CN106447588A - Fresnel transform domain chaotic double random phase encoding optical image encryption method - Google Patents

Abstract

The invention relates to the technical field of image information security and optical information processing, and aims at effectively avoiding the system error caused by complex optical elements in an optical integral imaging technology so that the security can be further guaranteed. The adopted technical scheme is a Fresnel transform domain chaotic double random phase encoding optical image encryption method comprising the following steps of 1) an image preprocessing part: an original image under encryption is modulated into an elemental image array similar to a hologram by using integral imaging calculation; 2) a chaotic key generation part: two random phase masks acting as master keys are respectively generated by two-dimensional Zaslavskii chaotic systems controlled by different chaotic parameters; and 3) an image encryption and decryption part: inverse transform of Fresnel transform of which the distance is z1 is performed on the modulated image, and finally the original image is reconstructed through the integral imaging calculation technology. The Fresnel transform domain chaotic double random phase encoding optical image encryption method is mainly used for the occasion of information security.

Description

Fresnel transform domain chaos Double random phase optical image encryption method

Technical field

The present invention relates to image information safety and optical information processing technical field, in more particularly, to a kind of fresnel transform domain Based on the optical image encryption method calculating integration imaging technology and chaos Double random phase.Concretely relate to Fresnel Transform domain chaos Double random phase optical image encryption method.

Background technology

Digital picture, as currently one of most popular multimedia form, has in fields such as politics, economic, military, education And be widely applied.In Internet technology highly developed today, how to protect digital picture exempt from distort, bootlegging and biography Broadcast and there is important practical significance.Research to image encryption technology has become one of the focus in current information security field.

Optical information processing technique is with its high processing rate, high degree of parallelism, quickly to realize convolution and related operation etc. excellent Point, causes the great interest (see document [1]) of people in image encryption research field.In optical image encryption technology, Representative is the Double random phase technology (see document [2]) of the propositions such as Javidi.This 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 this technology [3]).Additionally, optical integration imaging technique and fresnel transform have also obtained extensively in research fields such as image encryption, digital watermarkings General concern (see document [4] and [5]).

However, in the optical image encryption method based on Double random phase and optical integration imaging technique, existing Following problem：

1) key is the random phase mask of picture size, and therefore, key management and transmission are inconvenient (see document [6])；

2) because the inconvenience of random phase mask updates, therefore, encryption system is easily attacked by chosen -plain attact and known-plaintext Hit (see document [7] and [8]).

3) in optical integration imaging technique, the use of a large amount of optical elements, easily brings systematic error to imaging system, makes weight The quality degradation (see document [9]) of composition picture.

List of references：

[1]O.Matoba,T.Nomura,E.Perez-Cabre,M.Millan,and B.Javidi,Optical techniques forinformation security,Proceedings of IEEE 2009,97:1128-1148

[2]P.Réfrégier and B.Javidi,Optical image encryption based on input planeand Fourier plane random encoding,Opt.Lett.,1995,20:767-769

[3]S.Liu,C.Guo,and J.T.Sheridan,A review of optical image encryption techniques,Optics&Laser Technology,2014,57:327-342

[4]X.Li,I-K Lee,S.Kim,Improved integral imaging based image copyright protection algorithmusing 3-D computational integral imaging pickup and super-resolution reconstruction technique,Opt.Laser Eng.,2015,62:103-111

[5]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

[6]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

[7]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

[8]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

[9]D.Shin,H.Yoo,Image quality enhancement in 3D computational integral imaging by use ofinterpolation methods,Opt.Express,2007,15:12039- 12049.

Content of the invention

For overcoming the deficiencies in the prior art, it is contemplated that proposition is a kind of being added based on the optical imagery of Double random phase Decryption method and optical integration imaging technique scheme, realize being prevented effectively from what complicated optics in optical integration imaging technique were brought Systematic error is so that safety is further ensured.The technical solution used in the present invention is that fresnel transform domain chaos is double Optical Image Encryption Using Random Phase Mask method, step is as follows：

1) Image semantic classification part：Using calculating integration imaging, original image to be encrypted is modulated into similar hologram Pixel pattern matrix；

2) generating portion of chaotic key：Two pieces of random phase masks playing master key effect are respectively by different chaotic parameters The two-dimentional Zaslavskii chaos system controlling generates, and, as master key, Fresnel becomes for the initial value of chaos system and control parameter Change distance as the auxiliary key in encryption process；

3) image encryption and decryption portion：(1) in ciphering process, pixel pattern matrix is random by first piece of chaos first Phase mask is modulated, and then entering row distance is z₁Fresnel transform, the image after conversion is again by second piece of chaos random phase Mask is modulated, and then entering row distance is z₂Fresnel transform；(2) in decrypting process, the image after encryption enters line-spacing first From for z₂Fresnel transform inverse transformation, then modulated by the complex conjugate of second piece of chaos random phase masks, modulated after Image enter again row distance be z₁Fresnel transform inverse transformation, then again by first piece of chaos random phase masks multiple altogether Yoke is modulated, and is finally computed integration imaging technology reengineering and goes out original image.

Comprise the concrete steps that in one embodiment：

(1) Image semantic classification part：

Using calculating integration imaging, original image to be encrypted is modulated into the pixel pattern matrix of similar hologram, its In, (k, l) individual pixel image f of being obtained by original image O (x, y)_kl(x, y) is：

f_kl(x, y)=O (- xv+k γ ,-yv+l γ) (1)

Wherein, v is amplification factor, and γ is the spacing between lenslet；(x, y) is the position coordinateses of original image, (k, l) Position coordinateses for lenslet；

By pixel pattern matrix f (x, y) that each pixel image forms it is：

Wherein, p × q represents the quantity of pixel image.

(2) generating portion of chaotic key：

In encryption method, two pieces of chaos random phase masks play master key effect, two-dimentional Zaslavskii chaos system from The mathematic(al) representation of scattered form is：

Wherein, x_nAnd y_nIt is respectively the input value of chaos system, x_n+1And y_n+1It is respectively the iteration output valve of chaos system； Mod represents modulo operation, and π represents pi；W, μ, ν are the control parameter of chaos system, and the wherein form of μ is as follows：

When control parameter w=5, when v=0.2, r=2, two-dimentional Zaslavskii system is in chaos state；Join when controlling When number takes other numerical value, this system is likely to be 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 by the two-dimentional Zaslavskii chaos system of two groups of different chaos state modulator so as to iteration (M × N)/2 After secondary, obtain two groups of random number sequences X₁={ x₁′,x₂′,…,x′_(M×N)/2, Y₁={ y₁′,y₂′,…,y′_(M×N)/2And X₂= {x₁″,x₂″,…,x″_(M×N)/2, Y₂={ y₁″,y₂″,…,y″_(M×N)/2, wherein, x₁′,x₂′,…,x′_(M×N)/2, y₁′, y₂′,…,y′_(M×N)/2, x₁″,x₂″,…,x″_(M×N)/2And y₁″,y₂″,…,y″_(M×N)/2For the iteration output valve of chaos system, incite somebody to action This two groups of random number sequences are integrated into form Z of two two-dimensional matrixs respectively₁={ z_i′_,j| i=1,2 ..., M；J=1,2 ..., N } and Z₂=z "_i,j| i=1,2 ..., M；J=1,2 ..., N }, wherein z '_i,jWith z "_i,jFor the element of two-dimensional matrix, subscript i, j The position coordinateses of representing matrix element；Then obtain two pieces of chaos random phase masks, its mathematic(al) representation is respectively C₁(x₁,y₁) =exp (j2 π z_i′_,j) and C₂(x₂,y₂)=exp (j2 π z "_i,j), wherein, (x₁,y₁) and (x₂,y₂) represent respectively two pieces of chaos with The coordinate of machine phase mask present position, j represents imaginary unit, because chaos random phase mask is by the initial value of chaos system To control with control parameter, therefore, the initial value of chaos system and control parameter are as the master key of encryption system.

(3) image encryption and decryption portion：

1) in ciphering process, pixel pattern matrix f (x, y) is modulated by first piece of chaos random phase masks first, so Laggard row distance is z₁Fresnel transform, the image after conversion modulated by second piece of chaos random phase masks again, Ran Houjin Row distance is z₂Fresnel transform, through twice modulation and twice convert after can be obtained by encrypted image U (x ', y ')：

Wherein, FrT_λ,z{ } represents the fresnel transform for z for the distance, and its form is as follows：

Wherein, U₀(x₀,y₀) represent original image, U₁(x₁,y₁) represent the image after fresnel transform；(x₀,y₀) and (x₁,y₁) respectively represent original image and conversion after image position coordinateses；J is imaginary unit, and π is pi, and λ is Object light wave Wavelength；

2) in decrypting process, it is z that the image after encryption enters row distance first₂Fresnel transform inverse transformation, then Modulated by the complex conjugate of second piece of chaos random phase masks, modulated after image enter again row distance be z₁Fresnel transform Inverse transformation, then modulated it is possible to pixel figure after being deciphered again by the complex conjugate of first piece of chaos random phase masks As array f (x, y)：

Wherein, * represents complex conjugate operator；

The pixel pattern matrix obtaining after deciphering is computed integration imaging technology again and reduces it is possible to finally give reconstruct Original image O (x, y)：

The feature of the present invention and beneficial effect are：

In the optical image encryption method that the present invention provides, calculate the use of integration imaging technology, light can be prevented effectively from Learn the systematic error that in integration imaging technology, complicated optics are brought so that the quality of reconstructed image is significantly carried High.The use of chaotic key is so that this encryption method can be effective against known plain text attack and chosen -plain attact, and makes Key management and transmission become more convenient.Fresnel transform distance is as the auxiliary key in encryption process so that this adds The safety of decryption method has obtained further guarantee.

Brief description：

The principle schematic of the optical image encryption method that Fig. 1 provides for the present invention；

Fig. 2 (a) is original image to be encrypted；

The image that Fig. 2 (b) encrypts for this method；

Fig. 2 (c) is decrypted image when all keys are all correct；

Fig. 3 (a) is the initial value x of the two-dimentional Zaslavskii chaos system controlling second piece of random phase masks₂Mistake, its Decrypted image when its key is all correct；

Fig. 3 (b) is the initial value y of the two-dimentional Zaslavskii chaos system controlling second piece of random phase masks₂Mistake, its Decrypted image when its key is all correct；

Fig. 3 (c) is control parameter w of the two-dimentional Zaslavskii chaos system controlling second piece of random phase masks₂Wrong By mistake, decrypted image when other keys are all correct；

Fig. 3 (d) is control parameter v of the two-dimentional Zaslavskii chaos system controlling second piece of random phase masks₂Wrong By mistake, decrypted image when other keys are all correct；

Fig. 3 (e) is control parameter r of the two-dimentional Zaslavskii chaos system controlling second piece of random phase masks₂Wrong By mistake, decrypted image when other keys are all correct；

Fig. 3 (f) is fresnel transform apart from z₁Mistake, decrypted image when other keys are all correct；

Fig. 3 (g) is fresnel transform apart from z₂Mistake, decrypted image when other keys are all correct；

Fig. 4 (a) is the image obtaining from the encryption in figure deciphering of 12.5% information that lacks；

Fig. 4 (b) is the image obtaining from the encryption in figure deciphering of 25% information that lacks；

Fig. 4 (c) is the image obtaining from the encryption in figure deciphering of 50% information that lacks；

Fig. 5 (a) is the image obtaining from the deciphering of the encryption in figure containing 10% Gaussian noise；

Fig. 5 (b) is the image obtaining from the deciphering of the encryption in figure containing 10% salt-pepper noise；

Fig. 5 (c) is the image obtaining from the deciphering of the encryption in figure containing 10% speckle noise；

In accompanying drawing, the list of parts representated by each label is as follows：

CRPM₁：First piece of chaos random phase masks；CRPM₂：Second piece of chaos random phase masks；CRPM₁*：First The complex conjugate of block chaos random phase masks；CRPM₂*：The complex conjugate of second piece of chaos random phase masks；

Specific embodiment

The invention provides be based in a kind of fresnel transform domain calculating integration imaging technology and chaos double random phase volume The optical image encryption method of code.The present invention provide optical image encryption method by Image semantic classification part, chaotic key Generating portion, image encryption and decryption part are grouped into.In Image semantic classification part, calculating integration imaging technology can will be to be encrypted Original image be modulated into the pixel pattern matrix of similar hologram.Additionally, calculating the use of integration imaging technology, can be effective Avoid the systematic error that complicated optics are brought so that the quality of reconstructed image is significantly improved.Chaotic key Using so that this encryption method can be effective against known plain text attack and chosen -plain attact, and make key management and Transmission becomes more convenient.Fresnel transform distance is as the auxiliary key in encryption process so that the peace of this encryption method Full property is further ensured that.Additionally, many experiments show, this encryption method has good violence and attacks, counts and attack Hit, attacked by noise and shearing attack ability.Described below：

1) Image semantic classification part：Calculate integration imaging technology and original image to be encrypted can be modulated into similar holography The pixel pattern matrix of figure；Compared to optical integration imaging technique, calculating integration imaging technology does not need substantial amounts of optical element, The systematic error that optical element brings therefore can be prevented effectively from；Additionally, calculate integration imaging technology can be with effectively solving light Learn integration imaging technology in reconstructed image second-rate the problems such as.

2) generating portion of chaotic key：Two pieces of random phase masks playing master key effect are respectively by different chaotic parameters The two-dimentional Zaslavskii chaos system controlling generates, and the initial value of chaos system and control parameter are as master key.Fresnel becomes Change distance as the auxiliary key in encryption process.Because in encryption process, key updating is convenient, therefore, this encryption method Known plain text attack and chosen -plain attact can be effective against；Additionally, key management and transmission are also more convenient.

3) image encryption and decryption portion：(1) in ciphering process, pixel pattern matrix is random by first piece of chaos first Phase mask is modulated, and then entering row distance is z₁Fresnel transform, the image after conversion is again by second piece of chaos random phase Mask is modulated, and then entering row distance is z₂Fresnel transform；(2) in decrypting process, the image after encryption enters line-spacing first From for z₂Fresnel transform inverse transformation, then modulated by the complex conjugate of second piece of chaos random phase masks, modulated after Image enter again row distance be z₁Fresnel transform inverse transformation, then again by first piece of chaos random phase masks multiple altogether Yoke is modulated, and is finally computed integration imaging technology reengineering and goes out original image.

For making the object, technical solutions and advantages of the present invention clearer, below embodiment of the present invention is made further Ground describes in detail.

Embodiment 1

Based on the optical imagery calculating integration imaging technology and chaos Double random phase in a kind of fresnel transform domain Encryption method, its encryption principle schematic diagram is as shown in figure 1, encryption method is by Image semantic classification part, the generating unit of chaotic key Divide, image encryption and decryption part are grouped into.

(1) Image semantic classification part：

In the encryption method that the present invention provides, calculate integration imaging technology and original image to be encrypted can be modulated into class Pixel pattern matrix like hologram；Compared to optical integration imaging technique, calculating integration imaging technology does not need substantial amounts of light Learn element, therefore can be prevented effectively from the systematic error that optical element brings；Additionally, calculate integration imaging technology can also be effectively Solve optical integration imaging technique in reconstructed image second-rate the problems such as.

(2) generating portion of chaotic key：

In the encryption method that the present invention provides, two pieces of random phase masks playing master key effect are joined by different chaos respectively The two-dimentional Zaslavskii chaos system of numerical control generates, and the initial value of chaos system and control parameter are as master key.Additionally, it is luxuriant and rich with fragrance Alunite ear transformed distances are as the auxiliary key in encryption process.Because in encryption process, key updating is convenient, therefore, this adds Decryption method can be effective against known plain text attack and chosen -plain attact；Additionally, key management and transmission are also more convenient.

(3) image encryption and decryption portion：

1) in ciphering process, pixel pattern matrix is modulated by first piece of chaos random phase masks first, then carries out Distance is z₁Fresnel transform, the image after conversion is modulated by second piece of chaos random phase masks again, then enters row distance For z₂Fresnel transform；2) in decrypting process, it is z that the image after encryption enters row distance first₂Fresnel transform inversion Change, then modulated by the complex conjugate of second piece of chaos random phase masks, modulated after image enter again row distance be z₁Phenanthrene The inverse transformation of alunite ear conversion, is then modulated by the complex conjugate of first piece of chaos random phase masks again, is finally computed being integrated into As technology reengineering goes out original image.

In sum, calculate the use of integration imaging technology, complicated light can be prevented effectively from optical integration imaging technique The systematic error that element brings is so that the quality of reconstructed image is significantly improved.Chaotic key using so that This encryption method can be effective against known plain text attack and chosen -plain attact, and key management and transmission are become more Convenient.Fresnel transform distance is as the auxiliary key in encryption process so that the safety of this encryption method is entered The guarantee of one step.

Embodiment 2

With reference to Fig. 1, design principle, the scheme in embodiment 1 is introduced in detail, described below：

Based on the optical imagery calculating integration imaging technology and chaos Double random phase in a kind of fresnel transform domain Encryption method, its encryption principle schematic diagram is as shown in Figure 1.Encryption method is by Image semantic classification part, the generating unit of chaotic key Divide, image encryption and decryption part are grouped into.Specific embodiment with regard to this three part is described in detail respectively below.

(1) Image semantic classification part：

Calculate the pixel pattern matrix that original image to be encrypted can be modulated into similar hologram by integration imaging technology. Wherein, (k, l) the individual pixel image f being obtained by original image O (x, y)_kl(x, y) is：

f_kl(x, y)=O (- xv+k γ ,-yv+l γ) (1)

Wherein, v=l₂/ l is amplification factor, and γ is the spacing between lenslet；(x, y) is that the position of original image is sat Mark, (k, l) is the position coordinateses of lenslet.

By pixel pattern matrix f (x, y) that each pixel image forms it is：

Wherein, p × q represents the quantity of pixel image.

(2) generating portion of chaotic key：

In encryption method, two pieces of chaos random phase masks play master key effect.Below with regard to how using two dimension Zaslavskii chaos system generates this two pieces of chaos random phase masks and describes in detail.

The mathematic(al) representation of the discrete form of two-dimentional Zaslavskii chaos system is：

Wherein, x_nAnd y_nIt is respectively the input value of chaos system, x_n+1And y_n+1It is respectively the iteration output valve of chaos system； Mod represents modulo operation, and π represents pi；W, μ, ν are the control parameter of chaos system, and the wherein form of μ is as follows：

When control parameter w=5, when v=0.2, r=2, two-dimentional Zaslavskii system is in chaos state.Merit attention , when above-mentioned control parameter takes other value, two-dimentional Zaslavskii system is likely to be 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 by the two-dimentional Zaslavskii chaos system of two groups of different chaos state modulator so as to iteration (M × N)/2 After secondary, obtain two groups of random number sequences X₁={ x₁′,x₂′,…,x′_(M×N)/2, Y₁={ y₁′,y₂′,…,y′_(M×N)/2And X₂= {x₁″,x₂″,…,x″_(M×N)/2, Y₂={ y₁″,y₂″,…,y″_(M×N)/2}.Wherein, x₁′,x₂′,…,x′_(M×N)/2, y₁′, y₂′,…,y′_(M×N)/2, x₁″,x₂″,…,x″_(M×N)/2And y₁″,y₂″,…,y″_(M×N)/2Iteration output valve for chaos system.Will This two groups of random number sequences are integrated into form Z of two two-dimensional matrixs respectively₁={ z '_i,j| i=1,2 ..., M；J=1,2 ..., N } and Z₂=z "_i,j| i=1,2 ..., M；J=1,2 ..., N }, wherein z '_i,jWith z "_i,jFor the element of two-dimensional matrix, i, j represent The position coordinateses of matrix element；Then obtain two pieces of chaos random phase masks, its mathematic(al) representation is respectively C₁(x₁,y₁)=exp (j2πz′_i,j) and C₂(x₂,y₂)=exp (j2 π z "_i,j).Wherein, (x₁,y₁) and (x₂,y₂) represent the random phase of two pieces of chaos respectively The coordinate of position mask present position, j represents imaginary unit.Because chaos random phase mask is by the initial value of chaos system and control Controlling, therefore, the initial value of chaos system and control parameter are as the master key of encryption system for parameter processed.Due to master key and Auxiliary key is all some numerals, and therefore, managing and transmit these numerals will become very convenient；Additionally, in encryption process Updating these numerals also will become very convenient.

(3) image encryption and decryption portion：

1) in ciphering process, pixel pattern matrix f (x, y) is modulated by first piece of chaos random phase masks first, so Laggard row distance is z₁Fresnel transform, the image after conversion modulated by second piece of chaos random phase masks again, Ran Houjin Row distance is z₂Fresnel transform, through twice modulation and twice convert after can be obtained by encrypted image U (x, y)：

Wherein, FrT_λ,z{ } represents the fresnel transform for z for the distance, and its form is as follows：

Wherein, U₀(x₀,y₀) represent original image, U₁(x₁,y₁) represent the image after fresnel transform；(x₀,y₀) and (x₁,y₁) respectively represent original image and conversion after image position coordinateses；J is imaginary unit, and π is pi, and λ is Object light wave Wavelength.

2) in decrypting process, it is z that the image after encryption enters row distance first₂Fresnel transform inverse transformation, then Modulated by the complex conjugate of second piece of chaos random phase masks, modulated after image enter again row distance be z₁Fresnel transform Inverse transformation, then modulated it is possible to pixel figure after being deciphered again by the complex conjugate of first piece of chaos random phase masks As array f (x, y)：

Wherein, * represents complex conjugate operator.

The pixel pattern matrix obtaining after deciphering is computed integration imaging technology again and reduces it is possible to finally give reconstruct Original image O (x, y)：

In sum, calculate the use of integration imaging technology, complicated light can be prevented effectively from optical integration imaging technique The systematic error that element brings is so that the quality of reconstructed image is significantly improved.Chaotic key using so that This encryption method can be effective against known plain text attack and chosen -plain attact, and key management and transmission are become more Convenient.Fresnel transform distance is as the auxiliary key in encryption process so that the safety of this encryption method is entered The guarantee of one step.

Embodiment 3

With reference to specific accompanying drawing, feasibility checking is carried out to the scheme in embodiment 1 and 2, described below：

After piece image (as shown in Fig. 2 (a)) being encrypted using the encryption method that the present invention implements to provide, obtain Shown in encrypted image such as Fig. 2 (b).

By Fig. 2 (b) as can be seen that any information of original image is all hidden.When all keys are all correct, decrypt Image such as Fig. 2 (c) shown in.By Fig. 2 (c) as can be seen that original image can be very good to be reduced.Illustrate to adopt the system pair The encryption of gray level image and deciphering are successful.

Additionally, when other keys of some wrong cipher key are correct, shown in decrypted result such as Fig. 3 (a) -3 (g).Thus It can be seen that, the safety of the system is can be guaranteed.

Fig. 4 (a) -4 (c) is the decrypted image under encryption figure disappearance 12.5%, 25% and 50% information state.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 multiple needs in practical application.

To the model of each device in addition to doing specified otherwise, the model of other devices is not limited the embodiment of the present invention, As long as the device of above-mentioned functions can be completed.

It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention Sequence number is for illustration only, does not represent the quality of embodiment.

The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all spirit in the present invention and Within principle, any modification, equivalent substitution and improvement made etc., should be included within the scope of the present invention.

Claims (2)

1. a kind of fresnel transform domain chaos Double random phase optical image encryption method, is characterized in that, step is as follows：

1) Image semantic classification part：Using calculating integration imaging, original image to be encrypted is modulated into the pixel of similar hologram Pattern matrix；

2) generating portion of chaotic key：Two pieces of random phase masks playing master key effect are respectively by different chaos state modulator Two-dimentional Zaslavskii chaos system generate, the initial value of chaos system and control parameter as master key, fresnel transform away from From as the auxiliary key in encryption process；

3) image encryption and decryption portion：(1) in ciphering process, pixel pattern matrix is first by first piece of chaos random phase Mask is modulated, and then entering row distance is z₁Fresnel transform, the image after conversion is again by second piece of chaos random phase masks Modulation, then entering row distance is z₂Fresnel transform；(2) in decrypting process, it is z that the image after encryption enters row distance first₂ Fresnel transform inverse transformation, then modulated by the complex conjugate of second piece of chaos random phase masks, modulated after image Entering row distance again is z₁Fresnel transform inverse transformation, then adjusted by the complex conjugate of first piece of chaos random phase masks again System, is finally computed integration imaging technology reengineering and goes out original image.

2. fresnel transform domain as claimed in claim 1 chaos Double random phase optical image encryption method, its feature It is to comprise the concrete steps that in one embodiment：

(1) Image semantic classification part：

Using calculating integration imaging, original image to be encrypted is modulated into the pixel pattern matrix of similar hologram, wherein, by (k, l) individual pixel image f that original image O (x, y) obtains_kl(x, y) is：

f_kl(x, y)=O (- xv+k γ ,-yv+l γ) (1)

Wherein, v is amplification factor, and γ is the spacing between lenslet；(x, y) is the position coordinateses of original image, and (k, l) is little The position coordinateses of lens；

By pixel pattern matrix f (x, y) that each pixel image forms it is：

$f(x,y)=\underset{k=0}{\overset{p-1}{\Σ}}\underset{l=0}{\overset{q-1}{\Σ}}{f}_{kl}(x,y)---\left(2\right)$

Wherein, p × q represents the quantity of pixel image.

(2) generating portion of chaotic key：

In encryption method, two pieces of chaos random phase masks play master key effect, the discrete shape of two-dimentional Zaslavskii chaos system The mathematic(al) representation of formula is：

$\left\{\begin{array}{c}{x}_{n+1}=\[x_n+v(1+{\mathrm{\μy}}_n)+wv\mathrm{\μ}cos\left(2{\mathrm{\πx}}_n\right)\]\left(\mathrm{mod}1\right)\\ y_{n+1}=e^{-r}(y_n+wcos(2{\mathrm{\πx}}_n\left)\right)\end{array}\right.---\left(3\right)$

Wherein, x_nAnd y_nIt is respectively the input value of chaos system, x_n+1And y_n+1It is respectively the iteration output valve of chaos system；Mod table Show modulo operation, π represents pi；W, μ, ν are the control parameter of chaos system, and the wherein form of μ is as follows：

$\mathrm{\μ}=\frac{1-e^{-r}}{r}$

When control parameter w=5, when v=0.2, r=2, two-dimentional Zaslavskii system is in chaos state；When control parameter takes During other numerical value, this system is likely to be 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 by the two-dimentional Zaslavskii chaos system of two groups of different chaos state modulator so as to after iteration (M × N)/2 time, Obtain 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)/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 iteration output valve of chaos system, by this two groups Random number sequence is integrated into form Z of two two-dimensional matrixs respectively₁={ z '_i,j| i=1,2 ..., M；J=1,2 ..., N } and Z₂= {z′_i,j| i=1,2 ..., M；J=1,2 ..., N }, wherein z '_i,jWith z "_i,jFor the element of two-dimensional matrix, subscript i, j representing matrix The position coordinateses of element；Then obtain two pieces of chaos random phase masks, its mathematic(al) representation is respectively C₁(x₁,y₁)=exp (j2 π z′_i,j) and C₂(x₂,y₂)=exp (j2 π z "_i,j), wherein, (x₁,y₁) and (x₂,y₂) represent that two pieces of chaos random phases are covered respectively The coordinate of film present position, j represents imaginary unit, because chaos random phase mask is to be joined by the initial value of chaos system and control Controlling, therefore, the initial value of chaos system and control parameter are as the master key of encryption system for number.

(3) image encryption and decryption portion：

1) in ciphering process, pixel pattern matrix f (x, y) is modulated by first piece of chaos random phase masks first, Ran Houjin Row distance is the fresnel transform of z1, and the image after conversion is modulated by second piece of chaos random phase masks again, then enters line-spacing From the fresnel transform for z2, after converting through modulation twice and twice, can be obtained by encrypted image U (x ', y ')：

$U(x^{\′},y^{\′})={\mathrm{FrT}}_{\mathrm{\λ},z_2}\left\{{\mathrm{FrT}}_{\mathrm{\λ},z_1}\right\{f(x,y)C_1(x_1,y_1)\left\}{C}_2(x_2,y_2)\right\}---\left(4\right)$

Wherein, FrT_λ,z{ } represents the fresnel transform for z for the distance, and its form is as follows：

$\begin{array}{c}{U}_1\left(x_1,y_1\right)={\mathrm{FrT}}_{\mathrm{\λ},z}\[U_0\left(x_0,y_0\right)\]\\ =\frac{\exp \left(j2\mathrm{\π}z/\mathrm{\λ}\right)}{j\mathrm{\λ}z}\∫\∫U_0\left(x_0,y_0\right)\\ \×\exp \[j\mathrm{\π}\[{\left(x_0-x_1\right)}^2+{\left(y_0-y_1\right)}^2\]/\mathrm{\λ}z\]{\mathrm{dx}}_0{\mathrm{dy}}_0\end{array},$

Wherein, U₀(x₀,y₀) represent original image, U₁(x₁,y₁) represent the image after fresnel transform；(x₀,y₀) and (x₁,y₁) The position coordinateses of image after representing original image respectively and converting；J is imaginary unit, and π is pi, and λ is the wavelength of Object light wave；

2) in decrypting process, the image after encryption enters the inverse transformation of the fresnel transform that row distance is z2 first, then by the Two pieces of chaos random phase masks complex conjugate modulation, modulated after image enter again row distance be z1 fresnel transform inverse Conversion, is then modulated the pixel image battle array it is possible to after being deciphered by the complex conjugate of first piece of chaos random phase masks again Row f (x, y)：

$f(x,y)={\mathrm{FrT}}_{\mathrm{\λ},-z_1}\{{\mathrm{FrT}}_{\mathrm{\λ},-z_2}\[U(x^{\′},y^{\′})\]C_2^{*}(x_2,y_2)\}{C}_1^{*}(x_1,y_1)---\left(5\right)$

Wherein, * represents complex conjugate operator；

The pixel pattern matrix obtaining after deciphering is computed integration imaging technology again and reduces it is possible to finally give the original of reconstruct Image O (x, y)：

$O(x,y)=\underset{k=0}{\overset{p-1}{\Σ}}\underset{l=0}{\overset{q-1}{\Σ}}{f}_{kl}(-\frac{x}{\mathrm{\γ}}+lv,-\frac{y}{\mathrm{\γ}}+kv)---\left(6\right).$