CN106548042A - Four step broad sense phase shifts and multistep fresnel transform optical image encryption method - Google Patents
Four step broad sense phase shifts and multistep fresnel transform optical image encryption method Download PDFInfo
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Abstract
The present invention relates to image information safety and optical information processing technical field, are to be effective against known plain text attack and chosen -plain attact；Also generate from key and solve the problems, such as key management and transmission inconvenience, and safety is further ensured.The present invention, four step broad sense phase shifts and multistep fresnel transform optical image encryption method, step are as follows：1) key production portion：Two pieces of random phase masks for playing master key effect are generated by the Tinkerbell chaos systems of different chaos state modulators respectively, 2) image encryption part：Using four width holograies, encrypted image is obtained；3) image decryption part：Input picture enters row distance first for Z2Fresnel inverse transformation after modulated by the complex conjugate of second piece of chaos random phase masks, then the Fresnel inverse transformation of laggard row distance for Z, the image after being decrypted are modulated by the complex conjugate of first piece of chaos random phase masks.Present invention is mainly applied to and image information security applications.
Description
Technical field
The present invention relates to image information safety and optical information processing technical field, more particularly to it is a kind of based on four step broad sense phases
Move the optical image encryption method of digital hologram and multistep fresnel 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.The technology opens optical picture
As the frontier of encryption research, large quantities of optical encryption new methods and new technique are born (see Review literature based on the technology
[3]).It should be noted that in these methods and techniques, the encryption technology based on digital hologram can record plural letter with which
The advantages of breath, it is widely used in optical image encryption research field.In numerous Digital Holographies, based on phase shift
The digital hologram of technology can obtain high-quality reconstruction object light field, thus can be used for optical image encryption (see document [4]-
[6]).Further, since encryption system is without the need for lens, implement very convenient, the encryption method based on fresnel transform is also
To extensive research (see document [3] and [7]).
However, being based on unique step or fixed step size phase-shifted digital holographic technique, and the optical imagery of Double random phase
In encryption method, mostly there are the following problems：
1) when image to be encrypted is real-valued image, first piece of random phase mask can not make key (see document [8])；
2) random phase mask of the key for picture size, therefore, key management and transmission are inconvenient (see document [9])；
3) as the inconvenience of random phase mask updates, therefore, encryption system is easily attacked by chosen -plain attact and known-plaintext
Hit (see document [10] and [11])；
4) harshness is required to phase-shifter, and easily bring error to wavefront reconstruction etc. (see document [12]).
List of references：
[1]O.Matoba,T.Nomura,E.Perez-Cabre,M.Millan,and B.Javidi,Optical
techniques for information security,Proceedings of IEEE 2009,97:1128-1148
[2]P.Réfrégier and B.Javidi,Optical image encryption based on input
plane and 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]X.Meng,L.Cai,X.Xu,X.Yang,X.Shen,G.Dong,Y.Wang,Two step phase-
shifting interferometry and its application in image encryption,Opt.Lett.,
2006,31:1414-1416
[5]I.Yamaguchi,T.Zhang,Phase-shifting digital holography,Opt.Lett.,
1997,22:1268-1270
[6]S.Jeon,S.Gil,2-Step phase-shifting digital holographic optical
encryption and error analysis,J.Opt.Soc.Korea,2011,15:244-251
[7]S.Yuan,Y.Xin,M.Liu,S.Yao,and X.Sun,An improved method to enhance
the security of double random-phase encoding in the Fresnel domain,Opt.Laser
Technol.,2012,44:51-56
[8]W.Chen,B.Javidi and X.Chen,Advances in optical security systems,
Advances in Optics and Photonics,2014,6:120-155
[9]S.Yuan,Y.Xin,M.Liu,S.Yao,and X.Sun,An improved method to enhance
the security of double random-phase encoding in the Fresnel domain,Optics&
Laser Technology,2012,44:51-56
[10]X.Peng,H.Wei,and P.Zhang,Chosen-plaintext attack on lensless
double-random phase encoding in the Fresnel domain,Opt.Lett.,2006,31:3261-
3263
[11]U.Gopinathan,D.S.Monaghan,T.J.Naughton,and J.T.Sheridan,A known-
plaintext heuristic attack on the Fourier plane encryption
algorithm.Opt.Express,2006,14:3181-3186
[12]X.Li,C.Tang,X.Zhu,B.Li,L.Wang,and X.Yan,Image/video encryption
using single shot digital holography,Opt.Commun.,2015,342:218-223。
The content of the invention
To overcome the deficiencies in the prior art, it is contemplated that proposing image encryption method, known-plaintext can be effective against
Attack and chosen -plain attact；Additionally, also generate from key solving the problems, such as key management and transmission inconvenience.And safety
Further ensured.The technical solution used in the present invention is, four step broad sense phase shifts and multistep fresnel transform optical imagery
Encryption method, step are as follows：
1) key production portion：Play two pieces of random phase masks of master key effect respectively by different chaos state modulators
Tinkerbell chaos systems are generated, and the initial value and control parameter of Tinkerbell chaos systems is used as master key；Object light wavelength
With fresnel transform distance as auxiliary key；
2) image encryption part：Before the specific image of a width is encrypted, firstly for Tinkerbell chaos systems, setting
Suitable initial value and control parameter；The light wave of suitable wavelength is selected as incident light wave and reference light wave；The suitable phenanthrene alunite of setting
Ear diffraction distance, image to be encrypted enter the fresnel transform that row distance is Z under the irradiation of incident illumination, then mixed by first piece
Ignorant random phase masks modulation, the image Jing distances after modulation are Z1Fresnel transform after again by second piece of chaos random phase
Mask is modulated, and Jing distances are Z to the image after modulation again2Fresnel transform, in CCD planes, Jing is modulated and three luxuriant and rich with fragrance alunites twice
The Object light wave of image information is carried after ear conversion and reference light wave interferes to form the first width hologram；Then, made using phase-shifter
Reference light produce three phase shifts at any angle after, then with carry image information object light wave interference formed second and third, four width it is complete
Breath figure, using four width holograies, obtains encrypted image；
3) image decryption part：Using the image after encryption as decrypting process input picture, input picture carried out first
Distance is Z2Fresnel inverse transformation after modulated by the complex conjugate of second piece of chaos random phase masks, then enter row distance for Z1
Fresnel inverse transformation, then to be modulated laggard row distance by the complex conjugate of first piece of chaos random phase masks inverse for the Fresnel of Z
Conversion, the image after being decrypted.
In an example of the invention, comprise the following steps that：
(1) key production portion：
In encryption method, two pieces of chaos random phase masks play master key effect, Object light wave wavelength and fresnel transform distance
Play auxiliary key effect, the mathematic(al) representation of the discrete form of Tinkerbell chaos systems is：
Wherein, control parameter a=0.9, when b=-0.6013, c=2.0 and d=0.5, system is in chaos state；xnWith
ynThe respectively initial value of chaos system；xn+1And yn+1The respectively iteration output valve of chaos 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 Tinkerbell chaos systems by two groups of different chaos state modulators so as to iteration (M × N)/2 time
Afterwards, two groups of random number sequences X are obtained1={ x '1,x′2,…,x′(M×N)/2, Y1={ y '1,y′2,…,y′(M×N)/2And X2=
{x″1,x″2,…,x″(M×N)/2, Y2=y "1,y″2,…,y″(M×N)/2}；Wherein, x "1,x″2,…,x″(M×N) ,y′1,y
′2,…,y′(M×N)/2, x "1,x″2,…,x″(M×N)/2With y "1,y″2,…,y″(M×N)/2The respectively output valve of chaos system, by this
Two groups of random number sequences are integrated into form Z of two two-dimensional matrixs respectively1={ z 'm,n| m=1,2 ..., M；N=1,2 ..., N }
And Z2=z "m,n| m=1,2 ..., M；N=1,2 ..., N }, wherein z 'm,nWith z "m,nFor the element of two-dimensional matrix, m, n are matrix
The coordinate of element；Two pieces of chaos random phase masks can be then obtained, its mathematic(al) representation is respectively C1(x1,y1)=exp (j2 π
z′m,n) and C2(x2,y2)=exp (j2 π z "m,n)；Wherein, j is imaginary unit, and π is pi, (x1,y1) and (x2,y2) respectively
For the coordinate of two pieces of random phase mask present positions；
(2) 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, wavelength of the λ for Object light wave, U1(x1,y1) it is the object light that image information is carried before first piece of random phase mask
Ripple, (x1,y1) be first piece of random phase mask present position coordinate, (x0,y0) for the coordinate of input picture present position,
Above formula is rewritten as into following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)]. (3)
Wherein, FrTλ,z[] represents fresnel transform of the distance for z.
It is Z that image Jing after fresnel transform is modulated laggard row distance by first piece of chaos random phase masks1Fei Nie
Ear is converted, and it is Z that the image after conversion is modulated laggard row distance by second piece of chaos random phase masks again2Fresnel transform,
The expression formula that the Object light wave of image information is then carried at the CCD planes is：
Wherein, (x, y) is the position coordinateses at CCD planes；A0For the amplitude of Object light wave；For the phase place of Object light wave；
The Object light wave is interfered in CCD planes with reference light wave, obtains hologram：
Wherein, I1For the first width hologram, ArFor the amplitude of reference light.
Reference light is made to produce phase shift α at any angle using phase-shifter PZT1, α2And α3, and the dry of two-beam is recorded again
Relate to hologram：
Wherein, I2, I3And I4Be respectively second and third, four width holograies；
Then, utilize (5) formula to deduct (6) formula and (7) formula, obtain：
ByAnd (9) formula and (10) formula can obtain the expression-form of Object light wave at CCD planes
For：
The absolute value of above formula is the image after encryption；
(3) image decryption part：
Using U (x, y) as decrypting process input picture, input picture enters row distance first for Z2Fresnel inverse transformation
Modulated by the complex conjugate of second piece of chaos random phase masks afterwards, then enter row distance for Z1Fresnel inverse transformation, then by
The complex conjugate of one piece of chaos random phase masks modulates Fresnel inverse transformation of the laggard row distance for Z, the image after being decrypted
Wherein, FrTλ,-z{ } represents Fresnel inverse transformation of the distance for z, and * is complex conjugate operator.
The characteristics of of the invention and beneficial effect are：
In the optical image encryption method that the present invention is provided, the introducing of multistep fresnel transform causes two pieces of random phases to cover
Mould can play master key effect；The introducing of Tinkerbell chaos systems so that encryption method can be effective against known bright
Text is attacked and chosen -plain attact, and from key generation solves key management and transmission problem；Four step broad sense phase-shifted digitals
Holographic technique can be harsh with the requirement in effectively solving fixed step size or unique step four-step phase-shifting Digital Holography to phase-shifter, and
The problems such as easily bringing error to wavefront reconstruction；Object light wavelength and Fresnel diffraction distance make encryption method as auxiliary key
Safety is further guaranteed.
Description of the drawings：
The index path 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 image that () is encrypted for this method；
C () is decrypted image when all keys are correct；
Decrypted image comparison diagram under Fig. 3 difference error situations.In figure：
A () is the initial value x of the Tinkerbell chaos systems for controlling first piece of random phase masks1Mistake, other keys
Decrypted image when correct；
B () is the initial value y of the Tinkerbell chaos systems for controlling first piece of random phase masks1Mistake, other keys
Decrypted image when correct；
C () is control parameter a of the Tinkerbell chaos systems for controlling first piece of random phase masks1Mistake, other
Decrypted image when key is correct；
D () is control parameter b of the Tinkerbell chaos systems for controlling first piece of random phase masks1Mistake, other
Decrypted image when key is correct；
E () is control parameter c of the Tinkerbell chaos systems for controlling first piece of random phase masks1Mistake, other
Decrypted image when key is correct；
F () is control parameter d of the Tinkerbell chaos systems for controlling first piece of random phase masks1Mistake, other
Decrypted image when key is correct；
G () is 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；
I () is Fresnel diffraction apart from Z1Mistake, decrypted image when other keys are correct；
J () is Fresnel diffraction apart from Z2Mistake, decrypted image when other keys are correct；
Decrypted image comparison diagram under Fig. 4 difference deletion conditions.In figure：
A () is that the image for obtaining is decrypted from the encryption figure of 12.5% information of disappearance；
B () is that the image for obtaining is decrypted from the encryption figure of 25% information of disappearance；
C () is that the image for obtaining is decrypted from the encryption figure of 50% information of disappearance；
Fig. 5 difference noise image decryption 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；
In accompanying drawing, the list of parts representated by each label is as follows：
M1：Reflecting mirror； SF：Spatial filter；
L0：Lens； L：Lens；
BS1：Beam splitter； M2：Reflecting mirror；
CRPM1：Chaos random phase masks； CRPM2：Chaos random phase masks；
BS2：Beam splitter； PZT：Phase-shifter；
Z：Fresnel diffraction distance； Z1：Fresnel diffraction distance；
Z2：Fresnel diffraction distance； L1：Lens；
L2：Lens； D：Diaphragm；
1：Helium neon laser； 2：Computer；
3：CCD camera.
Specific embodiment
The invention provides a kind of optical imagery of and multistep fresnel transform holographic based on four step broad sense phase-shifted digitals adds
Decryption method.Two pieces of random phase masks of master key effect are generated by using Tinkerbell chaos systems so that this adds
Decryption method can be effective against known plain text attack and chosen -plain attact；Additionally, also generate from key solving key pipe
Reason and the problem of transmission inconvenience.The introducing of multistep fresnel transform so that two pieces of random phase masks all may be used in this encryption method
Using as the master key in encryption process.Four step broad sense phase-shifted digital holographic techniques can be with effectively solving fixed step size or unique step
In four-step phase-shifting Digital Holography, requirement to phase-shifter is harsh, and the problems such as easily bring error to wavefront reconstruction.Additionally, thing
Optical wavelength and Fresnel diffraction distance can be used as the auxiliary key in encryption process so that the safety of this encryption method is obtained
To further guarantee.It is described below：
1) key production portion：Play two pieces of random phase masks of master key effect respectively by different chaos state modulators
Tinkerbell chaos systems are generated, and the initial value and control parameter of Tinkerbell chaos systems is used as master key；Object light wavelength
With fresnel transform distance as auxiliary key.As in encryption process, key updating is convenient, therefore, this encryption method can be with
It is effective against known plain text attack and chosen -plain attact；Additionally, key management and transmission are also more convenient.
2) image encryption part：Before the specific image of a width is encrypted, firstly for Tinkerbell chaos systems, setting
Suitable initial value and control parameter；The light wave of suitable wavelength is selected as incident light wave and reference light wave；The suitable phenanthrene alunite of setting
Ear diffraction distance.Image to be encrypted enters the fresnel transform that row distance is Z under the irradiation of incident illumination, then mixed by first piece
Ignorant random phase masks modulation, the image Jing distances after modulation are Z1Fresnel transform after again by second piece of chaos random phase
Mask is modulated, and Jing distances are Z to the image after modulation again2Fresnel transform.In CCD planes, Jing is modulated and three luxuriant and rich with fragrance alunites twice
The Object light wave of image information is carried after ear conversion and reference light wave interferes to form the first width hologram；Then, made using phase-shifter
Reference light produce three phase shifts at any angle after, then with carry image information object light wave interference formed second and third, four width it is complete
Breath figure.Using four width holograies, it is possible to obtain encrypted image.
3) image decryption part：Using the image after encryption as decrypting process input picture, input picture carried out first
Distance is Z2Fresnel inverse transformation after modulated by the complex conjugate of second piece of chaos random phase masks, then enter row distance for Z1
Fresnel inverse transformation, then to be modulated laggard row distance by the complex conjugate of first piece of chaos random phase masks inverse for the Fresnel of Z
Conversion, it is possible to the image after being decrypted.
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 and multistep fresnel transform holographic based on four step broad sense phase-shifted digitals, its light path
Figure is as shown in figure 1, encryption method is made up of three parts：Key production portion, image encryption part and image decryption part.
Referring to Fig. 1, wherein key production portion includes the random phase of two pieces of chaos generated by Tinkerbell chaos systems
Bit mask CRPM1And CRPM2；Image encryption part and image decryption part include：Lens (L, L0, L1, L2), reflecting mirror (M1,
M2), spatial filter (SF), beam splitter (BS1, BS2), phase-shifter (PZT), laser instrument, CCD camera, computer etc..
(1) key production portion：
In the encryption method that the present invention is provided, two pieces of random phase masks keys are respectively by different chaos state modulators
Tinkerbell chaos systems are generated.The initial value and control parameter of Tinkerbell chaos systems can substitute two pieces of random phases
Mask is used as the master key in encryption process.Additionally, Object light wave wavelength and fresnel transform distance can be used as encryption and decryption mistakes
Auxiliary key in journey.
(2) image encryption part：
Before the specific image of a width is encrypted, firstly for Tinkerbell chaos systems, suitable initial value and control are set
Parameter processed；The light wave of suitable wavelength is selected as incident light wave and reference light wave；Set suitable Fresnel diffraction distance.It is to be added
Close image enters the fresnel transform that row distance is Z under the irradiation of incident illumination, then by first piece of chaos random phase masks
Modulation, the image Jing distances after modulation are Z1Fresnel transform after modulated by second piece of chaos random phase masks again, modulation
Jing distances are Z to image afterwards again2Fresnel transform.In CCD planes, Jing modulating twice and carrying figure after three fresnel transforms
As the Object light wave of information interferes to form the first width hologram with reference light wave；Then, reference light is made to produce three times using phase-shifter
At any angle after phase shift, then with carry image information object light wave interference formed second and third, four width holograies.Using four width
Hologram, it is possible to obtain encrypted image.
(3) image decryption part：
Using the image after encryption as decrypting process input picture, input picture enters row distance first for Z2Fresnel
Modulated by the complex conjugate of second piece of chaos random phase masks after inverse transformation, then enter row distance for Z1Fresnel inverse transformation,
Fresnel inverse transformation of the laggard row distance for Z is modulated by the complex conjugate of first piece of chaos random phase masks again, it is possible to obtain
Image after decryption.
In sum, the introducing of multistep fresnel transform causes two pieces of random phase masks play master key effect；
The introducing of Tinkerbell chaos systems so that encryption method can be effective against known plain text attack and chosen -plain attact,
And key management and transmission problem are solved from key generation；Four step broad sense phase-shifted digital holographic techniques can be fixed with effectively solving
Requirement in step-length or unique step four-step phase-shifting Digital Holography to phase-shifter is harsh, and easily brings error etc. to wavefront reconstruction
Problem；Object light wavelength and Fresnel diffraction distance make the safety of encryption method further be guaranteed as auxiliary key.
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 and multistep fresnel transform holographic based on four step broad sense phase-shifted digitals, which adds solution
The corresponding light path of close process is as shown in figure 1, encryption method is made up of three parts：Key production portion, image encryption part and figure
As decryption portion.Below the specific embodiment of this three part is described in detail respectively.
(1) key production portion：
In encryption method, two pieces of chaos random phase masks play master key effect, Object light wave wavelength and fresnel transform distance
Play auxiliary key effect.Carry out with regard to how to generate this two pieces of chaos random phase masks using Tinkerbell chaos systems below
It is discussed in detail.
The mathematic(al) representation of the discrete form of Tinkerbell chaos systems is：
Wherein, control parameter a=0.9, when b=-0.6013, c=2.0 and d=0.5, system is in chaos state；xnWith
ynThe respectively initial value of chaos system；xn+1And yn+1The respectively iteration output valve of chaos system.It should be noted that when above-mentioned
When control parameter takes other values, system is likely in chaos state.
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 Tinkerbell chaos systems by two groups of different chaos state modulators so as to iteration (M × N)/2 time
Afterwards, two groups of random number sequences X are obtained1={ x '1,x′2,…,x′(M×N)/2, Y1={ y '1,y′2,…,y′(M×N)/2And X2=
{x″1,x″2,…,x″(M×N)/2, Y2=y "1,y″2,…,y″(M×N)/2}；Wherein, x "1,x″2,…,x″(M×N),y′1,y′2,…,
y′(M×N)/2, x "1,x″2,…,x″(M×N)/2With y "1,y″2,…,y″(M×N)/2The respectively output valve of chaos system.By this two groups
Random number sequence is integrated into form Z of two two-dimensional matrixs respectively1={ z 'm,n| m=1,2 ..., M；N=1,2 ..., N } and Z2=
{z″m,n| m=1,2 ..., M；N=1,2 ..., N }, wherein z 'm,nWith z "m,nFor the element of two-dimensional matrix, m, n are matrix element
Coordinate；Two pieces of chaos random phase masks can be then obtained, its mathematic(al) representation is respectively C1(x1,y1)=exp (j2 π z 'm,n)
And C2(x2,y2)=exp (j2 π z "m,n)；Wherein, j is imaginary unit, and π is pi, (x1,y1) and (x2,y2) it is respectively two pieces
The coordinate of random phase mask present position.As chaos random phase mask is come by the initial value and control parameter of chaos system
Control, therefore, the master key of the initial value and control parameter of chaos system as encryption system.Due to master key and auxiliary key
All it is some numerals, therefore, managing and transmit these numerals will become very convenient；Additionally, updating these in encryption process
Numeral will also become very convenient.
(2) 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, wavelength of the λ for Object light wave, U1(x1,y1) it is the object light that image information is carried before first piece of random phase mask
Ripple, (x1,y1) be first piece of random phase mask present position coordinate, (x0,y0) for the coordinate of input picture present position.
For convenience, above formula is rewritten as into following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)]. (3)
Wherein, FrTλ,z[] represents fresnel transform of the distance for z.
It is Z that image Jing after fresnel transform is modulated laggard row distance by first piece of chaos random phase masks1Fei Nie
Ear is converted, and it is Z that the image after conversion is modulated laggard row distance by second piece of chaos random phase masks again2Fresnel transform,
The expression formula that the Object light wave of image information is then carried at the CCD planes is：
Wherein, (x, y) is the position coordinateses at CCD planes；A0For the amplitude of Object light wave；For the phase place of Object light wave.
The Object light wave is interfered in CCD planes with reference light wave, obtains hologram：
Wherein, I1For the first width hologram, ArFor the amplitude of reference light.
Reference light is made to produce phase shift α at any angle using PZT (phase-shifter)1, α2And α3, and two-beam is recorded again
Interfere hologram：
Wherein, I2, I3And I4Be respectively second and third, four width holograies.
Then, utilize (5) formula to deduct (6) formula and (7) formula, obtain：
ByAnd (9) formula and (10) formula can obtain the expression-form of Object light wave at CCD planes
For：
The absolute value of above formula is the image after encryption.
(3) image decryption part：
Using U (x, y) as decrypting process input picture, input picture enters row distance first for Z2Fresnel inverse transformation
Modulated by the complex conjugate of second piece of chaos random phase masks afterwards, then enter row distance for Z1Fresnel inverse transformation, then by
The complex conjugate of one piece of chaos random phase masks modulates Fresnel inverse transformation of the laggard row distance for Z, the image after being decrypted
Wherein, FrTλ,-z{ } represents Fresnel inverse transformation of the distance for z, and * is complex conjugate operator.
In sum, the introducing of multistep fresnel transform causes two pieces of random phase masks play master key effect；
The introducing of Tinkerbell chaos systems so that encryption method can be effective against known plain text attack and chosen -plain attact,
And key management and transmission problem are solved from key generation；Four step broad sense phase-shifted digital holographic techniques can be fixed with effectively solving
Requirement in step-length or unique step four-step phase-shifting Digital Holography to phase-shifter is harsh, and easily brings error etc. to wavefront reconstruction
Problem；Object light wavelength and Fresnel diffraction distance make the safety of encryption method further be guaranteed as auxiliary key.
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 very good to be reduced.Illustrate using the system pair
The encryption and decryption of gray level image is successful.
Additionally, when correct other keys of some wrong cipher key, shown in decrypted result such as Fig. 3 (a) -3 (j).Thus
It can be seen that, the safety of the system can be guaranteed.
Fig. 4 (a) -4 (c) is the decrypted image under encryption figure 12.5%, 25% and 50% information state of disappearance.Fig. 5 (a) -5
C () is encryption figure containing the decrypted image in the case of 10% Gaussian noise, salt-pepper noise and speckle noise.As can be seen here, even if
Encrypted image lacks a part of information or to a certain extent by sound pollution, and the embodiment of the present invention remains able to decrypt necessarily
The original image of quality, 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 phase shift of four steps broad sense and multistep fresnel transform optical image encryption method, is characterized in that,
1) key production portion：Play two pieces of random phase masks of master key effect respectively by different chaos state modulators
Tinkerbell chaos systems are generated, and the initial value and control parameter of Tinkerbell chaos systems is used as master key；Object light wavelength
With fresnel transform distance as auxiliary key；
2) image encryption part：Before the specific image of a width is encrypted, firstly for Tinkerbell chaos systems, setting is suitable
Initial value and control parameter；The light wave of suitable wavelength is selected as incident light wave and reference light wave；Set suitable Fresnel to spread out
Penetrate distance, image to be encrypted enters the fresnel transform that row distance is Z under the irradiation of incident illumination, then by first piece of chaos with
Machine phase mask is modulated, and the image Jing distances after modulation are Z1Fresnel transform after again by second piece of chaos random phase masks
Modulation, Jing distances are Z to the image after modulation again2Fresnel transform, in CCD planes, Jing is modulated twice and three Fresnel become
The Object light wave of image information is carried after changing and reference light wave interferes to form the first width hologram；Then, reference is made using phase-shifter
After light produces three phase shifts at any angle, then with the object light wave interference for carrying image information formed second and third, four width it is holographic
Figure, using four width holograies, obtains encrypted image；
3) image decryption part：Using the image after encryption as decrypting process input picture, input picture enters row distance first
For Z2Fresnel inverse transformation after modulated by the complex conjugate of second piece of chaos random phase masks, then enter row distance for Z1Phenanthrene
Alunite ear inverse transformation, then Fresnel inverse transformation of the laggard row distance for Z is modulated by the complex conjugate of first piece of chaos random phase masks,
Image after being decrypted.
2. four steps broad sense as claimed in claim 1 phase shift and multistep fresnel transform optical image encryption method, is characterized in that,
In one example, comprise the following steps that：
(1) key production portion：
In encryption method, two pieces of chaos random phase masks play master key effect, and Object light wave wavelength and fresnel transform distance are auxiliary
Key is helped to act on, the mathematic(al) representation of the discrete form of Tinkerbell chaos systems is：
Wherein, control parameter a=0.9, when b=-0.6013, c=2.0 and d=0.5, system is in chaos state；xnAnd ynPoint
Not Wei chaos system initial value；xn+1And yn+1The respectively iteration output valve of chaos system；
The size for assuming 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 Tinkerbell chaos systems by two groups of different chaos state modulators so as to after iteration (M × N)/2 time, obtain
Two groups of random number sequences X1={ x '1,x′2,…,x′(M×N), Y1={ y '1,y′2,…,y′(M×N)/2And X2=x "1,x
″2,…,x″(M×N)/2, Y2=y "1,y″2,…,y″(M×N)/2}；Wherein, x '1,x′2,…,x′(M×N)/2, y '1,y′2,…,
y′(M×N)/2, x "1,x″2,…,x″(M×N)/2With y "1,y″2,…,y″(M×N)/2The respectively output valve of chaos system, by this two groups
Random number sequence is integrated into form Z of two two-dimensional matrixs respectively1={ z 'm,n| m=1,2 ..., M；N=1,2 ..., N } and Z2=
{z″m,n| m=1,2 ..., M；N=1,2 ..., N }, wherein z 'm,nWith z "m,nFor the element of two-dimensional matrix, m, n are matrix element
Coordinate；Two pieces of chaos random phase masks can be then obtained, its mathematic(al) representation is respectively C1(x1,y1)=exp (j2 π z 'm,n)
And C2(x2,y2)=exp (j2 π z "m,n)；Wherein, j is imaginary unit, and π is pi, (x1,y1) and (x2,y2) it is respectively two pieces
The coordinate of random phase mask present position；
(2) 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, wavelength of the λ for Object light wave, U1(x1,y1) it is the Object light wave that image information is carried before first piece of random phase mask,
(x1,y1) be first piece of random phase mask present position coordinate, (x0,y0) for the coordinate of input picture present position, will be upper
Formula is rewritten as following form：
U1(x1,y1)=FrTλ,z[U0(x0,y0)]. (3)
Wherein, FrTλ,z[] represents fresnel transform of the distance for z.
It is Z that image Jing after fresnel transform is modulated laggard row distance by first piece of chaos random phase masks1Fresnel become
Change, it is Z that the image after conversion is modulated laggard row distance by second piece of chaos random phase masks again2Fresnel transform, then exist
At CCD planes, the expression formula of the Object light wave of carrying image information is：
Wherein, (x, y) is the position coordinateses at CCD planes；A0For the amplitude of Object light wave；For the phase place of Object light wave；
The Object light wave is interfered in CCD planes with reference light wave, obtains hologram：
Wherein, I1For the first width hologram, ArFor the amplitude of reference light.
Reference light is made to produce phase shift α at any angle using phase-shifter PZT1, α2And α3, and it is complete to record the interference of two-beam again
Breath figure：
Wherein, I2, I3And I4Be respectively second and third, four width holograies；
Then, utilize (5) formula to deduct (6) formula and (7) formula, obtain：
ByAnd the expression-form that (9) formula can obtain Object light wave at CCD planes with (10) formula is：
The absolute value of above formula is the image after encryption；
(3) image decryption part：
Using U (x, y) as decrypting process input picture, input picture enters row distance first for Z2Fresnel inverse transformation after by
The complex conjugate modulation of two pieces of chaos random phase masks, then enters row distance for Z1Fresnel inverse transformation, then by first piece of chaos
The complex conjugate of random phase masks modulates Fresnel inverse transformation of the laggard row distance for Z, the image after being decrypted
Wherein,Fresnel inverse transformation of the distance for z is represented, * is complex conjugate operator.
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