phase masks after leaf transformation, then carry out optical Fourier inverse transformation, then by
Carry out Fresnel inverse transformation, the image after being deciphered after the complex conjugate modulation of one piece of chaos random phase masks.
2. the double random phase optical image encryption method based on Fourier transformation as claimed in claim 1, is characterized in that,
In one example, step is as follows：
(1) key production portion：
In encryption method, two pieces of chaos random phase masks play master key effect, and the wavelength of Object light wave and fresnel transform distance rise
Auxiliary key acts on, and the mathematic(al) representation of the discrete form of dimensional Logistic chaos system is：
xn+1=μ xn(1-xn) (1)
Wherein, the span of control parameter be μ ∈ (3.56 ..., 4]；xnInitial value for chaos system；xn+1For chaos system
Iteration output valve；
The size of hypothesis image to be encrypted is M × N number of pixel, then the size of two pieces of chaos random phase masks is also M × N number of
Pixel.For, obtained so as to after iteration M × n times by the dimensional Logistic chaos of two groups of different chaos state modulator two with
Machine Number Sequence X1={ x '1,x′2,…,x′M×NAnd X2=x "1,x″2,…,x″M×N, wherein x '1,x′2,…,x′M×NWith x "1,
x″2,…,x″M×NIteration output valve for one-dimensional chaos system.This two random number sequences are integrated into two two-dimensional matrixs
Form Z1={ z 'i,j| i=1,2 ..., M；J=1,2 ..., N } and Z2=z "i,j| i=1,2 ..., M；J=1,2 ..., N }, its
Middle z 'i,jWith z "i,jFor the element of two-dimensional matrix, subscript i, j is the coordinate of matrix element；The random phase of two pieces of chaos then can be obtained
Position mask, its mathematic(al) representation is respectively C1(x1,y1)=exp (j2 π z 'i,j) and C2(x2,y2)=exp (j2 π z "i,j), wherein
(x1,y1) and (x2,y2) be respectively two pieces of chaos random phase masks position coordinateses, j be imaginary unit, π be pi.By
To be controlled by the initial value of chaos system and control parameter in chaos random phase mask, therefore, the initial value of chaos system and
Control parameter is as the master key of encryption system；
(2) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then through distance for the Fresnel diffraction of z after, its mathematic(al) representation is：
Wherein, λ is the wavelength of Object light wave, and π is pi, and j is imaginary unit；U1(x1,y1) for before first piece of random phase mask
Carry the Object light wave of image information, (x1,y1) be first piece of chaos random phase mask position coordinateses, (x0,y0) scheme for input
The position coordinateses of picture；For convenience, above formula is rewritten as following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)] (3)
Wherein, FrTλ,z[] represents fresnel transform；
Image after fresnel transform is placed in first piece of chaos random phase masks modulation on input plane, after modulation
Image is placed in second piece of chaos random phase masks modulation on Fourier transform plane after optical Fourier transform again, adjusts
Image after system encrypted after optical Fourier inverse transformation again after image U2(x′2,y′2)：
U2(x′2,y′2)=IFT { FT { U1(x1,y1)C1(x1,y1)}C2(x2,y2)} (4)
Wherein, FT { } represents optical Fourier transform, IFTRepresent optical Fourier inverse transformation；(x′2,y′2) at output face
Position coordinateses；
(3) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carries out after optical Fourier transform by second piece
The complex conjugate modulation of chaos random phase masks, then carries out optical Fourier inverse transformation, then by first piece of chaos random phase
Carry out Fresnel inverse transformation it is possible to image after being deciphered after the complex conjugate modulation of mask
Wherein, * is complex conjugate operator.
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| CN109544435A (en) * | 2018-10-22 | 2019-03-29 | 天津大学 | Gyrator converts chaos random phase encoding digital image encryption method |
| CN110312053A (en) * | 2019-05-10 | 2019-10-08 | 南通理工学院 | Based on sublevel Fourier spectral decomposition and the optical encryption method for mixing random mask |
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