CN106651736A - Optical image encryption method based on Gyrator transform and coupled chaos - Google Patents
Optical image encryption method based on Gyrator transform and coupled chaos Download PDFInfo
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Abstract
The invention relates to the technical field of image information security and optical information processing, and aims to effectively resist known plaintext attack and chosen plaintext attack and make key management and transmission more convenient. The technical scheme adopted in the invention is as follows: an optical image encryption method based on Gyrator transform and coupled chaos comprises the following steps: (1) construction of a coupled Logistic chaos: two one-dimensional Logistic chaos maps are associated together by a coupling parameter; (2) generation of a chaotic key: two random phase masks serving as a master key are generated by coupled Logistic chaos systems controlled by different chaotic parameters; and (3) image encryption and decryption based on Gyrator transform: first, a to-be-encrypted image is modulated by the first chaos random phase mask in the process of encryption, and second, the image is modulated by the complex conjugate of the first chaos random phase mask. The method is mainly applied to an image information security occasion.
Description
Technical field
The present invention relates to image information safety and optical information processing technical field, more particularly to one kind is based on Gyrator changes
Change and couple the optical image encryption method of Logistic chaos.
Background technology
Digital picture has as one of current most popular multimedia form in the field 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 with important practical significance.Research to image encryption technology has become one of the focus in current information security field.
Optical information processing technique with its high processing rate, high degree of parallelism, can quickly realize that convolution and related operation etc. are excellent
Point, in image encryption research field the great interest (see document [1]) of people is caused.In optical image encryption technology, most
Representative is the Double random phase technology (see document [2]) of the propositions such as Javidi.The technology opens optical picture
As the frontier of encryption research, large quantities of optical encryption new methods and new technology are born (see Review literature based on the technology
[3]).Additionally, used as a kind of Fourier transformation of broad sense, Gyrator conversion can also be used in optical image encryption (see document
[4])。
However, in the optical image encryption method based on Double random phase, mostly there are the following problems：
1) key is the random phase mask of picture size, therefore, key management and transmission are inconvenient (see document [5])；
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 [6] and [7]).
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]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
[6]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
[7]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。
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 and selecting to attack in plain text
Hit, and cause key management and transmission to become more convenient.The technical solution used in the present invention is that Gyrator is converted and coupled
Chaos optical image encryption method, step is as follows：
1) construction of Logistic chaos is coupled：By two dimensional Logistic chaotic maps by a coupling parameter connection
It is tied；
2) generation of chaotic key：Play two pieces of random phase masks of master key effect respectively by different chaos state modulators
Coupling Logistic chaos systems generate, the initial value and control parameter of chaos system is used as master key；Additionally, Gyrator becomes
Angle is changed as the auxiliary key in encryption process；
3) image encryption for being converted based on Gyrator and decryption：(1) in ciphering process, image to be encrypted first by
First piece of chaos random phase masks modulation, then carries out angle for a1Gyrator conversion, the image after conversion is again by second
Block chaos random phase masks are modulated, and then carry out angle for a2Gyrator conversion；(2) in decrypting process, after encryption
Image carries out first angle for a2Gyrator inverse transformations, then by the complex conjugate modulation of second piece of chaos random phase masks,
Image after modulated carries out again angle for a1Gyrator inverse transformations, finally again by first piece of chaos random phase masks
Complex conjugate is modulated.
Comprise the concrete steps that in one embodiment：
(1) construction of Logistic chaos is coupled：
The mathematic(al) representation of the discrete form of dimensional Logistic chaos system is：
xn+1=μ xn(1-xn) (1)
Wherein, xnFor the initial value of chaos system, xn+1For the iteration output valve of chaos system；And as control parameter μ ∈
(3.56,4] when, Logistic systems are in chaos state；
Introduce a coupling parameter ε, wherein meet ε ∈ (- 2,2), then couple Logistic chaos system discrete forms
Mathematic(al) representation is：
xn+1=μ xn(1-xn)+ε(yn-xn) (2)
yn+1=μ yn(1-yn)+ε(xn-yn) (3)
Wherein, xnAnd ynRespectively couple the initial value of Logistic chaos systems, xn+1And yn+1Respectively couple Logistic
The iteration output valve of chaos system, equally, when control parameter μ ∈ (3.56,4] when, coupling Logistic systems are in chaos shape
State；
(2) generation of chaotic key：
Two pieces of chaos random phase masks play master key effect in encryption method, and Gyrator translation-angles play auxiliary key
Effect.The size for assuming the 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
Individual pixel.For the coupling Logistic chaos systems by two groups of different chaos state modulators so as to after iteration (M × N)/2 time,
Obtain two groups of random number sequences X1={ x '1,x′2,…,x′(M×N)/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,y′1,y′2,…,y′(M×N)/2,
x″1,x″2,…,x″(M×N)/2With y "1,y″2,…,y″(M×N)/2The respectively iteration output valve of Coupled Chaotic Systems, by this two groups
Random number sequence is integrated into respectively form Z of two two-dimensional matrixs1={ 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 is matrix element
The coordinate of element, then can obtain two pieces of chaos random phase masks, and 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) be respectively residing for two pieces of random phase masks
The coordinate of position, j is imaginary unit, and π is pi, because chaos random phase mask is initial value and the control by chaos system
Parameter controlling, therefore, the master key of the initial value and control parameter of chaos system as encryption system；
(3) image encryption for being converted based on Gyrator and decryption：
1) in ciphering process, image U to be encrypted0(x0,y0) modulated by first piece of chaos random phase masks first,
Then angle is carried out for a1Gyrator conversion, the image after conversion modulated again by second piece of chaos random phase masks, then
Angle is carried out for a2Gyrator conversion, Jing modulate twice and twice convert after can be obtained by encrypted image U (x ', y ')：
U (x ', y ')=GTa2{GTa1{U0(x0,y0)C1(x1,y1)}C2(x2,y2)} (4)
Wherein, (x ', y ') is the position coordinates at output face；GTa{ } represents angle for the Gyrator conversion of a, its shape
Formula is as follows：
Wherein, U0(x0,y0) and U (x, y) represent respectively input picture and conversion after image；(x0,y0) and (x, y) is respectively
The coordinate of image present position after representing input picture and converting；Sin represents SIN function, and cos represents cosine function；
2) in decrypting process, the image U (x ', y ') after encryption carries out first angle for a2Gyrator inverse transformations, so
Afterwards by the complex conjugate modulation of second piece of chaos random phase masks, it is modulated after image carry out angle again for a1Gyrator
Inverse transformation, finally again by the complex conjugate modulation of first piece of chaos random phase masks, the image after being decrypted：
Wherein, * represents complex conjugate operator.
Of the invention the characteristics of and beneficial effect are：
In the optical image encryption method that the present invention is provided, the use of chaotic key so that this encryption method can be effective
Opposing known plain text attack and chosen -plain attact, and cause key management and transmission to become more convenient.Gyrator angle of transformation
Degree is used as the auxiliary key in encryption process so that the security of this encryption method has obtained further guarantee.
Description of the drawings：
The encryption process schematic diagram of the optical image encryption method that Fig. 1 present invention is provided.In figure：
The ciphering process schematic diagram of a optical image encryption method that () provides for the present invention；
The decrypting process schematic diagram of b optical image encryption method that () provides 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 method encryption；
C () is decrypted image when all keys are correct.
Decrypted image comparison diagram when Fig. 3 has mistake.In figure：
A () is the initial value x2 mistakes of the coupling Logistic chaos systems for controlling second piece of random phase masks, other are close
Decrypted image when key is correct；
B () is the initial value y2 mistakes of the coupling Logistic chaos systems for controlling second piece of random phase masks, other are close
Decrypted image when key is correct；
C () is the mistake of control parameter μ 2 of the coupling Logistic chaos systems for controlling second piece of random phase masks, its
Decrypted image when its key is correct；
(d) be Gyrator translation-angle a1 mistakes, decrypted image when other keys are correct；
(e) be Gyrator translation-angle a2 mistakes, decrypted image when other keys are correct；
There is disappearance decrypted image comparison diagram in Fig. 4.
A () is that the image for obtaining is decrypted from the encryption figure of 12.5% information of disappearance；
B () is that the image for obtaining is decrypted from the encryption figure of 25% information of disappearance；
C () is that the image for obtaining is decrypted from the encryption figure of 50% information of disappearance；
Fig. 5 difference Gaussian noise hypograph comparison diagrams.
A () is that the image for obtaining is decrypted from the encryption figure containing 10% Gaussian noise；
B () is that the image for obtaining is decrypted from the encryption figure containing 10% salt-pepper noise；
C () is that the image for obtaining is decrypted from the encryption figure containing 10% speckle noise；
In accompanying drawing, the list of parts representated by each label is as follows：
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；GT：Gyrator becomes
Change；IGT：Gyrator inverse transformations.
Specific embodiment
The invention provides a kind of optical image encryption method for being converted based on Gyrator and coupling Logistic chaos.
The optical image encryption method that the present invention is provided is based on by the construction for coupling Logistic chaos, the generation of chaotic key
The image encryption and decryption composition of Gyrator conversion.The use of chaotic key so that this encryption method can be effective against known
Plaintext attack and chosen -plain attact, and cause key management and transmission to become more convenient.Gyrator translation-angles as plus
Auxiliary key in decrypting process so that the security of this encryption method has obtained further guarantee.Many experiments show, this
Encryption method has good violence attack, statistical attack, attacked by noise and shearing attack ability.It is described below：
1) construction of Logistic chaos is coupled：Coupling Logistic chaos systems reflect two dimensional Logistic chaos
Penetrate and linked together by a coupling parameter；Compared to single dimensional Logistic chaos system, coupling Logistic is mixed
Ignorant system has bigger parameter space, more preferable pseudo-randomness and can produce more random number sequences.
2) generation of chaotic key：Play two pieces of random phase masks of master key effect respectively by different chaos state modulators
Coupling Logistic chaos systems generate, the initial value and control parameter of chaos system is used as master key；Additionally, Gyrator becomes
Angle is changed as the auxiliary key in encryption process.Because key updating is convenient in encryption process, 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 for being converted based on Gyrator and decryption：(1) in ciphering process, image to be encrypted first by
First piece of chaos random phase masks modulation, then carries out angle for a1Gyrator conversion, the image after conversion is again by second
Block chaos random phase masks are modulated, and then carry out angle for a2Gyrator conversion；(2) in decrypting process, after encryption
Image carries out first angle for a2Gyrator inverse transformations, then by the complex conjugate modulation of second piece of chaos random phase masks,
Image after modulated carries out again angle for a1Gyrator inverse transformations, finally again by first piece of chaos random phase masks
Complex conjugate is modulated.
To make the object, technical solutions and advantages of the present invention clearer, below further is made to embodiment of the present invention
Ground is described in detail.
Embodiment 1
A kind of optical image encryption method for being converted based on Gyrator and coupling Logistic chaos, its encryption process
Schematic diagram is as shown in figure 1, encryption method is become by the construction for coupling Logistic chaos, the generation of chaotic key based on Gyrator
The image encryption for changing and decryption composition.
(1) construction of Logistic chaos is coupled：
In the encryption method that the present invention is provided, Logistic chaos systems are coupled by two dimensional Logistic chaotic maps
Linked together by a coupling parameter；Compared to single dimensional Logistic chaos system, Logistic chaos is coupled
System has bigger parameter space, more preferable pseudo-randomness and can produce more random number sequences.
(2) generation of chaotic key：
In the encryption method that the present invention is provided, two pieces of random phase masks for playing master key effect are joined respectively by different chaos
The coupling Logistic chaos systems of numerical control are generated, and the initial value and control parameter of chaos system is used as master key；Additionally,
Gyrator translation-angles are used as the auxiliary key in encryption process.Because key updating is convenient in encryption process, therefore,
This encryption method can be effective against known plain text attack and chosen -plain attact；Additionally, key management and transmission are also more square
Just.
(3) image encryption for being converted based on Gyrator and decryption：
1) in ciphering process, image to be encrypted is modulated first by first piece of chaos random phase masks, is then carried out
Angle is a1Gyrator conversion, the image after conversion modulated again by second piece of chaos random phase masks, then carries out angle
For a2Gyrator conversion；2) in decrypting process, the image after encryption carries out first angle for a2Gyrator inverse transformations,
Then by the complex conjugate modulation of second piece of chaos random phase masks, it is modulated after image carry out angle again for a1's
Gyrator inverse transformations, finally again by the complex conjugate modulation of first piece of chaos random phase masks.
In sum, the use of chaotic key so that this encryption method can be effective against known plain text attack and selection
Plaintext attack, and cause key management and transmission to become more convenient.Gyrator translation-angles as encryption process in it is auxiliary
Help key so that the security of this encryption method has obtained further guarantee.
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 for being converted based on Gyrator and coupling Logistic chaos, its encryption process
Schematic diagram is as shown in Figure 1.Encryption method is become by the construction for coupling Logistic chaos, the generation of chaotic key based on Gyrator
The image encryption for changing and decryption composition.The specific embodiment of this three part is described in detail respectively below.
(1) construction of Logistic chaos is coupled：
The mathematic(al) representation of the discrete form of dimensional Logistic chaos system is：
xn+1=μ xn(1-xn) (1)
Wherein, xnFor the initial value of chaos system, xn+1For the iteration output valve of chaos system；And as control parameter μ ∈
(3.56,4] when, Logistic systems are in chaos state.
Introduce a coupling parameter ε, wherein meet ε ∈ (- 2,2), then couple Logistic chaos system discrete forms
Mathematic(al) representation is：
xn+1=μ xn(1-xn)+ε(yn-xn) (2)
yn+1=μ yn(1-yn)+ε(xn-yn) (3)
Wherein, xnAnd ynRespectively couple the initial value of Logistic chaos systems, xn+1And yn+1Respectively couple Logistic
The iteration output valve of chaos system.Equally, when control parameter μ ∈ (3.56,4] when, coupling Logistic systems are in chaos shape
State.
(2) generation of chaotic key：
Two pieces of chaos random phase masks play master key effect in encryption method, and Gyrator translation-angles play auxiliary key
Effect.It is situated between in detail with regard to how to generate this two pieces of chaos random phase masks using coupling Logistic chaos systems below
Continue.
The size for assuming the image to be encrypted is M × N number of pixel, then the size of two pieces of chaos random phase masks is also M
× N number of pixel.For the coupling Logistic chaos systems by two groups of different chaos state modulators so as to iteration (M × N)/2 time
Afterwards, two groups of random number sequences X are obtained1={ x '1,x′2,…,x′(M×N)/2, Y1={ y '1,y′2,…,y′(M×N)/2And X2=
{x″1,x″2,…,x″(M×N)/2, Y2=y "1,y″2,…,y″(M×N)/2}；Wherein, x '1,x′2,…,x′(M×N)/2, y '1,y
′2,…,y′(M×N)/2, x "1,x″2,…,x″(M×N)/2With y "1,y″2,…,y″(M×N)/2The iteration of respectively Coupled Chaotic Systems is defeated
Go out value.This two groups of random number sequences are integrated into into respectively form Z of two two-dimensional matrixs1={ 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 are the coordinate of matrix element.Two pieces of chaos random phase masks can be then obtained, its mathematic(al) representation is respectively C1(x1,y1)
=exp (j2 π z 'i,j) and C2(x2,y2)=exp (j2 π z "i,j)；Wherein, (x1,y1) and (x2,y2) it is respectively two pieces of random phases
The coordinate of mask present position, j is imaginary unit, and π is pi.Because chaos random phase mask is by the first of chaos system
Value and control parameter controlling, therefore, the master key of the initial value and control parameter of chaos system as encryption system.Due to master
Key and auxiliary key are all some numerals, therefore, managing and transmit these numerals will become very convenient；Additionally, encryption and decryption
During update these numerals and will also become very convenient.
(3) image encryption for being converted based on Gyrator and decryption：
1) in ciphering process, image U to be encrypted0(x0,y0) modulated by first piece of chaos random phase masks first,
Then angle is carried out for a1Gyrator conversion, the image after conversion modulated again by second piece of chaos random phase masks, then
Angle is carried out for a2Gyrator conversion, Jing modulate twice and twice convert after can be obtained by encrypted image U (x ', y ')：
U (x ', y ')=GTa2{GTa1{U0(x0,y0)C1(x1,y1)}C2(x2,y2)} (4)
Wherein, (x ', y ') is the position coordinates at output face；GTa{ } represents angle for the Gyrator conversion of a, its shape
Formula is as follows：
Wherein, U0(x0,y0) and U (x, y) represent respectively input picture and conversion after image；(x0,y0) and (x, y) is respectively
The coordinate of image present position after representing input picture and converting；Sin represents SIN function, and cos represents cosine function.
2) in decrypting process, the image U (x ', y ') after encryption carries out first angle for a2Gyrator inverse transformations, so
Afterwards by the complex conjugate modulation of second piece of chaos random phase masks, it is modulated after image carry out angle again for a1Gyrator
Inverse transformation, finally again by the complex conjugate modulation of first piece of chaos random phase masks, the image after being decrypted：
Wherein, * represents complex conjugate operator.
In sum, the use of chaotic key so that this encryption method can be effective against known plain text attack and selection
Plaintext attack, and cause key management and transmission to become more convenient.Gyrator translation-angles as encryption process in it is auxiliary
Help key so that the security of this encryption method has obtained further guarantee.
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 some wrong cipher key during correct other keys, shown in decrypted result such as Fig. 3 (a) -3 (e).Thus
It can be seen that, the security of the system can be guaranteed.
Fig. 4 (a) -4 (c) is the decrypted image under encryption figure 12.5%, 25% and 50% information state of disappearance.Fig. 5 (a) -5
C () is encryption figure containing the decrypted image in the case of 10% Gaussian noise, salt-pepper noise and speckle noise.As can be seen here, even if
Encrypted image lacks a part of information or to a certain extent by noise pollution, and the embodiment of the present invention remains able to decrypt necessarily
The original image of quality, demonstrates the feasibility of the system, meets the various needs in practical application.
To the model of each device in addition to specified otherwise is done, the model of other devices is not limited the embodiment of the present invention,
As long as the device of above-mentioned functions can be completed.
It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
Sequence number is for illustration only, does not represent the quality of embodiment.
The foregoing is only presently preferred embodiments of the present invention, not to limit the present invention, all spirit in the present invention and
Within principle, any modification, equivalent substitution and improvements made etc. should be included within the scope of the present invention.
Claims (2)
1. a kind of Gyrator conversion and Coupled Chaotic optical image encryption method, is characterized in that, step is as follows：
1) construction of Logistic chaos is coupled：Two dimensional Logistic chaotic maps are existed by a coupling parameter contact
Together；
2) generation of chaotic key：Play two pieces of random phase masks of master key effect respectively by the coupling of different chaos state modulators
Close Logistic chaos systems to generate, the initial value and control parameter of chaos system is used as master key；Additionally, Gyrator angle of transformation
Degree is used as the auxiliary key in encryption process；
3) image encryption for being converted based on Gyrator and decryption：(1) in ciphering process, image to be encrypted is first by first
Block chaos random phase masks are modulated, and then carry out angle for a1Gyrator conversion, the image after conversion is mixed by second piece again
Ignorant random phase masks modulation, then carries out angle for a2Gyrator conversion；(2) image in decrypting process, after encryption
Angle is carried out first for a2Gyrator inverse transformations, then by the complex conjugate modulation of second piece of chaos random phase masks, Jing is adjusted
Image after system carries out again angle for a1Gyrator inverse transformations, finally again by first piece of chaos random phase masks it is multiple altogether
Yoke is modulated.
2. Gyrator conversion as claimed in claim 1 and Coupled Chaotic optical image encryption method, is characterized in that, a reality
Apply in example and comprise the concrete steps that：
(1) construction of Logistic chaos is coupled：
The mathematic(al) representation of the discrete form of dimensional Logistic chaos system is：
xn+1=μ xn(1-xn) (1)
Wherein, xnFor the initial value of chaos system, xn+1For the iteration output valve of chaos system；And when control parameter μ ∈ (3.56,4]
When, Logistic systems are in chaos state；
Introduce a coupling parameter ε, wherein meet ε ∈ (- 2,2), then couple Logistic chaos system discrete forms mathematics
Expression formula is：
xn+1=μ xn(1-xn)+ε(yn-xn) (2)
yn+1=μ yn(1-yn)+ε(xn-yn) (3)
Wherein, xnAnd ynRespectively couple the initial value of Logistic chaos systems, xn+1And yn+1Respectively couple Logistic chaos
The iteration output valve of system, equally, when control parameter μ ∈ (3.56,4] when, coupling Logistic systems are in chaos state；
(2) generation of chaotic key：
Two pieces of chaos random phase masks play master key effect in encryption method, and Gyrator translation-angles play auxiliary key effect.
The size for assuming the 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 picture
Element.For the coupling Logistic chaos systems by two groups of different chaos state modulators so as to after iteration (M × N)/2 time, obtain
Two groups of random number sequences X1={ x '1,x′2,…,x′(M×N)/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)/2The respectively iteration output valve of Coupled Chaotic Systems,
This two groups of random number sequences are integrated into into respectively form Z of two two-dimensional matrixs1={ 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, under
Mark i, j is the coordinate of matrix element, then can obtain two pieces of chaos random phase masks, and 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) it is respectively two pieces of random phases
The coordinate of position mask present position, j is imaginary unit, and π is pi, because chaos random phase mask is by chaos system
Initial value and control parameter controlling, therefore, the master key of the initial value and control parameter of chaos system as encryption system；
(3) image encryption for being converted based on Gyrator and decryption：
1) in ciphering process, image U to be encrypted0(x0,y0) modulated by first piece of chaos random phase masks first, then
Angle is carried out for a1Gyrator conversion, the image after conversion modulated again by second piece of chaos random phase masks, then carried out
Angle is a2Gyrator conversion, Jing modulate twice and twice convert after can be obtained by encrypted image U (x ', y ')：
U (x ', y ')=GTa2{GTa1{U0(x0,y0)C1(x1,y1)}C2(x2,y2)} (4)
Wherein, (x ', y ') is the position coordinates at output face；GTa{ } represents that the Gyrator that angle is a is converted, and its form is such as
Under：
Wherein, U0(x0,y0) and U (x, y) represent respectively input picture and conversion after image；(x0,y0) and (x, y) represent respectively
The coordinate of image present position after input picture and conversion；Sin represents SIN function, and cos represents cosine function；
2) in decrypting process, the image U (x ', y ') after encryption carries out first angle for a2Gyrator inverse transformations, then by
The complex conjugate modulation of second piece of chaos random phase masks, it is modulated after image carry out angle again for a1Gyrator inversions
Change, finally again by the complex conjugate modulation of first piece of chaos random phase masks, the image after being decrypted：
Wherein, * represents complex conjugate operator.
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| CN108898540A (en) * | 2018-05-23 | 2018-11-27 | 西安理工大学 | Dual image encryption method based on discrete fraction angular transformation and chaology |
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| CN109544435B (en) * | 2018-10-22 | 2023-07-18 | 天津大学 | Gyrater transformation chaotic random phase coding digital image encryption method |
| CN109492414A (en) * | 2018-11-07 | 2019-03-19 | 上海师范大学 | More image encryptions and authentication method based on biometric keys |
| CN109918927A (en) * | 2019-03-04 | 2019-06-21 | 首都师范大学 | A kind of image encryption method and device |
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| CN110516461A (en) * | 2019-08-29 | 2019-11-29 | 首都师范大学 | Multichannel image encryption method, device, storage medium and electronic equipment |
| CN111314048A (en) * | 2020-03-04 | 2020-06-19 | 广东工业大学 | Chaotic secret optical communication system based on double random phase codes |
| CN112364357A (en) * | 2020-10-12 | 2021-02-12 | 天津大学 | Optical image encryption method based on vector decomposition and chaotic phase coding |
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