CN106504175A - Nonlinear optics image encryption method in Gyrator transform domains - Google Patents

Abstract

The present invention relates to information security and optical information processing technical field, are that realization is effective against multiple cryptographic attacks such as known plain text attack, chosen -plain attact so that the security of encryption method is further ensured.Additionally, also having the ability of stronger violence attack, statistical attack, attacked by noise and shearing attack etc..The present invention, the nonlinear optics image encryption method in Gyrator transform domains, step are as follows：1) the encryption part of image：In ciphering process, image to be encrypted is modulated by first piece of random phase masks first, then carries out angle under the irradiation of planar light for a₁Gyrator conversion；Image after being encrypted；2) decryption portion of image：The phase distribution partial modulation that image after encryption is obtained by second cut operation first, then carries out the inverse transformation of Gyrator conversion, the image after being decrypted under the irradiation of planar light.Present invention is mainly applied to information security occasion.

Description

Nonlinear optics image encryption method in Gyrator transform domains

Technical field

The present invention relates in information security and optical information processing technical field, more particularly to a kind of Gyrator transform domains Nonlinear optics image encryption method.

Background technology

Digital picture has in fields such as politics, economic, military, education as currently one of 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.One of the focus in current information security field has been become to the research of image encryption technology.

As optical information processing technique has high processing rate, high degree of parallelism, can quickly realize convolution and related operation The advantages of, in recent years, the great interest (see document [1]) that digital image encryption causes people is carried out using optical means.? In optical image encryption technology, most representational be the propositions such as Javidi based on Optical processing system double random phase compile Code method (see document [2]).The technology opens the frontier of optical image encryption, has been born large quantities of optics based on the technology New Method for Encryption and new technology (see Review literature [3]).Additionally, used as a kind of Fourier transformation of broad sense, Gyrator is converted Can be used for (see document [4]) in optical image encryption.

However, great majority are linear symmetric cryptographic systems based on the image encryption system of Double random phase method, i.e., Ciphering process is identical with the key that decrypting process is used.Such linear symmetric cryptographic system is easily by chosen -plain attact and known bright (see document [5] and [6]) such as text attacks.

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]J.Rodrigo,T.Alieva,M.Calvo,Gyrator transform:properties andapplications,Opt.Express,2007,15:2190-2203

[5]X.Peng,P.Zhang,H.Wei,and B.Yu,Known-plaintext attack on opticalencryption based on double random phase keys,Opt.Lett.,2006,31:1044- 1046

[6]W.Stallings,Cryptography and Network Security:Principles and Practice,4th ed.(Prentice Hall,2006)

Content of the invention

For overcoming the deficiencies in the prior art, it is contemplated that realizing being effective against known plain text attack, chosen -plain attact Etc. multiple cryptographic attacks so that the security of encryption method is further ensured.Additionally, also having stronger violence to attack Hit, the ability of statistical attack, attacked by noise and shearing attack etc..The technical solution used in the present invention is, in Gyrator transform domains Nonlinear optics image encryption method, step is as follows：

1) the encryption part of image：In ciphering process, image to be encrypted is adjusted by first piece of random phase masks first System, then carries out angle under the irradiation of planar light for a₁Gyrator conversion；To being a through angle₁Gyrator conversion after The image of plural form carries out cut bit manipulation, obtains distribution of amplitudes part and phase distribution part；Distribution of amplitudes part is by Two pieces of random phase masks modulation, then carry out angle under the irradiation of planar light for a₂Gyrator conversion；To through angle being a₂Gyrator conversion after the image of plural form carry out cut bit manipulation again, obtain distribution of amplitudes part and phase place branch Part, wherein distribution of amplitudes part are the image after encryption；

2) decryption portion of image：In decrypting process, decruption key is the gained of cut bit manipulation twice in ciphering process The phase distribution part that arrives；The phase distribution partial modulation that image after encryption is obtained by second cut operation first, then Angle is carried out under the irradiation of planar light for a₂Gyrator conversion inverse transformation；The image of the plural form after transformed The phase distribution partial modulation that mould is obtained by first time cut operation, then carries out angle under the irradiation of planar light for a₁'s The inverse transformation of Gyrator conversion；Image delivery to the plural form after above-mentioned conversion, the image after being decrypted.

Key used in ciphering process be two pieces of random phase masks, its mathematic(al) representation be respectively exp [j φ (x, Y)] andWherein, φ (x, y) andFor two-dimensional random matrix；(x, y) and (u, v) be respectively two pieces with The coordinate of machine phase mask present position, j represent imaginary unit, and image P (x, y) to be encrypted is first by first piece of random phase Mask exp [j φ (x, y)] is modulated, and then carries out angle under the irradiation of planar light for a₁Gyrator conversion, obtain as follows Form：

Wherein, W (u, v) is the Object light wave of carrying image information before second piece of random phase mask,For angle it is a₁Gyrator conversion, angle is converted for the two-dimentional Gyrator of a following form：

Wherein, U₀(x₀,y₀) represent that input picture, U (x, y) are represented through the image after Gyrator conversion；(x₀,y₀) and (x, Y) coordinate of image after representing input picture respectively and converting；π represents pi；

Cut bit manipulation is carried out to formula (1), distribution of amplitudes part A is obtained_w(u, v) and phase distribution part P_w(u,v)：

A_w(u, v)=| W (u, v) | (2)

P_w(u, v)=W (u, v)/| W (u, v) | (3)

Distribution of amplitudes part A_w(u, v) is by second piece of random phase masksModulation, then in planar light Irradiation under carry out angle for a₂Gyrator conversion, obtain following form：

Wherein, O (ξ, η) is the Object light wave for carrying image information at output face, and (ξ, η) is the coordinate at output face,It is a for angle₂Gyrator conversion；

Cut bit manipulation is carried out to formula (4), distribution of amplitudes part A is obtained_o(ξ, η) and phase distribution part P_o(ξ,η)：

A_o(ξ, η)=| O (ξ, η) | (5)

P_o(ξ, η)=O (ξ, η)/| O (ξ, η) | (6)

Wherein, A_o(ξ, η) is exactly the image after encryption；

In decrypting process, decruption key is P_w(u, v) and P_o(ξ, η), the image A after encryption_o(ξ, η) is first by P_o(ξ, η) modulate, under the irradiation of planar light, angle is then carried out for a₂Gyrator conversion inverse transformation；Plural shape after transformed The mould of the image of formula is by P_w(u, v) is modulated, and then carries out angle under the irradiation of planar light for a₁Gyrator conversion inversion Change；Image delivery to the plural form after above-mentioned conversion, it is possible to the image after being decrypted

The characteristics of of the invention and beneficial effect are：

In the image encryption method that the present invention is provided, the key used by ciphering process is with the key used by decrypting process not With.The nonlinear optics image encryption method can be effective against multiple passwords such as known plain text attack, chosen -plain attact and attack Hit.Gyrator translation-angles as encryption process in auxiliary key so that the security of encryption method has been obtained further Guarantee.Additionally, substantial amounts of numerical simulation experiment shows that the nonlinear optics image encryption method also has stronger violence The ability of attack, statistical attack, attacked by noise and shearing attack etc..

Description of the drawings：

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

Fig. 2 encryption and decryption image schematic diagrames of the present invention.In figure：

A () is original image to be encrypted；

B () is the image of this encryption method encryption；

C () is decrypted image when all keys are correct；

Fig. 3 decrypted image comparison diagrams.In figure：

A () is the image obtained using first piece of random phase masks decryption；

B () is the image obtained using second piece of random phase masks decryption；

C () is the P using mistake_wThe image that (u, v) decryption is obtained；

D () is the P using mistake_oThe image that (ξ, η) decryption is obtained；

E () is the image obtained using wrong Gyrator translation-angles a1 decryption；

F () is the image obtained using wrong Gyrator translation-angles a2 decryption；

Fig. 4 difference noise decrypted image comparison diagrams.In figure：

A () is to decrypt the image for obtaining from the encryption figure containing 10% Gaussian noise；

B () is to decrypt the image for obtaining from the encryption figure containing 10% salt-pepper noise；

C () is to decrypt the image for obtaining from the encryption figure containing 10% speckle noise；

Decrypted image comparison diagram after the different shearings of Fig. 5.In figure：

A () is to decrypt the image for obtaining from the encryption figure for cutting off 12.5%；

B () is to decrypt the image for obtaining from the encryption figure for cutting off 25%；

C () is to decrypt the image for obtaining from the encryption figure for cutting off 50%.

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

M1：First piece of random phase masks；M2：Second piece of random phase masks；GT：Gyrator is converted.

Specific embodiment

The invention provides the nonlinear optics image encryption method in a kind of Gyrator transform domains.In encryption method, plus Key used by close process is different from the key used by decrypting process.The nonlinear optics image encryption method can be effective against Multiple cryptographic attacks such as known plain text attack, chosen -plain attact.Gyrator translation-angles as encryption process in auxiliary Key so that the security of encryption method has obtained further guarantee.Additionally, substantial amounts of numerical simulation experiment shows that this is non- Linear optics image encryption method also has the energy of stronger violence attack, statistical attack, attacked by noise and shearing attack etc. Power.Described below：

1) the encryption part of image：In ciphering process, image to be encrypted is adjusted by first piece of random phase masks first System, then carries out angle under the irradiation of planar light for a₁Gyrator conversion；To being a through angle₁Gyrator conversion after The image of plural form carries out cut bit manipulation, obtains distribution of amplitudes part and phase distribution part；Distribution of amplitudes part is by Two pieces of random phase masks modulation, then carry out angle under the irradiation of planar light for a₂Gyrator conversion；To through angle being a₂Gyrator conversion after the image of plural form carry out cut bit manipulation again, obtain distribution of amplitudes part and phase place branch Part, wherein distribution of amplitudes part are the image after encryption.

2) decryption portion of image：In decrypting process, decruption key is the gained of cut bit manipulation twice in ciphering process The phase distribution part that arrives；The phase distribution partial modulation that image after encryption is obtained by second cut operation first, then Angle is carried out under the irradiation of planar light for a₂Gyrator conversion inverse transformation；The image of the plural form after transformed The phase distribution partial modulation that mould is obtained by first time cut operation, then carries out angle under the irradiation of planar light for a₁'s The inverse transformation of Gyrator conversion；Image delivery to the plural form after above-mentioned conversion, it is possible to the image after being decrypted.

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

Embodiment 1

A kind of nonlinear optics image encryption method in Gyrator transform domains, its add solution principle schematic such as Fig. 1 institutes Show, encryption method is made up of the encryption part of image and the decryption portion of image.

(1) the encryption part of image：

In ciphering process, image to be encrypted is modulated by first piece of random phase masks first, then in planar light Angle is carried out under irradiation for a₁Gyrator conversion；To being a through angle₁Gyrator conversion after the image of plural form enter Row cut bit manipulation, obtains distribution of amplitudes part and phase distribution part；Distribution of amplitudes part is by second piece of random phase masks Modulation, then carries out angle under the irradiation of planar light for a₂Gyrator conversion；To being a through angle₂Gyrator conversion after The image of plural form carry out cut bit manipulation again, obtain distribution of amplitudes part and phase place branch portion, wherein distribution of amplitudes Part is the image after encryption.

(2) decryption portion of image：

In decrypting process, decruption key is the phase distribution part in ciphering process obtained by cut bit manipulation twice； The phase distribution partial modulation that image after encryption is obtained by second cut operation first, then enters under the irradiation of planar light Row angle is a₂Gyrator conversion inverse transformation；The mould of the image of the plural form after transformed is operated by first time cut The phase distribution partial modulation for obtaining, then carries out angle under the irradiation of planar light for a₁Gyrator conversion inverse transformation； Image delivery to the plural form after above-mentioned conversion, it is possible to the image after being decrypted.

In sum, in this encryption method, the key used by ciphering process is different from the key used by decrypting process.This is non- Linear optics image encryption method can be effective against multiple cryptographic attacks such as known plain text attack, chosen -plain attact. Gyrator translation-angles as encryption process in auxiliary key so that the security of encryption method has been obtained further Ensure.Additionally, substantial amounts of numerical simulation experiment shows, also there is the nonlinear optics image encryption method stronger violence to attack Hit, the ability of statistical attack, attacked by noise and shearing attack etc..

Embodiment 2

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

A kind of nonlinear optics image encryption method in Gyrator transform domains, its encryption principle figure is as shown in figure 1, add Decryption method is made up of the encryption part of image and the decryption portion of image.Below this two-part specific embodiment is given respectively With detailed description.

(1) the encryption part of image：

The key used during image encryption be two pieces of random phase masks, its mathematic(al) representation be respectively exp [j φ (x, y)] andWherein, φ (x, y) andFor two-dimensional random matrix；(x, y) and (u, v) is respectively two The coordinate of block random phase mask present position, j represent imaginary unit, and image P (x, y) to be encrypted is random by first piece first Phase mask exp [j φ (x, y)] is modulated, and is then carried out the Gyrator that angle is a1 under the irradiation of planar light and is converted, obtains Following form：

Wherein, W (u, v) is the Object light wave of carrying image information before second piece of random phase mask,For angle it is a₁Gyrator conversion, angle is converted for the two-dimentional Gyrator of a following form：

Wherein, U₀(x₀,y₀) represent that input picture, U (x, y) are represented through the image after Gyrator conversion；(x₀,y₀) and (x, Y) coordinate of image after representing input picture respectively and converting；π represents pi.

Cut bit manipulation is carried out to formula (1), distribution of amplitudes part A is obtained_w(u, v) and phase distribution part P_w(u,v)：

A_w(u, v)=| W (u, v) | (2)

P_w(u, v)=W (u, v)/| W (u, v) | (3)

Distribution of amplitudes part A_w(u, v) is by second piece of random phase masksModulation, then in planar light Irradiation under carry out angle for a₂Gyrator conversion, obtain following form：

Wherein, O (ξ, η) is the Object light wave for carrying image information at output face, and (ξ, η) is the coordinate at output face,It is a for angle₂Gyrator conversion.

Cut bit manipulation is carried out to formula (4), distribution of amplitudes part A is obtained_o(ξ, η) and phase distribution part P_o(ξ,η)：

A_o(ξ, η)=| O (ξ, η) | (5)

P_o(ξ, η)=O (ξ, η)/| O (ξ, η) | (6)

Wherein, A_o(ξ, η) is exactly the image after encryption.

(2) decryption portion of image：

In decrypting process, decruption key is P_w(u, v) and P_o(ξ,η).Image A after encryption_o(ξ, η) is first by P_o(ξ, η) modulate, under the irradiation of planar light, angle is then carried out for a₂Gyrator conversion inverse transformation；Plural shape after transformed The mould of the image of formula is by P_w(u, v) is modulated, and then carries out angle under the irradiation of planar light for a₁Gyrator conversion inversion Change；Image delivery to the plural form after above-mentioned conversion, it is possible to the image after being decrypted

In sum, in this encryption method, the key used by ciphering process is different from the key used by decrypting process.This is non- Linear optics image encryption method can be effective against multiple cryptographic attacks such as known plain text attack, chosen -plain attact. Gyrator conversion angle as encryption process in auxiliary key so that the security of encryption method has been obtained further Guarantee.Additionally, substantial amounts of numerical simulation experiment shows that the nonlinear optics image encryption method also has stronger violence The ability of attack, statistical attack, attacked by noise and shearing attack etc..

Embodiment 3

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

After the encryption method for implementing offer using the present invention is encrypted to piece image (as shown in Fig. 2 (a)), obtain Shown in encrypted image such as Fig. 2 (b).

By Fig. 2 (b) as can be seen that any information of original image is all hidden.When all keys are correct, decrypt Image such as Fig. 2 (c) shown in.By Fig. 2 (c) as can be seen that original image can be reduced completely.Illustrate using the system to ash The encryption and decryption of degree image is successful.

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

Fig. 4 (a) -4 (c) is encryption figure containing the decryption figure in the case of 10% Gaussian noise, salt-pepper noise and speckle noise Picture.Fig. 5 (a) -5 (c) is respectively to encrypt and schemes to lack the decrypted image in the case of 12.5%, 25% and 50%.As can be seen here, even if To a certain extent by noise pollution or lack part information, the embodiment of the present invention remains able to decrypt certain matter encrypted image The original image of amount, demonstrates the feasibility of the system, meets the multiple needs in practical application.

To the model of each device in addition to 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 in order to limit the present invention, all spirit in the present invention and Within principle, any modification, equivalent substitution and improvements that is made etc. should be included within the scope of the present invention.

Claims (2)

1. the nonlinear optics image encryption method in a kind of Gyrator transform domains, is characterized in that, step is as follows：

1) the encryption part of image：In ciphering process, image to be encrypted is modulated by first piece of random phase masks first, so Angle is carried out under the irradiation of planar light afterwards for a₁Gyrator conversion；To being a through angle₁Gyrator conversion after plural number The image of form carries out cut bit manipulation, obtains distribution of amplitudes part and phase distribution part；Distribution of amplitudes part is by second piece Random phase masks are modulated, and then carry out angle under the irradiation of planar light for a₂Gyrator conversion；To being a through angle₂'s The image of the plural form after Gyrator conversion carries out cut bit manipulation again, obtains distribution of amplitudes part and phase place branch portion, Wherein distribution of amplitudes part is the image after encryption；

2) decryption portion of image：In decrypting process, obtained by decruption key is for cut bit manipulation twice in ciphering process Phase distribution part；The phase distribution partial modulation that image after encryption is obtained by second cut operation first, then flat Angle is carried out under the irradiation of face light for a₂Gyrator conversion inverse transformation；The mould quilt of the image of the plural form after transformed The phase distribution partial modulation that first time cut operation is obtained, then carries out angle under the irradiation of planar light for a₁'s The inverse transformation of Gyrator conversion；Image delivery to the plural form after above-mentioned conversion, the image after being decrypted.

2. the nonlinear optics image encryption method in Gyrator transform domains as claimed in claim 1, is characterized in that, encryption During the key that uses be two pieces of random phase masks, its mathematic(al) representation be respectively exp [j φ (x, y)] andWherein, φ (x, y) andFor two-dimensional random matrix；(x, y) and (u, v) is respectively two pieces of random phases The coordinate of position mask present position, j represent imaginary unit, and image P (x, y) to be encrypted is first by first piece of random phase masks Exp [j φ (x, y)] is modulated, and then carries out angle under the irradiation of planar light for a₁Gyrator conversion, obtain following form：

$W(u,v)={\mathrm{GT}}_{a_1}\{P(x,y)\exp \[j\mathrm{\φ}(x,y)\]\}---\left(1\right)$

Wherein, W (u, v) is the Object light wave of carrying image information before second piece of random phase mask,It is angle for a1 Gyrator is converted, and angle has following form for the two-dimentional Gyrator conversion of a：

$\begin{array}{c}U(x,y)={\mathrm{GT}}_a\left\{U_0(x_0,y_0)\right\}(x,y)\\ =\frac{1}{\left|\sin a\right|}\underset{-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\∫}}\underset{-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\∫}}{U}_0(x_0,y_0)\exp \left\{j2\mathrm{\π}\frac{(xy+x_0{y}_0)\cos a-(x_{0}y+{\mathrm{xy}}_0)}{\sin a}\right\}{\mathrm{dx}}_0{\mathrm{dy}}_0\end{array}$

Wherein, U₀(x₀,y₀) represent that input picture, U (x, y) are represented through the image after Gyrator conversion；(x₀,y₀) and (x, y) point Not Biao Shi input picture and conversion after image coordinate；π represents pi；

Cut bit manipulation is carried out to formula (1), distribution of amplitudes part A is obtained_w(u, v) and phase distribution part P_w(u,v)：

A_w(u, v)=| W (u, v) | (2)

P_w(u, v)=W (u, v)/| W (u, v) | (3)

Distribution of amplitudes part A_w(u, v) is by second piece of random phase masksModulation, then in the irradiation of planar light Under carry out angle be a2 Gyrator convert, obtain following form：

Wherein, O (ξ, η) is the Object light wave for carrying image information at output face, and (ξ, η) is the coordinate at output face,For Angle is converted for the Gyrator of a2；

Cut bit manipulation is carried out to formula (4), distribution of amplitudes part A is obtained_o(ξ, η) and phase distribution part P_o(ξ,η)：

A_o(ξ, η)=| O (ξ, η) | (5)

P_o(ξ, η)=O (ξ, η)/| O (ξ, η) | (6)

Wherein, A_o(ξ, η) is exactly the image after encryption；

In decrypting process, decruption key is P_w(u, v) and P_o(ξ, η), the image A after encryption_o(ξ, η) is first by P_o(ξ, η) is adjusted System, then carries out the inverse transformation that the Gyrator that angle is a2 is converted under the irradiation of planar light；Plural form after transformed The mould of image is by P_w(u, v) is modulated, and then carries out the inverse transformation that the Gyrator that angle is a1 is converted under the irradiation of planar light； Image delivery to the plural form after above-mentioned conversion, it is possible to the image after being decrypted

$\hat{P}(x,y)=\left|{\mathrm{GT}}_{-a_1}\right\{|{\mathrm{GT}}_{-a_2}\[A_o(\mathrm{\ξ},\mathrm{\η})P_o(\mathrm{\ξ},\mathrm{\η})\]|P_w(u,v)\left\}\right|---\left(7\right).$