CN106530363A - Optical image encryption method based on phase cut fractional Fourier transform - Google Patents

Abstract

The invention relates to the technical field of information security and optical information processing. Known plaintext attacks, chosen plaintext attacks and other password attacks are effectively resisted. The safety is further ensured. The method can strongly resist violent attacks, statistical attacks, noise attacks, cropping attacks and the like. The optical image encryption method based on phase cut fractional Fourier transform comprises the steps of image encryption and image decryption. According to the step of image encryption, an image to be encrypted is first modulated by a first random phase mask during an encryption process; fractional Fourier transform with the order a1 is carried out under the irradiation of plane light; phase cutting is carried out on the image in the complex form after the first fractional Fourier transform to acquire an amplitude distribution part and a phase distribution part; and the amplitude distribution part is modulated by a second random phase mask. According to the step of image decryption, the decrypted image is acquired. The method provided by the invention is mainly applied to design and manufacturing occasions.

Description

Optical image encryption method based on cut fractional fourier transform

Technical field

The present invention relates to information security and optical information processing technical field, more particularly to it is a kind of based on cut fractional Fourier The optical image encryption method of conversion.

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.

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, carry out the great interest that digital image encryption causes people using optical meanss (see document [1]). In optical image encryption technology, most it is 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 technique (see Review literature [3]).Additionally, the encryption method based on fractional fourier transform has also been obtained extensively General concern and research are (see document [4] and [5]).

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 easily receives chosen -plain attact and known bright (see document [6] and [7]) such as text attacks.

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]Unnikrishnan G,Joseph J,Singh K.Optical encryption by double- randomphase encoding in the fractional Fourier domain.Optics Letters,2000,25: 887-889

[5]A.Sinha,K.Singh,Image encryption by using fractional Fourier transform andjigsaw transform in image bit planes.Optical Engineering,2005, 44:057001

[6]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

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

The content of the invention

To overcome the deficiencies in the prior art, it is contemplated that realizing being effective against known plain text attack, chosen -plain attact Deng cryptographic attack, safety is further ensured, also with stronger violence attack, statistical attack, attacked by noise and The ability of shearing attack etc..The technical solution used in the present invention is, the optical image encryption based on cut fractional fourier transform Method, step are 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 order for a under the irradiation of planar light₁Fractional fourier transform；To Jing first time fractional fourier transforms The image of plural form afterwards carries out cut operation, obtains distribution of amplitudes part and PHASE DISTRIBUTION part；Distribution of amplitudes part quilt Second piece of random phase masks modulation, then carries out order for a under the irradiation of planar light₂Fractional fourier transform；To Jing The image of the plural form after second fractional fourier transform carries out cut operation again, obtains distribution of amplitudes part and phase place point Portion part, wherein distribution of amplitudes part are the image after encryption；

2) decryption portion of image：In decrypting process, obtained by decruption key is for the operation of cut twice in ciphering process PHASE DISTRIBUTION part；The PHASE DISTRIBUTION partial modulation that image after encryption is obtained by second cut operation first, Ran Hou Order is carried out under the irradiation of planar light for a₂Fractional fourier transform 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 order for a under the irradiation of planar light₁Point The inverse transformation of number Fourier transformation；Image delivery to the plural form after above-mentioned conversion, the image after being decrypted.

Comprise the concrete steps that in an example of the present invention：

(1) the encryption part of image：

Key used in ciphering process be two pieces of random phase masks, its mathematic(al) representation be respectively exp [j φ (x, Y)] andWherein, j is imaginary unit, φ (x, y) andThe respectively phase of two pieces of random phase masks Bit function, (x, y) and (u, v) are respectively the coordinate of two pieces of random phase mask present positions, and image P (x, y) to be encrypted is first First modulated by first piece of random phase masks exp [j φ (x, y)], then order is carried out under the irradiation of planar light for a₁Point Number Fourier transformation, obtains following form：

W (u, v)=FrFT_a1{P(x,y)exp[jφ(x,y)]} (1)

Wherein, W (u, v) is the Object light wave of carrying image information before second piece of random phase mask；FrFT_a{ } represents rank The secondary fractional fourier transform for a, its form is：

Wherein, U_a(x_a,y_a) represent the image after conversion, (x_a,y_a) represent conversion after image present position coordinate；U(x, Y) original image is represented, (x, y) represents the coordinate of original image present position；Sgn () represents sign function.Formula (1) is cut Mutually operate, obtain distribution of amplitudes part A_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 order for a₂Fractional fourier transform, obtain following form：

Wherein, Object light waves of the O (ξ, η) for carrying image information at output face, (ξ, η) is the position coordinateses at output face. Cut operation 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), the image A after encryption_o(ξ, η) is first by P_o(ξ, η) modulate, then order is carried out under the irradiation of planar light for a₂Fractional fourier transform inverse transformation；Answering after transformed The mould of the image of number form formula is by P_w(u, v) is modulated, and then carries out order under the irradiation of planar light for a₁Fractional fourier transform Inverse transformation；Image delivery to the plural form after above-mentioned conversion, 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 Together.The asymmetrical optical image encryption method can be effective against the cryptographic attacks such as known plain text attack, chosen -plain attact.Point Number Fourier transformation order is used as the additional keys in encryption process so that the safety of encryption method has been obtained further Ensure.Additionally, substantial amounts of numerical simulation experiment shows, also there is the asymmetrical optical image encryption method stronger violence to attack Hit, the ability of 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 comparison figures.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；

The various situation decrypted image comparison diagrams of Fig. 3.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 fractional fourier transform order a using mistake₁The image that decryption is obtained；

F () is the fractional fourier transform order a using mistake₂The image that decryption is obtained；

Decrypted image comparison diagram under the various noise conditions of Fig. 4.In figure：

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

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

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

Fig. 5 shears different proportion decrypted image comparison diagram.In figure：

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

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

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

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

M₁：First piece of random phase masks；M₂：Second piece of random phase masks；FrFT：Fractional fourier transform.

Specific embodiment

The invention provides a kind of optical image encryption method based on cut fractional fourier transform.In encryption method, Key used by ciphering process is different from the key used by decrypting process.The asymmetrical optical image encryption method effectively can be supported The cryptographic attacks such as anti-known plain text attack, chosen -plain attact.Fractional fourier transform order is used as the volume in encryption process Outer key so that the safety of encryption method has obtained further guarantee.Additionally, substantial amounts of numerical simulation experiment shows, should Asymmetrical optical image encryption method also has stronger violence attack, statistical attack, attacked by noise and shearing attack etc. Ability.It is 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 order for a under the irradiation of planar light₁Fractional fourier transform；To Jing first time fractional fourier transforms The image of plural form afterwards carries out cut operation, obtains distribution of amplitudes part and PHASE DISTRIBUTION part；Distribution of amplitudes part quilt Second piece of random phase masks modulation, then carries out order for a under the irradiation of planar light₂Fractional fourier transform；To Jing The image of the plural form after second fractional fourier transform carries out cut operation again, obtains distribution of amplitudes part and phase place point Portion part, wherein distribution of amplitudes part are the image after encryption.

2) decryption portion of image：In decrypting process, obtained by decruption key is for the operation of cut twice in ciphering process PHASE DISTRIBUTION part；The PHASE DISTRIBUTION partial modulation that image after encryption is obtained by second cut operation first, Ran Hou Order is carried out under the irradiation of planar light for a₂Fractional fourier transform 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 order for a under the irradiation of planar light₁Point The inverse transformation of number Fourier transformation；Image delivery to the plural form after above-mentioned conversion, it is possible to the image after being decrypted.

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

Embodiment 1

A kind of optical image encryption method based on cut fractional fourier transform, which adds 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 Order is carried out under irradiation for a₁Fractional fourier transform；Image to the plural form Jing after first time fractional fourier transform Cut operation is carried out, distribution of amplitudes part and PHASE DISTRIBUTION part is obtained；Distribution of amplitudes part is by second piece of random phase masks Modulation, then carries out order for a under the irradiation of planar light₂Fractional fourier transform；Second fractional Fourier of Jing is become The image of the plural form after changing carries out cut operation again, obtains distribution of amplitudes part and phase place branch portion, wherein amplitude point Cloth part is the image after encryption.

(2) decryption portion of image：

In decrypting process, decruption key is the resulting PHASE DISTRIBUTION part of the operation of cut twice in ciphering process；Plus The PHASE DISTRIBUTION partial modulation that image after close is obtained by second cut operation first, is then carried out under the irradiation of planar light Order is a₂Fractional fourier transform 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 order for a under the irradiation of planar light₁Fractional fourier transform 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- Symmetrical optical image encryption method can be effective against the cryptographic attacks such as known plain text attack, chosen -plain attact.In fraction Fu Leaf transformation order is used as the additional keys in encryption process so that the safety of encryption method has obtained further guarantee. Additionally, substantial amounts of numerical simulation experiment shows, also there is the asymmetrical optical image encryption method stronger violence to attack, system The ability of meter 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, it is described below：

A kind of optical image encryption method based on cut fractional fourier transform, its encryption principle figure as shown in figure 1, plus 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：

Key used in ciphering process be two pieces of random phase masks, its mathematic(al) representation be respectively exp [j φ (x, Y)] andWherein, j is imaginary unit, φ (x, y) andThe respectively phase of two pieces of random phase masks Bit function, (x, y) and (u, v) are respectively the coordinate of two pieces of random phase mask present positions.Image P (x, y) to be encrypted is first First modulated by first piece of random phase masks exp [j φ (x, y)], then order is carried out under the irradiation of planar light for a₁Point Number Fourier transformation, obtains following form：

Wherein, W (u, v) is the Object light wave of carrying image information before second piece of random phase mask；FrFT_a{ } represents rank The secondary fractional fourier transform for a, its form is：

Wherein, U_a(x_a,y_a) represent the image after conversion, (x_a,y_a) represent conversion after image present position coordinate；U(x, Y) original image is represented, (x, y) represents the coordinate of original image present position；Sgn () represents sign function.Formula (1) is cut Mutually operate, obtain distribution of amplitudes part A_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 order for a₂Fractional fourier transform, obtain following form：

Wherein, Object light waves of the O (ξ, η) for carrying image information at output face, (ξ, η) is the position coordinateses at output face. Cut operation 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), the image A after encryption_o(ξ, η) is first by P_o(ξ, η) modulate, then order is carried out under the irradiation of planar light for a₂Fractional fourier transform inverse transformation；Answering after transformed The mould of the image of number form formula is by P_w(u, v) is modulated, and then carries out order under the irradiation of planar light for a₁Fractional fourier transform 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- Symmetrical optical image encryption method can be effective against the cryptographic attacks such as known plain text attack, chosen -plain attact.In fraction Fu Leaf transformation order is used as the additional keys in encryption process so that the safety of encryption method has obtained further guarantee. Additionally, substantial amounts of numerical simulation experiment shows, also there is the asymmetrical optical image encryption method stronger violence to attack, system The ability of meter 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, it is described below：

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

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

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

Fig. 4 (a) -4 (c) is encryption figure containing the decryption figure in the case of 10% Gaussian noise, salt-pepper noise and speckle noise Picture.Fig. 5 (a) -5 (c) respectively encrypts the decrypted image in the case of figure disappearance 12.5%, 25% and 50%.As can be seen here, even if To a certain extent by sound 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 various needs in practical application.

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

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

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

Claims (2)

1. a kind of optical image encryption method based on cut fractional fourier transform, 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 Order is carried out under the irradiation of planar light for a afterwards₁Fractional fourier transform；To answering Jing after first time fractional fourier transform The image of number form formula carries out cut operation, 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 order under the irradiation of planar light for a₂Fractional fourier transform；To Jing for the second time The image of the plural form after fractional fourier transform carries out cut operation again, obtains distribution of amplitudes part and portion of phase place branch Point, wherein distribution of amplitudes part is the image after encryption；

2) decryption portion of image：In decrypting process, decruption key is the resulting phase of the operation of cut twice in ciphering process Bit distribution part；The PHASE DISTRIBUTION partial modulation that image after encryption is obtained by second cut operation first, then in plane Order is carried out under the irradiation of light for a₂Fractional fourier transform 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 order for a under the irradiation of planar light₁Fraction Fu In leaf transformation inverse transformation；Image delivery to the plural form after above-mentioned conversion, the image after being decrypted.

2. the optical image encryption method based on cut fractional fourier transform as claimed in claim 1, is characterized in that, one Comprise the concrete steps that in example：

(1) the encryption part of image：

Key used in ciphering process be two pieces of random phase masks, its mathematic(al) representation be respectively exp [j φ (x, y)] andWherein, j is imaginary unit, φ (x, y) andThe phase place letter of respectively two pieces of random phase masks Number, the coordinate of (x, y) and (u, v) respectively two pieces of random phase mask present positions, image P (x, y) to be encrypted first by The modulation of first piece of random phase masks exp [j φ (x, y)], then carries out fraction Fu that order is a1 under the irradiation of planar light In leaf transformation, obtain following form：

$W(u,v)={\mathrm{FrFT}}_{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；FrFT_a{ } represents that order is a Fractional fourier transform, its form is：

$\begin{array}{c}{U}_a(x_a,y_a)={\mathrm{FrFT}}_a\left\{U(x,y)\right\}(x_a,y_a)\\ =\frac{\exp \[-j\mathrm{\π}\mathrm{sgn}\left(\sin \frac{a\mathrm{\π}}{2}\right)/4+ja\mathrm{\π}/4\]}{|\sin \frac{a\mathrm{\π}}{2}{|}^{1/2}}\\ \×{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}U(x,y)\exp \left\{j\mathrm{\π}(\frac{x^2+x_a^2}{\tan \frac{a\mathrm{\π}}{2}}-\frac{2({\mathrm{xx}}_a+{\mathrm{yy}}_a)}{\sin \frac{a\mathrm{\π}}{2}}+\frac{y^2+y_a^2}{\tan \frac{a\mathrm{\π}}{2}})\right\}dxdy\end{array}$

Wherein, U_a(x_a,y_a) represent the image after conversion, (x_a,y_a) represent conversion after image present position coordinate；U (x, y) table Show original image, (x, y) represents the coordinate of original image present position；Sgn () represents sign function.Cut behaviour is carried out to formula (1) Make, obtain distribution of amplitudes part A_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 order for a₂Fractional fourier transform, obtain following form：

Wherein, Object light waves of the O (ξ, η) for carrying image information at output face, (ξ, η) is the position coordinateses at output face.To formula (4) cut operation is carried out, obtains distribution of amplitudes part A_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), the image A after encryption_o(ξ, η) is first by P_o(ξ, η) is adjusted System, then carries out order for a under the irradiation of planar light₂Fractional fourier transform 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 order under the irradiation of planar light for a₁Fractional fourier transform it is inverse Conversion；Image delivery to the plural form after above-mentioned conversion, the image after being decrypted

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