CN110086953A - The color image encrypting method with Gyrator transformation is decomposed based on QR - Google Patents

The color image encrypting method with Gyrator transformation is decomposed based on QR Download PDF

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CN110086953A
CN110086953A CN201910185874.1A CN201910185874A CN110086953A CN 110086953 A CN110086953 A CN 110086953A CN 201910185874 A CN201910185874 A CN 201910185874A CN 110086953 A CN110086953 A CN 110086953A
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image
obtains
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唐晨
陶珊
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Tianjin University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/14—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using a plurality of keys or algorithms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
    • H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
    • H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
    • H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
    • H04N1/32154—Transform domain methods
    • H04N1/3216—Transform domain methods using Fourier transforms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
    • H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
    • H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
    • H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
    • H04N1/32267—Methods relating to embedding, encoding, decoding, detection or retrieval operations combined with processing of the image
    • H04N1/32272—Encryption or ciphering
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
    • H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
    • H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
    • H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
    • H04N1/32309—Methods relating to embedding, encoding, decoding, detection or retrieval operations in colour image data

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  • Signal Processing (AREA)
  • Multimedia (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Image Processing (AREA)
  • Facsimile Transmission Control (AREA)
  • Two-Way Televisions, Distribution Of Moving Picture Or The Like (AREA)

Abstract

The invention belongs to Digital Image Processing and optical encryption field, and to propose a kind of novel color image encrypting method, this method has biggish key space and higher safety.The present invention is based on QR to decompose the color image encrypting method with Gyrator transformation, and steps are as follows: image encryption part: two color channels of R, G being encoded to complex matrix, gained complex matrix is decomposed into orthonomal matrix Q and upper triangular matrix R two parts through QR；Then Q with R two parts are multiplied after carrying out GT (Gyrator) transformation respectively；Obtained result carries out phase truncation and is encoded to complex matrix with channel B again, and gained complex matrix is decomposed into Q and R two parts through QR again；Then Q with R two parts carry out the image finally encrypted that is multiplied after GT transformation respectively；It is decoded as coding inverse process.Present invention is mainly applied to digital image encryption occasions.

Description

The color image encrypting method with Gyrator transformation is decomposed based on QR
Technical field
The invention belongs to Digital Image Processing and optical encryption field, and in particular to decomposed based on QR and Gyrator is converted Color image encrypting method.
Background technique
Image is one of important carrier of information, how to guarantee safety of the image in transmission process, researchers are in recent years Do method to propose many solutions, sum up and can be mainly divided into two major classes: one kind is that image information is hidden, i.e., will be secret Image is hidden into some way in specific carrier, is allowed to be hidden, such as digital watermarking；Another kind of is the side of cryptography Given image encryption not identifying original graph by method by certain algorithm, rule at a width noise like image Picture, to achieve the purpose that protect original image.Color image includes information more more than gray level image, since color image has There is red, green, blue three-component, if encrypted respectively to three components, encryption system will certainly be made complicated, therefore single channel is color Color image encryption system becomes the primary study problem in image encryption.Existing single channel color image encryption has Yang etc. What people proposed is transformed into color image in the space HSI, carries out quarter-phase random coded skill as original image to be encrypted to I component Art encrypts it；One width color image encoding is that gray level image carries out random phase encoding again with chromatic grating by Gao et al. Technology encrypts it.
Matrix decomposition is applied widely in image procossing research, and wherein singular value decomposition (svd decomposition) is also always It is research hotspot, matrix decomposition is three parts by singular value decomposition, it is assumed that A is the matrix of M*N, the singular value decomposition of matrix A Are as follows: A=USVT, wherein T is the operation of matrix transposition.QR is decomposed and a kind of method of matrix decomposition, by matrix decomposition at one Orthonomal matrix Q and upper triangular matrix R, wherein R is n × n upper triangular matrix, and Q is the unitary matrice of a n × n:
[Q, R]=qr (A)
A=Q × R
Singular value decomposition ratio QR decomposition complexity is big, and matrix decomposition used in the invention is QR decomposition.GT (Gyrator) transformation is a kind of popularizing form of Fourier transformation, the mathematical expression of the two-dimentional Gyrator transformation of function f (x, y) Formula are as follows:
Gα{ f (x, y) }=f'(x', y')=∫ ∫ f (x, y) Kα(x,y,x',y')dxdy
Its transformation kernel are as follows:
Wherein, (x, y) is the coordinate of input plane, and (x', y') is output plane coordinate.
The inverse transformation mathematic(al) representation of the two-dimentional Gyrator transformation of function f (x, y) are as follows:
G-αF'(x', y') } and=f (x, y)=∫ ∫ f'(x', y') K-α(x,y,x',y')dx'dy'
It is identical transformation as α=0；When α=pi/2, the Fourier transformation of pi/2 is rotated for coordinate；As α=π, it is The inverse transformation of Gyrator transformation；When α=3 pi/2, the inverse Fourier transform of pi/2 is rotated for coordinate；When rotation angle [alpha] is other When value, its transformation kernel Kα(xi,yi,x0,y0) there are constant amplitude and hyperbolic phase structure.
Summary of the invention
In order to overcome the deficiencies of the prior art, the present invention is directed to propose a kind of novel color image encrypting method, this method With biggish key space and higher safety.The present invention is based on QR to decompose the color image encryption with Gyrator transformation Method, steps are as follows:
(1) image encryption part: color image to be encrypted is decomposed into R, tri- Color Channels of G, B first；Then by R, G Two color channels are encoded to complex matrix, and gained complex matrix is decomposed into orthonomal matrix Q and upper triangular matrix R two through QR Point；Then Q with R two parts are multiplied after carrying out GT (Gyrator) transformation respectively；It is logical with B again that obtained result carries out phase truncation Road is encoded to complex matrix, and gained complex matrix is decomposed into Q and R two parts through QR again；Then Q and R two parts carry out GT transformation respectively Be multiplied the image finally encrypted afterwards；
(2) image decryption part:, which obtaining two parts, carries out after the image of encryption is multiplied with key and respectively GT transformation Inverse transformation；Acquired results take imaginary part to operate to obtain the B color channel of decrypted image after being multiplied, and take real part operation and two keys Two parts are obtained after being multiplied respectively and carry out the inverse transformation of GT transformation respectively；Acquired results take imaginary part to operate and are solved after being multiplied The G Color Channel of close image takes real part to operate to obtain the R Color Channel of decrypted image, and by R, tri- Color Channels of G, B are integrated into Color image after being decrypted together.
Specific step is as follows:
Step 1: color image f to be encrypted being decomposed into tri- Color Channel f of RGB firstR, fGAnd fB, then by fRWith fGChannel coding is complex matrix I:
I=fr+i·fg
Wherein i is imaginary unit.
Step 2: QR decomposition being carried out to obtained complex matrix I, obtains Q1、R1, and respectively to Q1、R1Carry out α rank and β rank GT transformation, obtains g1And g2:
g1=G α (Q1)
g2=Gβ(R1)
First key g has been obtained simultaneously11And g22:
g11=1/g2
g22=1/g1
Step 3: by g1And g2The laggard row amplitude that is multiplied is truncated and phase truncation obtains second key p1And X1, indicate are as follows:
p1=AT (g1×g2)
X1=PT (g1×g2)
Step 4: the X that will be obtained after phase truncation1And fbForm I2, indicate are as follows:
I2=X1+i·fb
Step 5: to I2QR decomposition is carried out, Q is obtained2、R2, and respectively to Q2、R2The GT transformation for carrying out α rank and β rank, obtains g3 And g4:
g3=Gα(Q2)
g4=Gβ(R2)
Step 6: by g3And g4Multiplication obtains encrypted image X2, indicate are as follows:
X2=g3×g4
The 4th and the 5th key g are obtained simultaneously33And g44:
g33=1/g4
g44=1/g3
Wherein Gα() indicates α rank GT transformation；
Decrypting process is as follows:
Step 1: by image to be decrypted respectively with key g33And g44It is multiplied, obtains g333And g444R2, it is expressed as follows:
g333=X2×g33
g444=X2×g44
Step 2: to obtained g333And g444The GT for being-α and-β respectively is converted, and obtains Q22And R22:
Q22=G-α(g333)
R22=G-β(g444)
Step 3: by Q22And R22Real part is taken after multiplication and imaginary part is taken to operate, and obtains X11And fbb:
X11=real (Q22×R22)
fbb=imag (Q22×R22)
Step 4: by X11With first key p1After multiplication respectively with key g11And g22Multiplication obtains g111And g222:
g111=(X11×p1)×g11
g222=(X11×p1)×g22
Step 5: by g111And g222The GT for being-α and-β respectively is converted, and obtains Q11And R11:
Q11=G-α(g111)
R11=G-β(g222)
Step 6: the Q that will be obtained11And R11Real part is taken after multiplication and imaginary part is taken to operate, and obtains frrAnd fgg, it is expressed as follows:
frr=real (Q11×R11)
fgg=imag (Q11×R11)
Step 7: three Color Channels after decryption being combined, the image after being decrypted.
The features of the present invention and beneficial effect are:
Similitude is small between encrypted image and original image, and encrypted image is horizontal again, in vertical and diagonal direction Correlation is small between adjacent pixel.
Detailed description of the invention:
Fig. 1 is the image of web encryption；
Fig. 2 is encrypted image；
Fig. 3 is the image decrypted；
Fig. 4 flow chart of the present invention.
Specific embodiment
The present invention is based on QR to decompose the color image encrypting method with Gyrator transformation, and steps are as follows:
(1) image encryption part: color image to be encrypted is decomposed into R, tri- Color Channels of G, B first；Then by R, G Two color channels are encoded to complex matrix, and gained complex matrix is decomposed into orthonomal matrix Q and upper triangular matrix R two through QR Point；Then Q with R two parts are multiplied after carrying out GT transformation respectively；Obtained result carries out phase truncation and is encoded to again with channel B again Matrix, gained complex matrix are decomposed into Q and R two parts through QR again；Then Q with R two parts are multiplied to obtain after carrying out GT transformation respectively The image finally encrypted；
(2) image decryption part:, which obtaining two parts, carries out after the image of encryption is multiplied with key and respectively GT transformation Inverse transformation；Acquired results take imaginary part to operate to obtain the B color channel of decrypted image after being multiplied, and take real part operation and two keys Two parts are obtained after being multiplied respectively and carry out the inverse transformation of GT transformation respectively；Acquired results take imaginary part to operate and are solved after being multiplied The G Color Channel of close image takes real part to operate to obtain the R Color Channel of decrypted image, and by R, tri- Color Channels of G, B are integrated into Color image after being decrypted together.
Next specific example is combined, present invention be described in more detail.
It is proposed by the present invention based on QR decompose and Gyrator transformation multicolor image encryption algorithm to a width color image into Row encryption, the specific steps are as follows:
Step 1: color image f to be encrypted being decomposed into tri- Color Channel f of RGB firstR, fGAnd fB, then by fRWith fGChannel coding is complex matrix I:
I=fr+i·fg
I is imaginary unit.
Step 2: QR decomposition being carried out to obtained complex matrix I, obtains Q1、R1, and respectively to Q1、R1Carry out α rank and β rank GT transformation, obtains g1And g2:
g1=Gα(Q1)
g2=Gβ(R1)
Wherein, Gα() indicates that α rank GT transformation experimental section α takes 0.3 π, β to take 0.4 π.
First key g has been obtained simultaneously11And g22:
g11=1/g2
g22=1/g1
Step 3: by g1And g2The laggard row amplitude that is multiplied is truncated and phase truncation obtains second key p1And X1, indicate are as follows:
p1=AT (g1×g2)
X1=PT (g1×g2)
Step 4: the X that will be obtained after phase truncation1And fbForm I2, indicate are as follows:
I2=X1+i·fb
Step 5: to I2QR decomposition is carried out, Q is obtained2、R2, and respectively to Q2、R2The GT transformation for carrying out α rank and β rank, obtains g3 And g4:
g3=Gα(Q2)
g4=Gβ(R2)
Wherein Gα() indicates α rank GT transformation, and experimental section α takes 0.3 π, β to take 0.4 π.
Step 6: by g3And g4Multiplication obtains encrypted image X2, indicate are as follows:
X2=g3×g4
The 4th and the 5th key g are obtained simultaneously33And g44:
g33=1/g4
g44=1/g3
Decrypting process is as follows:
Step 1: by image to be decrypted respectively with key g33And g44It is multiplied, obtains g333And g444 R2, it is expressed as follows:
g333=X2×g33
g444=X2×g44
Step 2: to obtained g333And g444The GT for being-α and-β respectively is converted, and obtains Q22And R22:
Q22=G-α(g333)
R22=G-β(g444)
Step 3: by Q22And R22Real part is taken after multiplication and imaginary part is taken to operate, and obtains X11And fbb:
X11=real (Q22×R22)
fbb=imag (Q22×R22)
Step 4: by X11With first key p1After multiplication respectively with key g11And g22Multiplication obtains g111And g222:
g111=(X11×p1)×g11
g222=(X11×p1)×g22
Step 5: by g111And g222The GT for being-α and-β respectively is converted, and obtains Q11And R11:
Q11=G-α(g111)
R11=G-β(g222)
Step 6: the Q that will be obtained11And R11Real part is taken after multiplication and imaginary part is taken to operate, and obtains frrAnd fgg, it is expressed as follows:
frr=real (Q11×R11)
fgg=imag (Q11×R11)
Step 7: three Color Channels after decryption being combined, the image after being decrypted.
For the validity of verification method, experimental results.
Fig. 1 is image to be encrypted, and Fig. 2 is encrypted image, and Fig. 3 is the image decrypted, obtained decrypted image Similitude between original image is 0.9880, can verify the feasibility of this method.Table 1 the result is that encrypted image distinguish In correlations diagonal, horizontal, on three directions of vertical direction between adjacent pixel, it can be seen that between three direction adjacent pixels Correlation all very littles, illustrate the multilated of the original pixel of encrypted image, cannot get original image and obtain useful letter Breath.
Correlation of 1 encrypted image of table on horizontal, vertical and diagonal three directions between adjacent pixel
CC
Diagonally -0.0034 -0.0047 -0.0013 -0.0021 -0.0017 -0.0037
Vertically -0.0033 -0.0027 -0.0045 -0.0036 -0.0044 -0.0032
It is horizontal -0.0029 -0.0027 -0.0037 -0.0043 -0.0021 -0.0044
It will be appreciated by those skilled in the art that attached drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention Serial number is for illustration only, does not represent the advantages or disadvantages of the embodiments.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.

Claims (2)

1. a kind of color image encrypting method decomposed based on QR and Gyrator is converted, characterized in that steps are as follows:
(1) image encryption part: color image to be encrypted is decomposed into R, tri- Color Channels of G, B first；Then by R, G two Color channel is encoded to complex matrix, and gained complex matrix is decomposed into orthonomal matrix Q and upper triangular matrix R two parts through QR； Then Q with R two parts are multiplied after carrying out GT (Gyrator) transformation respectively；Obtained result carries out phase truncation and compiles again with channel B Code is complex matrix, and gained complex matrix is decomposed into Q and R two parts through QR again；Then Q and R two parts carry out phase after GT transformation respectively It is multiplied to the image finally encrypted；
(2) image decryption part: the inversion for obtaining two parts after the image of encryption is multiplied with key and converting respectively It changes；Acquired results take imaginary part to operate to obtain the Color Channel of decrypted image after being multiplied, and real part operation is taken to distinguish phase with two keys The inverse transformation for obtaining two parts after multiplying and being converted respectively；Acquired results take imaginary part to operate to obtain decrypted image after being multiplied Color Channel takes real part to operate to obtain the Color Channel of decrypted image, will, three Color Channels are integrated together and are decrypted Color image afterwards.
2. the color image encrypting method with Gyrator transformation is decomposed based on QR as described in claim 1, characterized in that tool Steps are as follows for body:
Step 1: color image f to be encrypted being decomposed into tri- Color Channel f of RGB firstR, fGAnd fB, then by fRAnd fGIt is logical Road is encoded to complex matrix I:
I=fr+i·fg
Wherein i is imaginary unit.
Step 2: QR decomposition being carried out to obtained complex matrix I, obtains Q1、R1, and respectively to Q1、R1The GT for carrying out α rank and β rank becomes It changes, obtains g1And g2:
g1=Gα(Q1)
g2=Gβ(R1)
First key g has been obtained simultaneously11And g22:
g11=1/g2
g22=1/g1
Step 3: by g1And g2The laggard row amplitude that is multiplied is truncated and phase truncation obtains second key p1And X1, indicate are as follows:
p1=AT (g1×g2)
X1=PT (g1×g2)
Step 4: the X that will be obtained after phase truncation1And fbForm I2, indicate are as follows:
I2=X1+i·fb
Step 5: to I2QR decomposition is carried out, Q is obtained2、R2, and respectively to Q2、R2The GT transformation for carrying out α rank and β rank, obtains g3And g4:
g3=Gα(Q2)
g4=Gβ(R2)
Step 6: by g3And g4Multiplication obtains encrypted image X2, indicate are as follows:
X2=g3×g4
The 4th and the 5th key g are obtained simultaneously33And g44:
g33=1/g4
g44=1/g3
Wherein Gα() indicates α rank GT transformation；
Decrypting process is as follows:
Step 1: by image to be decrypted respectively with key g33And g44It is multiplied, obtains g333And g444R2, it is expressed as follows:
g333=X2×g33
g444=X2×g44
Step 2: to obtained g333And g444The GT for being-α and-β respectively is converted, and obtains Q22And R22:
Q22=G-α(g333)
R22=G-β(g444)
Step 3: by Q22And R22Real part is taken after multiplication and imaginary part is taken to operate, and obtains X11And fbb:
X11=real (Q22×R22)
fbb=imag (Q22×R22)
Step 4: by X11With first key p1After multiplication respectively with key g11And g22Multiplication obtains g111And g222:
g111=(X11×p1)×g11
g222=(X11×p1)×g22
Step 5: by g111And g222The GT for being-α and-β respectively is converted, and obtains Q11And R11:
Q11=G-α(g111)
R11=G-β(g222)
Step 6: the Q that will be obtained11And R11Real part is taken after multiplication and imaginary part is taken to operate, and obtains frrAnd fgg, it is expressed as follows:
frr=real (Q11×R11)
fgg=imag (Q11×R11)
Step 7: three Color Channels after decryption being combined, the image after being decrypted.
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CN112188119A (en) * 2020-09-15 2021-01-05 西安万像电子科技有限公司 Image data transmission method and device and computer readable storage medium

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