CN106530201A - Optical image encryption method based on combination of Fresnel transform and linear canonical transform - Google Patents
Optical image encryption method based on combination of Fresnel transform and linear canonical transform Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- 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 fields of image information safety and optical information processing, especially to an image encryption method, thereby realizing effective violence resistance, statistical attack resistance, and noise attack resistance. The optical image encryption method based on combination of Fresnel transform and linear canonical transform comprises the following steps: step one, implementing an image encryption part; to be specific, carrying out Fresnel transform on a to-be-encrypted image under irradiation of incident light, carrying out first random phase mask modulation, carrying out first linear canonical transform, carrying out second random phase mask modulation, carrying out second linear canonical transform, and then obtaining an encrypted noise-like image after the Fresnel transform, linear canonical transform twice, and random phase mask modulation twice; and step two, implementing an image decryption part; to be specific, carrying out decryption to obtain a decrypted image. The method is mainly applied to image information safety and optical information processing occasions.
Description
Technical field
The present invention relates to image information safety and optical information processing technical field, more particularly to one kind combines fresnel transform
With the optical image encryption method of linear canonical transform.
Background technology
Digital picture has in the field such as politics, economic, military, education as one of current most popular multimedia form
And be widely applied.In Internet technology highly developed today, how to protect digital picture exempt from distort, bootlegging and biography
Broadcast with important practical significance.Research to image encryption technology has become one of the focus in current information security field.
Optical information processing technique with its high processing rate, high degree of parallelism, can quickly realize that convolution and related operation etc. are excellent
Point, causes the great interest (see document [1]) of people in image encryption research field.In optical image encryption technology, most
Representative is the Double random phase technology (see document [2]) of the propositions such as Javidi.Light in fresnel transform domain
Learn the extensive concern that image encryption has also obtained researcher (see document [3]).Additionally, becoming as a kind of fractional Fourier of broad sense
Change, linear canonical transform can also be used for (see document [4]) in optical image encryption.
However, during great majority are based on the optical image encryption method of Double random phase technology, when image to be encrypted
For real-valued image when, first piece of random phase masks can not make key (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.Yuan,Y.Xin,M.Liu,S.Yao,and X.Sun,An improved method to enhance
the security of double random-phaseencoding in the Fresnel domain,Opt.Laser
Technol.,2012,44:51-56
[4]A.Sahin,H.Ozaktas,D.Mendlovic,Optical implementations of
twodimensional fractional Fourier transforms and linear canonical
transformswith arbitrary parameters.Applied Optics,1998,37:2130-41
[5]A.Sinha,K.Singh,Image encryption by using fractional Fourier
transform andjigsaw transform in image bit planes.Optical Engineering,2005,
44:057001。
The content of the invention
To overcome the deficiencies in the prior art, it is contemplated that propose image encryption method, realization be effective against brute force attack,
Statistical attack and attacked by noise etc..The technical solution used in the present invention is, with reference to fresnel transform and linear canonical transform
Optical image encryption method, comprises the following steps that：
1) image encryption part：Image to be encrypted carries out fresnel transform first under the irradiation of incident illumination, then by
One piece of random phase masks modulation, then carries out first time linear canonical transform；Jing after first time linear canonical transform, then by
Two pieces of random phase masks modulation, then carry out second linear canonical transform；Jing fresnel transforms, twice linear canonical transform
And after random phase masks modulation twice, it is possible to the noise like image after being encrypted；
2) image decryption part：Using the image after encryption as decrypting process input picture, input picture carried out first
The inverse transformation of second linear canonical transform, is then modulated by the complex conjugate of second piece of random phase masks；After modulated, then enter
The inverse transformation of row first time linear canonical transform, is then modulated by the complex conjugate of first piece of random phase masks；After modulated, then
Carry out inverse fresnel transform, it is possible to the image after being decrypted.
Comprise the concrete steps that in a specific embodiment of the invention,
(1) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then after the Fresnel diffraction Jing distance for z, its mathematic(al) representation is：
Wherein, U1(x1,y1) it is the Object light wave that image information is carried before first piece of random phase mask；(x1,y1) for first
The coordinate of block random phase mask present position, (x0,y0) for the coordinate of original image present position；Wavelength of the λ for Object light wave, j is
Imaginary unit, π represent pi；Above formula is rewritten as into following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)]. (2)
Wherein, FrTλ,z[] represents fresnel transform of the distance for z；
Image Jing after fresnel transform is by first piece of random phase masks exp [j φ (x1,y1)] modulation, then carry out the
Once linear contact transformation；Jing after first time linear canonical transform, then by second piece of random phase masks
Modulation, then carries out second linear canonical transform, image U (x, y) after being encrypted：
Wherein, φ (x1,y1) be first piece of random phase mask phase function, (x1,y1) cover for first piece of random phase
The coordinate of film present position；For the phase function of second piece of random phase mask, (x2,y2) for second piece of random phase
The coordinate of position mask present position；LCTα,β,γ{ } represents two-dimensional linear contact transformation, and its form is：
Wherein, U (x, y) represents the image after conversion, U0(x0,y0) represent original image；(x, y) is residing for image after conversion
The coordinate of position, (x0,y0) for the coordinate of original image present position；α, parameter of the beta, gamma for linear canonical transform, in formula (3),
α1,β1,γ1And α2,β2,γ2There is following form respectively：
Wherein, wavelength of the λ for Object light wave, focal lengths of the f for lens, d1,d2,d3,d4Respectively linear canonical transform system
Geometric parameter；
(2) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carry out first the second sublinear canonical change
The inverse transformation changed, is then modulated by the complex conjugate of second piece of random phase masks；After modulated, then carry out the first sublinear canonical
The inverse transformation of conversion, is then modulated by the complex conjugate of first piece of random phase masks；After modulated, then carry out inverse Fresnel change
Change, the image after being decrypted
The characteristics of of the invention and beneficial effect are：
In the image encryption method that the present invention is provided, the introducing of fresnel transform causes all of random phase masks can
Play master key effect；The geometric parameter of linear canonical transform system, object light wavelength, fresnel transform distance are used as encryption and decryption mistake
Auxiliary key in journey, makes the safety of encryption method obtain further guarantee.
Description of the drawings：
The principle schematic of the optical image encryption method that Fig. 1 is provided for the present invention；
Fig. 2 encryption and decryption image comparison figures.In figure：
A () is original image to be encrypted；
B () is the image after encryption；
C () is decrypted image when all keys are correct；
The lower decrypted image comparison diagram of the different mistakes of Fig. 3.In figure：
Decrypted image when () is first piece of random phase masks mistake a；
Decrypted image when () is second piece of random phase masks mistake b；
The geometric parameter d of (c) for linear canonical transform system1Decrypted image during mistake；
The geometric parameter d of (d) for linear canonical transform system2Decrypted image during mistake；
The geometric parameter d of (e) for linear canonical transform system3Decrypted image during mistake；；
The geometric parameter d of (f) for linear canonical transform system4Decrypted image during mistake；
G () is object light wavelength X mistake, decrypted image when other keys are correct；
H () is Fresnel diffraction apart from z mistakes, decrypted image when other keys are correct；
Fig. 4 contains different noise decrypted image comparison diagrams.In figure：
A () is that the image for obtaining is decrypted from the encryption figure containing 10% Gaussian noise；
B () is that the image for obtaining is decrypted from the encryption figure containing 10% salt-pepper noise；
C () is that the image for obtaining is decrypted from the encryption figure containing 10% speckle noise；
Fig. 5 shears different proportion decrypted image comparison diagram.In figure：
A () is that the image for obtaining is decrypted from the encryption figure for cutting off 12.5%；
B () is that the image for obtaining is decrypted from the encryption figure for cutting off 25%；
C () is that the image for obtaining is decrypted from the encryption figure for cutting off 50%.
In accompanying drawing, the list of parts representated by each label is as follows：
M1：First piece of random phase masks；M2：Second piece of random phase masks；L1, L2：Lens.
Specific embodiment
The invention provides a kind of optical image encryption method of combination fresnel transform and linear canonical transform.The present invention
In the optical image encryption method of offer, the introducing of fresnel transform so that all random phase masks in encryption system are equal
Can be used as master key；The geometric parameter of linear canonical transform system, object light wavelength, fresnel transform distance all can be used as encryption systems
Auxiliary key in system.Substantial amounts of numerical simulation experiment shows that this encryption method can be effective against brute force attack, statistics and attack
Hit, and attacked by noise etc., it is described below：
1) image encryption part：Image to be encrypted carries out fresnel transform first under the irradiation of incident illumination, then by
One piece of random phase masks modulation, then carries out first time linear canonical transform；Jing after first time linear canonical transform, then by
Two pieces of random phase masks modulation, then carry out second linear canonical transform；Jing fresnel transforms, twice linear canonical transform
And after random phase masks modulation twice, it is possible to the noise like image after being encrypted.
2) image decryption part：Using the image after encryption as decrypting process input picture, input picture carried out first
The inverse transformation of second linear canonical transform, is then modulated by the complex conjugate of second piece of random phase masks；After modulated, then enter
The inverse transformation of row first time linear canonical transform, is then modulated by the complex conjugate of first piece of random phase masks；After modulated, then
Carry out inverse fresnel transform, it is possible to the image after being decrypted.
In the image encryption method that the present invention is provided, the introducing of fresnel transform causes all of random phase masks can
Play master key effect；The geometric parameter of linear canonical transform system, object light wavelength, fresnel transform distance are used as encryption and decryption mistake
Auxiliary key in journey, makes the safety of encryption method obtain further guarantee.
To make the object, technical solutions and advantages of the present invention clearer, further is made to embodiment of the present invention below
Ground is described in detail.
Embodiment 1
A kind of optical image encryption method of combination fresnel transform and linear canonical transform, its encryption principle schematic diagram is such as
Shown in Fig. 1, encryption method is made up of two parts：Image encryption part and image decryption part.
(1) image encryption part：
Before the specific image of a width is encrypted, the light wave of suitable wavelength is selected first as Object light wave, and sets suitable
Fresnel transform distance.Image to be encrypted carries out fresnel transform first under the irradiation of incident illumination, then random by first piece
Phase mask is modulated, and then carries out first time linear canonical transform；It is Jing after first time linear canonical transform then random by second piece
Phase mask is modulated, and then carries out second linear canonical transform；Jing fresnel transforms, twice linear canonical transform and twice with
After the modulation of machine phase mask, it is possible to the noise like image after being encrypted.
(2) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carry out first the second sublinear canonical change
The inverse transformation changed, is then modulated by the complex conjugate of second piece of random phase masks；After modulated, then carry out the first sublinear canonical
The inverse transformation of conversion, is then modulated by the complex conjugate of first piece of random phase masks；After modulated, then carry out inverse Fresnel change
Change, it is possible to the image after being decrypted.
In sum, in the present invention, the introducing of fresnel transform causes all of random phase masks play master key
Effect；The geometric parameter of linear canonical transform system, object light wavelength, fresnel transform distance are used as the auxiliary in encryption process
Key, makes the safety of encryption method obtain further guarantee.
Embodiment 2
The scheme in embodiment 1 is introduced in detail with reference to Fig. 1, design principle, it is described below：
A kind of optical image encryption method of combination fresnel transform and linear canonical transform, its encryption principle schematic diagram is such as
Shown in Fig. 1, encryption method is made up of two parts：Image encryption part and image decryption part.It is two-part concrete with regard to this below
Embodiment is described in detail respectively.
(1) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then after the Fresnel diffraction Jing distance for z, its mathematic(al) representation is：
Wherein, U1(x1,y1) it is the Object light wave that image information is carried before first piece of random phase mask；(x1,y1) for first
The coordinate of block random phase mask present position, (x0,y0) for the coordinate of original image present position；Wavelength of the λ for Object light wave, j is
Imaginary unit, π represent pi.
For convenience, above formula is rewritten as into following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)]. (2)
Wherein, FrTλ,z[] represents fresnel transform of the distance for z.
Image Jing after fresnel transform is by first piece of random phase masks exp [j φ (x1,y1)] modulation, then carry out the
Once linear contact transformation；Jing after first time linear canonical transform, then by second piece of random phase masks
Modulation, then carries out second linear canonical transform, image U (x, y) after being encrypted：
Wherein, φ (x1,y1) be first piece of random phase mask phase function, (x1,y1) cover for first piece of random phase
The coordinate of film present position；For the phase function of second piece of random phase mask, (x2,y2) for second piece of random phase
The coordinate of position mask present position；LCTα,β,γ{ } represents two-dimensional linear contact transformation, and its form is：
Wherein, U (x, y) represents the image after conversion, U0(x0,y0) represent original image；(x, y) is residing for image after conversion
The coordinate of position, (x0,y0) for the coordinate of original image present position；The parameter of α, β, γ for linear canonical transform.In formula (3),
α1,β1,γ1And α2,β2,γ2There is following form respectively：
Wherein, wavelength of the λ for Object light wave, focal lengths of the f for lens, d1,d2,d3,d4Respectively linear canonical transform system
Geometric parameter.
(2) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carry out first the second sublinear canonical change
The inverse transformation changed, is then modulated by the complex conjugate of second piece of random phase masks；After modulated, then carry out the first sublinear canonical
The inverse transformation of conversion, is then modulated by the complex conjugate of first piece of random phase masks；After modulated, then carry out inverse Fresnel change
Change, the image after being decrypted
In sum, in the present invention, the introducing of fresnel transform causes all of random phase masks play master key
Effect；The geometric parameter of linear canonical transform system, object light wavelength, fresnel transform distance are used as the auxiliary in encryption process
Key, makes the safety of encryption method obtain further guarantee.
Embodiment 3
Feasibility checking is carried out to the scheme in embodiment 1 and 2 with reference to specific accompanying drawing, it is described below：
After the encryption method for implementing offer using the present invention is encrypted to piece image (as shown in Fig. 2 (a)), 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 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 and decryption of degree image is successful.
Additionally, when correct other keys of some wrong cipher key, shown in decrypted result such as Fig. 3 (a) -3 (h).Thus
It can be seen that, the safety of the system can be guaranteed.
Fig. 4 (a) -4 (c) is encryption figure containing the decryption figure in the case of 10% Gaussian noise, salt-pepper noise and speckle noise
Picture.Fig. 5 (a) -5 (c) is that encryption figure lacks the decrypted image in the case of 12.5%, 25% and 50%.As can be seen here, even if encryption
To a certain extent by sound pollution or lack part information, the embodiment of the present invention remains able to decrypt certain mass image
Original image, demonstrates the feasibility of the system, meets the various needs in practical application.
To the model of each device in addition to specified otherwise is done, 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 to limit the present invention, all spirit in the present invention and
Within principle, any modification, equivalent substitution and improvements made etc. should be included within the scope of the present invention.
Claims (2)
1. a kind of optical image encryption method of combination fresnel transform and linear canonical transform, is characterized in that, concrete steps are such as
Under：
1) image encryption part：Image to be encrypted carries out fresnel transform first under the irradiation of incident illumination, then by first piece
Random phase masks are modulated, and then carry out first time linear canonical transform；Jing after first time linear canonical transform, then by second piece
Random phase masks are modulated, and then carry out second linear canonical transform；Jing fresnel transforms, twice linear canonical transform and two
After secondary random phase masks modulation, it is possible to the noise like image after being encrypted；
2) image decryption part：Using the image after encryption as decrypting process input picture, input picture carries out second first
The inverse transformation of sublinear contact transformation, is then modulated by the complex conjugate of second piece of random phase masks；After modulated, then carry out
The inverse transformation of once linear contact transformation, is then modulated by the complex conjugate of first piece of random phase masks；After modulated, then carry out
Inverse fresnel transform, it is possible to the image after being decrypted.
2. the optical image encryption method of fresnel transform and linear canonical transform, its feature are combined as claimed in claim 1
It is to comprise the concrete steps that in a specific embodiment,
(1) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then after the Fresnel diffraction Jing distance for z, its mathematic(al) representation is：
Wherein, U1(x1,y1) it is the Object light wave that image information is carried before first piece of random phase mask；(x1,y1) for first piece with
The coordinate of machine phase mask present position, (x0,y0) for the coordinate of original image present position；Wavelength of the λ for Object light wave, j is imaginary number
Unit, π represent pi；Above formula is rewritten as into following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)]. (2)
Wherein, FrTλ,z[] represents fresnel transform of the distance for z；
Image Jing after fresnel transform is by first piece of random phase masks exp [j φ (x1,y1)] modulation, then carry out for the first time
Linear canonical transform；Jing after first time linear canonical transform, then by second piece of random phase masksModulation,
Then second linear canonical transform is carried out, image U (x, y) after being encrypted：
Wherein, φ (x1,y1) be first piece of random phase mask phase function, (x1,y1) for first piece of random phase mask institute
The coordinate of place position；For the phase function of second piece of random phase mask, (x2,y2) cover for second piece of random phase
The coordinate of film present position；LCTα,β,γ{ } represents two-dimensional linear contact transformation, and its form is：
Wherein, U (x, y) represents the image after conversion, U0(x0,y0) represent original image；(x, y) is image present position after conversion
Coordinate, (x0,y0) for the coordinate of original image present position；α, parameter of the beta, gamma for linear canonical transform, in formula (3), α1,β1,
γ1And α2,β2,γ2There is following form respectively：
Wherein, wavelength of the λ for Object light wave, focal lengths of the f for lens, d1,d2,d3,d4The respectively geometry of linear canonical transform system
Parameter；
(2) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carries out second linear canonical transform first
Inverse transformation, is then modulated by the complex conjugate of second piece of random phase masks；After modulated, then carry out first time linear canonical transform
Inverse transformation, then by first piece of random phase masks complex conjugate modulate；After modulated, then inverse fresnel transform is carried out, obtained
Image to after decryption
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| CN109413299A (en) * | 2018-09-11 | 2019-03-01 | 天津大学 | Linear canonical transform and chaos Double random phase dual image encryption method |
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| US6519340B1 (en) * | 1998-03-17 | 2003-02-11 | The University Of Connecticut | Method and apparatus for encryption using partial information |
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| 叶飞，袁操今: "灰度图像的Gyrator变换加密研究", 《科技视界》 * |
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