CN106529311A - Three-step generalized phase-shifting and cascade fractional Fourier transform optical image encryption method - Google Patents

Three-step generalized phase-shifting and cascade fractional Fourier transform optical image encryption method Download PDF

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CN106529311A
CN106529311A CN201610945702.6A CN201610945702A CN106529311A CN 106529311 A CN106529311 A CN 106529311A CN 201610945702 A CN201610945702 A CN 201610945702A CN 106529311 A CN106529311 A CN 106529311A
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image
chaos
light wave
random phase
fourier transform
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唐晨
苏永钢
李碧原
谷帆
程佳佳
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Tianjin University
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Tianjin University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/60—Protecting data
    • G06F21/602—Providing cryptographic facilities or services
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use

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Abstract

The invention relates to the technical field of image information security and optical information processing, and provides an optical image encryption method capable of effectively resisting known plaintext attacks and selecting plaintext attacks. The problems of key management and transmission inconvenience are solved. A three-step generalized phase-shifting and cascade fractional Fourier transform optical image encryption method comprises the following concrete steps of (1) a key generation part: two random phase masks achieving the effect of main keys are respectively generated by Duffing chaotic systems controlled by different chaotic parameters; (2) an image encryption part: an image to be encrypted is subjected to Fresnel transform under the irradiation of incident light, and is then modulated by the first chaotic random phase mask; and the modulated image is subjected to fractional Fourier transform with the order being a1 and is then modulated by the second chaotic random phase mask; and (3) an image decryption part: the decrypted image is obtained. The optical image encryption method is mainly applied to image information security and optical information processing occasions.

Description

Three step broad sense phase shifts and cascade fractional fourier transform optical image encryption method
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 three step broad sense phases Move the optical image encryption method of digital hologram and cascade fractional fourier 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 technology 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 extra auxiliary key can be provided, the encryption method based on fractional fourier transform has also been obtained extensively 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]).
Bibliography：
[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]X.Meng,L.Cai,X.Xu,X.Yang,X.Shen,G.Dong,Y.Wang,Twostep 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 encryptionand error analysis,J.Opt.Soc.Korea,2011,15:244-251
[7]Unnikrishnan G,Joseph J,Singh K.Optical encryption by double- randomphase encoding in the fractional Fourier domain.Optics Letters,2000,25: 887-889
[8]W.Chen,B.Javidiand 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-phaseencoding 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-randomphase 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- plaintextheuristic 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 to be effective against known plain text attack and selecting in plain text The optical image encryption method of attack；Additionally, also generate from key solving the problems, such as key management and transmission inconvenience.Fei Nie The introducing of ear conversion so that two pieces of random phase masks can serve as the master key in encryption process in this encryption method. Three step broad sense phase-shifted digital holographic techniques can with three step phase-shifted digital holographic technique of effectively solving fixed step size or unique step to phase The requirement for moving device is harsh, and the problems such as easily bring error to wavefront reconstruction.Additionally, object light wavelength, Fresel diffraction distance and Fractional fourier transform order can serve as the auxiliary key in encryption process so that the security of this encryption method is obtained It is further to ensure.The technical solution used in the present invention is, three step broad sense phase shifts and cascade fractional fourier transform optical imagery Encryption method, comprises the following steps that：
1) key production portion：Play two pieces of random phase masks of master key effect respectively by different chaos state modulators Duffing chaos systems are generated, and the initial value and control parameter of Duffing chaos systems is used as master key；Object light wavelength, Fresnel Transformed distances and fractional fourier transform order are used as auxiliary key；
2) image encryption part：Before the specific image of a width is encrypted, firstly for Duffing chaos systems, setting is closed 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 Diffraction distance, image to be encrypted carry out fresnel transform under the irradiation of incident light, then by first piece of chaos random phase Mask is modulated, and the image Jing orders after modulation are a1Fractional fourier transform after adjusted by second piece of chaos random phase masks again System, Jing orders are a to the image after modulation again2Fractional fourier transform, in CCD planes, Jing after modulating twice and convert carry The Object light wave of image information interferes to form the first width hologram with reference light wave；Then, reference light is made to produce two using phase-shifter After secondary phase shift at any angle, then the second width and the 3rd width hologram are formed with the object light wave interference for carrying image information, utilize Three width holograms, obtain encrypted image.
3) image decryption part：Using the image after encryption as decrypting process input picture, input picture carried out first Order is a2Fractional Inverse Fourier Transform after by second piece of chaos random phase masks complex conjugate modulate, then carry out order For a1Fractional Inverse Fourier Transform, then by first piece of chaos random phase masks complex conjugate modulation after carry out Fresnel inversion Change, the image after being decrypted.
In an instantiation of the invention, comprise the following steps that：(1) key production portion：Duffing chaos systems from The mathematic(al) representation of scattered form is：
Wherein, control parameter a=2.75 and during b=0.2, Duffing systems are in chaos state；xnAnd ynRespectively mix The initial value of ignorant 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 Duffing chaos systems by two groups of different chaos state modulators so as to after iteration (M × N)/2 time, obtain To two groups of random number sequences X1={ 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)/,2y′1,y′0,…, y′(M×N)/2, x "1, x "2..., x "(M×N)/2With y "1,y″2,…,y″(M×N)/2It is for the output valve of chaos system, random by this two groups 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 Position coordinates, then can obtain two pieces of chaos random phase masks, and 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, (x1,y1) and (x2,y2) it is respectively the position of two pieces of random phase masks Coordinate is put, j is imaginary unit, and π is pi；
(2) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then after the Fresel 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；(x0,y0) for artwork As the coordinate of present position；Wavelength of the λ for Object light wave.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 a that image Jing after fresnel transform is modulated laggard row order time by first piece of chaos random phase masks1Fraction Fourier transformation, the image after conversion are a laggard row order time is modulated by second piece of chaos random phase masks2Fraction Fu in Leaf transformation, then the expression formula that the Object light wave of image information is carried at the CCD planes is：
Wherein, A0For the amplitude components of Object light wave,For the phase bit position of Object light wave, (x, y) is the position at CCD planes Coordinate, FrFTa{ } represents fractional fourier transform of the order for a, and its form is：
Wherein, Ua(xa,ya) image after conversion is represented, U (x, y) represents original image；(xa,ya) represent image after converting Coordinate, (x, y) represent the coordinate of original image；Sgn () is sign function；
The Object light wave is interfered in CCD planes with reference light wave, obtains hologram：
Wherein, I1For the first width hologram, ArRepresent reference light wave；
Reference light is made to produce phase shift α at any angle using PZT (phase-shifter)1And α2, and the interference of two-beam is recorded again Hologram：
Wherein, I2And I3It is respectively second and third width hologram；
Then, utilize (5) formula to deduct (6) formula and (7) formula, obtain：
Simultaneous (8) formula and (9) formula, can obtain the real part and imaginary part of Object light wave complex amplitude：
ByThe expression-form that Object light wave at CCD planes can be obtained 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 carries out order first for a2Fractional Fourier it is inverse Modulated by the complex conjugate of second piece of chaos random phase masks after conversion, order is then carried out for a1Fractional Fourier inversion Change, then Fresnel inverse transformation is carried out after being modulated by the complex conjugate of first piece of chaos random phase masks, the image after being decrypted
Wherein, * 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 fresnel transform causes two pieces of random phase masks all Master key effect can be played；The introducing of Duffing 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；Three step broad sense phase-shifted digital holographic techniques Can be harsh with the requirement in three step phase-shifted digital holographic technique of effectively solving fixed step size or unique step to phase-shifter, and easily give wavefront The problems such as reproduction brings error；Object light wavelength, Fresel diffraction distance and fractional fourier transform order are made as auxiliary key The security of encryption method 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 different situations.In figure：
A () is the initial value x of the Duffing chaos systems for controlling first piece of random phase masks1Mistake, other keys are just Decrypted image when really；
B () is the initial value y of the Duffing chaos systems for controlling first piece of random phase masks1Mistake, other keys are just Decrypted image when really；
C () is control parameter a of the Duffing chaos systems for controlling first piece of random phase masks1Mistake, other keys Decrypted image when correct；
D () is control parameter b of the Duffing chaos systems for controlling first piece of random phase masks1Mistake, other keys Decrypted image when correct；
E () is wavelength X mistake, decrypted image when other keys are correct；
F () is Fresel diffraction apart from Z mistakes, decrypted image when other keys are correct；
G () is fractional fourier transform order a1Mistake, decrypted image when other keys are correct；
H () is fractional fourier transform order a2Mistake, decrypted image when other keys are correct；
Fig. 4 is disappearance different proportion image decryption image comparison figure.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；
Decrypted image comparison diagram under Fig. 5 difference noises.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：Speculum；SF：Spatial filter；
L0：Lens；L：Lens；
BS1：Beam splitter；M2：Speculum；
CRPM1：Chaos random phase masks；CRPM2：Chaos random phase masks；
BS2：Beam splitter；PZT：Phase-shifter；
Z：Fresel diffraction distance；L1：Lens；
L2：Lens；L3：Lens；
L4：Lens；L5：Lens；
D：Diaphragm；1：He-Ne laser；
2：Computer；3：CCD camera.
Specific embodiment
The invention provides a kind of optical picture of and cascade fractional fourier transform holographic based on three step broad sense phase-shifted digitals As encryption method.Two pieces of random phase masks of master key effect are generated by using Duffing 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 fresnel transform so that two pieces of random phase masks can be made in this encryption method For the master key in encryption process.Three step broad sense phase-shifted digital holographic techniques can be with three step of effectively solving fixed step size or unique step In phase-shifted digital holographic technique, requirement to phase-shifter is harsh, and the problems such as easily bring error to wavefront reconstruction.Additionally, Object light wave Long, Fresel diffraction distance and fractional fourier transform order can serve as the auxiliary key in encryption process so that The security of this encryption method is further ensured.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 Duffing chaos systems are generated, and the initial value and control parameter of Duffing chaos systems is used as master key；Object light wavelength, Fresnel Transformed distances and fractional fourier transform order are used as auxiliary key.As in encryption process, key updating is convenient, therefore, this Encryption method can be 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 Duffing chaos systems, setting is closed 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 Diffraction distance.Image to be encrypted carries out fresnel transform under the irradiation of incident light, then by first piece of chaos random phase Mask is modulated, and the image Jing orders after modulation are a1Fractional fourier transform after adjusted by second piece of chaos random phase masks again System, Jing orders are a to the image after modulation again2Fractional fourier transform.In CCD planes, carry Jing after modulating twice and convert The Object light wave of image information interferes to form the first width hologram with reference light wave；Then, reference light is made to produce two using phase-shifter After secondary phase shift at any angle, then the second width and the 3rd width hologram are formed with the object light wave interference for carrying image information.Utilize Three width holograms, 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 Order is a2Fractional Inverse Fourier Transform after by second piece of chaos random phase masks complex conjugate modulate, then carry out order For a1Fractional Inverse Fourier Transform, then by first piece of chaos random phase masks complex conjugate modulation after carry out Fresnel inversion Change, 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 cascade fractional fourier transform holographic based on three step broad sense phase-shifted digitals, its Index path 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 being covered by two pieces of chaos random phases that Duffing chaos systems are generated Mould CRPM1And CRPM2；Image encryption part and image decryption part include：Lens (L, L0, L1, L2, L3, L4, L5), speculum (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 Duffing chaos systems are generated.The initial value and control parameter of Duffing chaos systems can substitute two pieces of random phase masks and make For the master key in encryption process.Additionally, Object light wave wavelength, fresnel transform distance and fractional fourier transform order can be with As the auxiliary key in encryption process.
(2) image encryption part：
Before the specific image of a width is encrypted, firstly for Duffing chaos systems, suitable initial value and control ginseng are set Number；The light wave of suitable wavelength is selected as incident light wave and reference light wave；Set suitable Fresel diffraction distance.To be encrypted Image carries out fresnel transform under the irradiation of incident light, is then modulated by first piece of chaos random phase masks, after modulation Image Jing orders are a1Fractional fourier transform after modulated by second piece of chaos random phase masks again, the image after modulation is again Jing orders are a2Fractional fourier transform.In CCD planes, carry Jing after modulating twice and convert the Object light wave of image information with Reference light wave interferes to form the first width hologram；Then, reference light is made to produce after phase shift at any angle twice using phase-shifter, The second width and the 3rd width hologram are formed with the object light wave interference for carrying image information again.Using three width holograms, it is possible to To encrypted image.
(3) image decryption part：
Using the image after encryption as decrypting process input picture, input picture carries out order first for a2Fraction Fu In modulated by the complex conjugate of second piece of chaos random phase masks after leaf inverse transformation, then carry out order for a1Fractional Fourier Inverse transformation, then Fresnel inverse transformation is carried out after being modulated by the complex conjugate of first piece of chaos random phase masks, it is possible to solved Image after close.
In sum, the introducing of fresnel transform causes two pieces of random phase masks play master key effect； The introducing of Duffing chaos systems so that encryption method can be effective against known plain text attack and chosen -plain attact, and from Key solves key management and transmission problem on generating；Three step broad sense phase-shifted digital holographic techniques can be with effectively solving fixed step size Or the requirement in three step phase-shifted digital holographic technique of unique step to phase-shifter is harsh, and easily error etc. is brought to ask to wavefront reconstruction Topic；Object light wavelength, Fresel diffraction distance and fractional fourier transform order make the security of encryption method as auxiliary key Further it is guaranteed.
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 cascade fractional fourier transform holographic based on three step broad sense phase-shifted digitals, its The corresponding light path of encryption process is as shown in figure 1, encryption method is made up of three parts：Key production portion, image encryption part With image decryption part.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, fresnel transform distance And fractional fourier transform order plays auxiliary key effect.Mix with regard to how to generate this two pieces using Duffing chaos systems below Ignorant random phase mask describes in detail.
The mathematic(al) representation of the discrete form of Duffing chaos systems is：
Wherein, control parameter a=2.75 and during b=0.2, Duffing systems are in chaos state；xnAnd ynRespectively mix The initial value of ignorant 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 Duffing chaos systems by two groups of different chaos state modulators so as to after iteration (M × N)/2 time, obtain To two groups of random number sequences X1={ 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)/,2y′1,y′2,…, y′(M×N)/2, x "1,x″2,…,x″(M×N)/2With y "1,y″2,…,y″(M×N)/2For the output valve of chaos system.It is random by this two groups 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 Position coordinates.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, (x1,y1) and (x2,y2) it is respectively the position of two pieces of random phase masks Coordinate is put, j is imaginary unit, and π is pi.As chaos random phase mask is by the initial value and control parameter of chaos system Come what is controlled, therefore, the master key of the initial value and control parameter of chaos system as encryption system.Due to master key and auxiliary it is close Key is all some numerals, therefore, managing and transmit these numerals will become very convenient；Additionally, updating this in encryption process A little numerals will also become very convenient.
(2) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then after the Fresel 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；(x0,y0) for artwork As the coordinate of present position；Wavelength of the λ for Object light wave.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 a that image Jing after fresnel transform is modulated laggard row order time by first piece of chaos random phase masks1Fraction Fourier transformation, the image after conversion are a laggard row order time is modulated by second piece of chaos random phase masks2Fraction Fu in Leaf transformation, then the expression formula that the Object light wave of image information is carried at the CCD planes is：
Wherein, A0For the amplitude components of Object light wave,For the phase bit position of Object light wave, (x, y) is the position at CCD planes Coordinate, FrFTa{ } represents fractional fourier transform of the order for a, and its form is：
Wherein, Ua(xa,ya) image after conversion is represented, U (x, y) represents original image；(xa,ya) represent image after converting Coordinate, (x, y) represent the coordinate of original image；Sgn () is sign function.
The Object light wave is interfered in CCD planes with reference light wave, obtains hologram：
Wherein, I1For the first width hologram, ArRepresent reference light wave.
Reference light is made to produce phase shift α at any angle using PZT (phase-shifter)1And α2, and the interference of two-beam is recorded again Hologram：
Wherein, I2And I3It is respectively second and third width hologram.
Then, utilize (5) formula to deduct (6) formula and (7) formula, obtain：
Simultaneous (8) formula and (9) formula, can obtain the real part and imaginary part of Object light wave complex amplitude：
ByThe expression-form that Object light wave at CCD planes can be obtained 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 carries out order first for a2Fractional Fourier it is inverse Modulated by the complex conjugate of second piece of chaos random phase masks after conversion, order is then carried out for a1Fractional Fourier inversion Change, then Fresnel inverse transformation is carried out after being modulated by the complex conjugate of first piece of chaos random phase masks, the image after being decrypted
Wherein, * is complex conjugate operator.
In sum, the introducing of fresnel transform causes two pieces of random phase masks play master key effect； The introducing of Duffing chaos systems so that encryption method can be effective against known plain text attack and chosen -plain attact, and from Key solves key management and transmission problem on generating；Three step broad sense phase-shifted digital holographic techniques can be with effectively solving fixed step size Or the requirement in three step phase-shifted digital holographic technique of unique step to phase-shifter is harsh, and easily error etc. is brought to ask to wavefront reconstruction Topic；Object light wavelength, Fresel diffraction distance and fractional fourier transform order make the security of encryption method as auxiliary key Further it is guaranteed.
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 (h).Thus It can be seen that, the security 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 noise 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 three steps broad sense and cascade fractional fourier transform optical image encryption method, is characterized in that, concrete steps It is as follows：
1) key production portion：Play two pieces of random phase masks of master key effect respectively by different chaos state modulators Duffing chaos systems are generated, and the initial value and control parameter of Duffing chaos systems is used as master key；Object light wavelength, Fresnel Transformed distances and fractional fourier transform order are used as auxiliary key；
2) image encryption part：Before the specific image of a width is encrypted, firstly for Duffing 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 Fresel diffraction Distance, image to be encrypted carry out fresnel transform under the irradiation of incident light, then by first piece of chaos random phase masks Modulation, the image Jing orders after modulation are a1Fractional fourier transform after modulated by second piece of chaos random phase masks again, Jing orders are a to image after modulation again2Fractional fourier transform, in CCD planes, carry image Jing after modulating twice and convert The Object light wave of information interferes to form the first width hologram with reference light wave；Then, produce reference light using phase-shifter to appoint twice After the phase shift of meaning angle, then the second width and the 3rd width hologram are formed with the object light wave interference for carrying image information, using three width Hologram, obtains encrypted image；
3) image decryption part：Using the image after encryption as decrypting process input picture, input picture carries out order first For a2Fractional Inverse Fourier Transform after modulated by the complex conjugate of second piece of chaos random phase masks, then carry out order for a1 Fractional Inverse Fourier Transform, then by first piece of chaos random phase masks complex conjugate modulation after carry out Fresnel inverse transformation, Image after being decrypted.
2. three steps broad sense as claimed in claim 1 phase shift and cascade fractional fourier transform optical image encryption method, which is special Levying is, in an instantiation, comprises the following steps that：
(1) key production portion：The mathematic(al) representation of the discrete form of Duffing chaos systems is：
x n + 1 = y n y n + 1 = - bx n + ay n - y n 3 - - - ( 1 )
Wherein, control parameter a=2.75 and during b=0.2, Duffing systems are in chaos state；xnAnd ynRespectively chaos system The initial value of system；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 Duffing chaos systems by two groups of different chaos state modulators so as to after iteration (M × N)/2 time, obtain two Group random number sequence X1={ 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)/2, y '1,y′2,…,y′(M×N)/2, x ″1,x″2,…,x″(M×N)/2With y "1,y″2,…,y″(M×N)/2For the output valve of chaos system, this two groups of random number sequences are distinguished It is integrated into form Z of two two-dimensional matrixs1={ 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 the position coordinates of matrix element, then Two pieces of chaos random phase masks can be 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, (x1,y1) and (x2,y2) position coordinates of two pieces of random phase masks is respectively, j is imaginary number Unit, π are pi；
(2) image encryption part：
Assume that image to be encrypted is U0(x0,y0), then after the Fresel diffraction Jing distance for z, its mathematic(al) representation is：
U 1 ( x 1 , y 1 ) = exp ( j 2 π z / λ ) j λ z ∫ ∫ U 0 ( x 0 , y 0 ) × exp [ j π [ ( x 0 - x 1 ) 2 + ( y 0 - y 1 ) 2 ] / λ z ] dx 0 dy 0 , - - - ( 2 )
Wherein, U1(x1,y1) it is the Object light wave that image information is carried before first piece of random phase mask；(x0,y0) for original image institute The coordinate of place position；Wavelength of the λ for Object light wave.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 a that image Jing after fresnel transform is modulated laggard row order time by first piece of chaos random phase masks1Fractional Fourier Conversion, the image after conversion are a laggard row order time is modulated by second piece of chaos random phase masks2Fractional Fourier become Change, then the expression formula of the Object light wave for carrying image information at CCD planes is：
Wherein, A0For the amplitude components of Object light wave,For the phase bit position of Object light wave, (x, y) is the position coordinates at CCD planes, FrFTa{ } represents fractional fourier transform of the order for a, and its form is：
U a ( x a , y a ) = FrFT a { U ( x , y ) } ( x a , y a ) = exp [ - j π sgn ( sin a π 2 ) / 4 + j a π / 4 ] | sin a π 2 | 1 / 2 × ∫ - ∞ + ∞ ∫ - ∞ + ∞ U ( x , y ) exp { j π ( x 2 + x a 2 tan a π 2 - 2 ( xx a + yy a ) sin a π 2 + y 2 + y a 2 tan a π 2 ) } d x d y
Wherein, Ua(xa,ya) image after conversion is represented, U (x, y) represents original image；(xa,ya) represent conversion after image seat Mark, (x, y) represent the coordinate of original image；Sgn () is sign function；
The Object light wave is interfered in CCD planes with reference light wave, obtains hologram：
Wherein, I1For the first width hologram, ArRepresent reference light wave；
Reference light is made to produce phase shift α at any angle using PZT (phase-shifter)1And α2, and it is holographic to record the interference of two-beam again Figure：
Wherein, I2And I3It is respectively second and third width hologram；
Then, utilize (5) formula to deduct (6) formula and (7) formula, obtain：
Simultaneous (8) formula and (9) formula, can obtain the real part and imaginary part of Object light wave complex amplitude：
ByThe expression-form that Object light wave at CCD planes can be obtained 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 carries out order first for a2Fractional Inverse Fourier Transform Modulated by the complex conjugate of second piece of chaos random phase masks afterwards, order is then carried out for a1Fractional Inverse Fourier Transform, then Fresnel inverse transformation is carried out after being modulated by the complex conjugate of first piece of chaos random phase masks, the image after being decrypted
Wherein, * is complex conjugate operator.
CN201610945702.6A 2016-10-26 2016-10-26 Three-step generalized phase-shifting and cascade fractional Fourier transform optical image encryption method Pending CN106529311A (en)

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