CN107770406A - Image encryption method and device based on the conversion of multi-parameter fractional order and semi-tensor product - Google Patents
Image encryption method and device based on the conversion of multi-parameter fractional order and semi-tensor product Download PDFInfo
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- 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
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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
- H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
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- 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
- H04N1/32203—Spatial or amplitude domain methods
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- 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
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- 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
- H04N1/44—Secrecy systems
- H04N1/448—Rendering the image unintelligible, e.g. scrambling
- H04N1/4486—Rendering the image unintelligible, e.g. scrambling using digital data encryption
Abstract
The embodiments of the invention provide the image encryption method and device based on the conversion of multi-parameter fractional order and semi-tensor product.Method includes：The pixel of encrypted image is treated, changes the position of its pixel using Scrambling Matrix, obtains spatial domain scramble image；Phase code is carried out to the spatial domain scramble image according to preset rules and Multiple-Parameter Discrete Fractional rank converts, obtains changing image；One dimension of generation is the factor of the dimension of the changing image and the square formation not equal to 1, as cipher key matrix；By the changing image, uniformly it is divided into multiple submatrixs according to the dimension of the cipher key matrix；Cipher key matrix is carried out to semi-tensor product computing with each submatrix respectively, obtains the operation result of each submatrix；The operation result of the multiple submatrix is integrated, obtains encrypted image.Combination of embodiment of the present invention spatial domain scramble, score field conversion and semi-tensor product theoretical log word image are encrypted, and improve encrypted image confrontation statistical attack, the ability that attacked by noise and pixel are lost.
Description
Technical field
The present invention relates to image encryption technical field, more particularly to what is accumulated based on the conversion of multi-parameter fractional order and semi-tensor
Image encryption method and device.
Background technology
With the rapid development of Internet technology and image processing techniques, digital picture can be convenient, fast on network
Ground transmits, but this also brings image information security hidden trouble simultaneously.It is and very high due to having between the pixel of digital picture
The features such as correlation, redundancy, traditional text based encryption method are no longer desirable for the encryption of digital picture.Numeral
Image encryption technology turns into the technology that a practicality urgently develops again.
Existing image encryption method is broadly divided into two major classes：AES based on spatial domain and the encryption based on transform domain
Algorithm.
Resume image based on spatial domain is a pseudo-random sequence to be generated by a kind of method, based on the pseudorandom sequence
Row carry out disorder processing to digital picture, so as to obtain close figure；Image encryption method based on transform domain is to pass through a kind of mathematics
Conversion, is a linear representation being made up of one group of mutually orthogonal matrix by digital service unit to be encrypted, by the table
Pixel value of the coefficient of each matrix as each pixel in encrypted image up in formula, so as to obtain encrypted image.
However, the existing image encryption method based on spatial domain only changes the position of pixel, original pixel is not changed
Value, causes security often not high.Moreover, the obtained close figure of spatial domain scramble in transmitting procedure by attacked by noise or part
Close figure loses the quality that all can seriously reduce decrypted image.The mathematic(al) manipulation mode of image encryption method based on transform domain may
In the presence of periodically, a kind of mathematic(al) manipulation mode is caused multiple decruption keys to be present, while selectable mathematic(al) manipulation mode is less,
So that decryption figure is easily cracked, the safe transmission of digital picture can not be ensured.
The content of the invention
The purpose of the embodiment of the present invention is to provide the image encryption side based on the conversion of multi-parameter fractional order and semi-tensor product
Method and device, to realize safely and effectively encrypting digital image.Concrete technical scheme is as follows：
Image encryption method provided by the invention based on the conversion of multi-parameter fractional order and semi-tensor product, methods described bag
Include：
The pixel of encrypted image is treated, changes the position of its pixel using Scrambling Matrix, obtains spatial domain scramble image；
Phase code is carried out to the spatial domain scramble image according to preset rules and Multiple-Parameter Discrete Fractional rank converts, is obtained
Changing image；
One dimension of generation is the factor of the changing image dimension and the square formation not equal to 1, as cipher key matrix；
By the changing image, uniformly it is divided into multiple submatrixs according to the dimension of the cipher key matrix；
Cipher key matrix is carried out to semi-tensor product computing with each submatrix respectively, obtains the operation result of each submatrix；
The operation result of the multiple submatrix is integrated, obtains encrypted image.
Further, it is described that phase code and discrete point of multi-parameter are carried out to the spatial domain scramble image according to preset rules
Number rank conversion, obtains changing image, including：
The dimension matrix equal with the dimension of the spatial domain scramble image is generated, as phase mask；
The length vector equal with the row dimension of the spatial domain scramble image is generated, and is made with the vectorial each element
For parameter, Multiple-Parameter Discrete Fractional rank operator is generated；
Spatial domain scramble image is handled according to the following formula, obtains changing image：
Wherein I is the spatial domain scramble image, and O is the changing image, and j is complex unit, and π is pi, and α is described
Phase mask,For Multiple-Parameter Discrete Fractional rank operator.
Further, it is described that cipher key matrix is carried out to semi-tensor product computing with each submatrix respectively, obtain every sub- square
The operation result of battle array, including：
Cipher key matrix is carried out to semi-tensor product computing according to the following formula with each submatrix respectively, obtains the fortune of each submatrix
Calculate result：
S is the cipher key matrix in formula,Operator is accumulated for semi-tensor, Q is the submatrix, Rowi(S) for matrix S's
I-th row, Coli(Q) it is matrix Q the i-th row, N is the row dimension of the submatrix, and M is the dimension of the cipher key matrix.
Further, encrypted image is treated described, before the position for changing its pixel using Scrambling Matrix, in addition to：
Pixel value using four summits of image to be encrypted enters to the four systemses state variable of default chaos system
Row initialization；
Chaos system described in iteration, the four systemses of each iteration output are preserved since present count contents iteration
The numerical value of state variable；
Using the numerical value of preservation, the pseudo-random sequence of the first number preset length is generated, stops iteration；
To each pseudo-random sequence, by recording the size sequence of each element in the pseudo-random sequence, generation
Pseudorandom address sequence；
By two of the generation pseudorandom address sequences, respectively as the row index sequence of Scrambling Matrix nonzero element
With row index series to generate a new Scrambling Matrix, until the second number Scrambling Matrix of generation.
Further, it is described that phase code and discrete point of multi-parameter are carried out to the spatial domain scramble image according to preset rules
Number rank conversion, obtains changing image, in addition to：
Generate two dimensions matrix equal with the dimension of the spatial domain scramble image, respectively as first phase mask with
Second phase mask；
Two length vector equal with the row dimension of the spatial domain scramble image is generated, is utilized respectively in two vectors
Element generates the first Multiple-Parameter Discrete Fractional rank operator and the second Multiple-Parameter Discrete Fractional rank operator as parameter；
Phase is carried out to the spatial domain scramble image using first phase mask and the first Multiple-Parameter Discrete Fractional rank operator
Coding and the conversion of Multiple-Parameter Discrete Fractional rank, obtain transfer image acquisition；
Phase code is carried out to the transfer image acquisition using second phase mask and the second Multiple-Parameter Discrete Fractional rank operator
Converted with Multiple-Parameter Discrete Fractional rank, obtain changing image.
Image encrypting apparatus based on the conversion of multi-parameter fractional order and semi-tensor product, including：
Scramble module, for treating the pixel of encrypted image, change the position of its pixel using Scrambling Matrix, obtain spatial domain
Scramble image；
Conversion module, for carrying out phase code and Multiple-Parameter Discrete Fractional rank to the spatial domain scramble image according to default
Conversion, obtains changing image；
Cipher key module, for generating the square formation that a dimension is the factor of the changing image dimension, as cipher key matrix；
Submatrix module, for by the changing image, being uniformly divided into more sub- squares according to the dimension of the cipher key matrix
Battle array；
Semi-tensor volume module, for cipher key matrix to be carried out to semi-tensor product computing with each submatrix respectively, obtain each
The operation result of submatrix；
Module is integrated, the operation result of the multiple submatrix is integrated, obtains encrypted image.
Further, the conversion module, including：
Mask cell, the matrix equal with the dimension of the spatial domain scramble image for generating a dimension, as phase
Mask；
Operator unit, for generating the length vector equal with the dimension of the spatial domain scramble image, and with this to
The each element of amount generates Multiple-Parameter Discrete Fractional rank operator as parameter；
Converter unit, spatial domain scramble image is handled according to the following formula, obtains changing image：
I is the spatial domain scramble image in formula, and O is the changing image, and j is complex unit, and π is pi, and α is described
Phase mask,For Multiple-Parameter Discrete Fractional rank operator.
Further, the semi-tensor volume module, is specifically used for：
Cipher key matrix is carried out to semi-tensor product computing according to the following formula with each submatrix respectively, obtains the fortune of each submatrix
Calculate result：
S is the cipher key matrix in formula,Operator is accumulated for semi-tensor, Q is the submatrix, Rowi(S) for matrix S's
I-th row, Coli(Q) it is matrix Q the i-th row, N is the row dimension of the submatrix, and M is the dimension of the cipher key matrix.
Further, described device, in addition to：
Initialization module, the pixel value for four summits using image to be encrypted is to four of default chaos system
System state variables is initialized；
Iteration module, for chaos system described in iteration, each iteration output is preserved since present count contents iteration
The four systemses state variable numerical value；
Pseudo-random sequence module, for utilizing the numerical value preserved, the pseudorandom of the first number preset length of generation
Sequence；
Address sequence module, for each pseudo-random sequence, by recording each member in the pseudo-random sequence
The size sequence of element, generates pseudorandom address sequence；
Scrambling Matrix module, it is non-respectively as Scrambling Matrix for by two of the generation pseudorandom address sequences
The row index sequence and row index series of neutral element are to generate a new Scrambling Matrix, until the second number scramble square of generation
Battle array.
Further, the conversion module, including：
Phase mask unit, the matrix equal with the dimension of the spatial domain scramble image for generating two length, respectively
As first phase mask and second phase mask；
Multiple-Parameter Discrete Fractional rank operator module, two length of generation are equal with the row dimension of the spatial domain scramble image
Vector, the element in two vectors is utilized respectively as parameter, generates the first Multiple-Parameter Discrete Fractional rank operator and more than second ginsengs
Number Discrete Fractional operator；
Transitional module, for utilizing first phase mask and the first Multiple-Parameter Discrete Fractional rank operator to the spatial domain scramble
Image carries out phase code and the conversion of Multiple-Parameter Discrete Fractional rank, obtains transfer image acquisition；
Conversion module, for utilizing second phase mask and the second Multiple-Parameter Discrete Fractional rank operator to the transfer image acquisition
Phase code and the conversion of Multiple-Parameter Discrete Fractional rank are carried out, obtains changing image.
Image encryption method and device provided in an embodiment of the present invention based on the conversion of multi-parameter fractional order and semi-tensor product,
Computing can be accumulated by phase code and semi-tensor so that the information of each pixel is divided into some in image to be encrypted
It is stored in respectively in all pixels point in close figure, even if interference or lost part pixel of the close figure by noise signal, its shadow
Sound can also be shared on all pixels point in decryption figure after decryption, enhances close figure and anti-noise signal and pixel are lost
Ability.Image encryption after the scramble of spatial domain is projected into score field, and combines semi-tensor product computing, has been widened in ciphering process
The space of parameter selection, the periodicity of score field conversion is avoided, add the ability of decrypted image confrontation statistical attack, improve
The security of Digital Image Transmission.Certainly, implement any product of the present invention or method must be not necessarily required to reach simultaneously with
Upper described all advantages.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is the required accompanying drawing used in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with
Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is the image encryption method provided in an embodiment of the present invention based on the conversion of multi-parameter fractional order and semi-tensor product
A kind of schematic flow sheet；
Fig. 2 is a kind of schematic flow sheet of Scrambling Matrix generation method provided in an embodiment of the present invention；
Fig. 3 is the image encrypting apparatus provided in an embodiment of the present invention based on the conversion of multi-parameter fractional order and semi-tensor product
A kind of structural representation；
Fig. 4 a are sample picture A pixel distribution histogram；
Fig. 4 b are sample picture B pixel distribution histogram；
Fig. 4 c are the pixel distribution histogram for the encrypted image that sample picture A is obtained after the embodiment of the present invention is encrypted；
Fig. 4 d are the pixel distribution histogram for the encrypted image that sample picture B is obtained after the embodiment of the present invention is encrypted；
The horizontal pixel that Fig. 5 a are sample picture C is distributed scatter diagram；
Fig. 5 b are that the horizontal pixel for the encrypted image that sample picture C is obtained after the embodiment of the present invention is encrypted is distributed scatterplot
Figure；
Fig. 5 c are sample picture C longitudinal pixel distribution scatter diagram；
Fig. 5 d are the longitudinal pixel distribution scatterplot for the encrypted image that sample picture C is obtained after the embodiment of the present invention is encrypted
Figure；
Fig. 5 e are sample picture C diagonal pixel distribution scatter diagram；
Fig. 5 f are the diagonal pixel point for the encrypted image that sample picture C is obtained after the embodiment of the present invention is encrypted
Cloth scatter diagram.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, rather than whole embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other under the premise of creative work is not made
Embodiment, belong to the scope of protection of the invention.
Referring to Fig. 1, Fig. 1 show the figure provided in an embodiment of the present invention based on the conversion of multi-parameter fractional order and semi-tensor product
As a kind of schematic flow sheet of encryption method, may comprise steps of：
S101, the pixel of encrypted image is treated, change the position of its pixel using Scrambling Matrix, obtain spatial domain scramble figure
Picture.
Wherein, the Scrambling Matrix can be the matrix of default one or one group fixation, or pass through specific method
One or one group of matrix of generation.Change the position of its pixel using Scrambling Matrix, can change in image to be encrypted to own
The position of pixel, or only change the position of partial pixel in image to be encrypted.
In the present embodiment, in the case where image to be encrypted is not square formation, by adding frame to image to be encrypted
Mode, it is changed into square formation.
In a kind of preferable implementation, the pixel of encrypted image is treated, changes the position of its pixel using Scrambling Matrix
Put, obtain spatial domain scramble image, including：
The pixel of every a line of encrypted image is treated, changes the position of its pixel using different Scrambling Matrixes, obtained
Cross scramble image；To the pixel of each row of transition scramble image, change the position of its pixel using different Scrambling Matrixes, obtain
To spatial domain scramble image.
From the implementation, it can fully change the position of each pixel of image to be encrypted, increase encrypted image
Complexity, improve decryption difficulty.
S102, phase code is carried out to the spatial domain scramble image according to preset rules and Multiple-Parameter Discrete Fractional rank becomes
Change, obtain changing image.
In a kind of optional implementation, phase code and more is carried out to the spatial domain scramble image according to preset rules
Parameter discrete fractional order converts, including：
The dimension matrix equal with the dimension of the spatial domain scramble image is generated, as phase mask α；Generation one
The length vector equal with the row dimension of the spatial domain scramble image, and using the vectorial each element as parameter, generate join more
Number Discrete Fractional operatorSpatial domain scramble image is handled according to the following formula, obtains changing image：
I is spatial domain scramble image in formula, and O is changing image, and j is complex unit, and π is pi.
In a kind of preferable implementation, phase code and more is carried out to the spatial domain scramble image according to preset rules
Parameter discrete fractional order converts, including：
Two dimensions matrix equal with the dimension of spatial domain scramble image is generated, respectively as first phase mask α1With
Two phase mask α2；Two length vector equal with the row dimension of spatial domain scramble image is generated, is utilized respectively in two vectors
Element as parameter, generate the first Multiple-Parameter Discrete Fractional rank operatorWith the second Multiple-Parameter Discrete Fractional rank operatorProfit
Use α1WithPhase code is carried out to spatial domain scramble image I according to the following formula and Multiple-Parameter Discrete Fractional rank converts, obtains transition figure
As O '：
Recycle α2WithTransfer image acquisition O ' carry out phase codes and Multiple-Parameter Discrete Fractional rank are converted according to the following formula, obtained
To changing image O：
From the implementation, can be converted by phase code twice and Multiple-Parameter Discrete Fractional rank so as to be encrypted
The pixel value of each pixel is more uniformly divided into some and is stored in respectively all in changing image in image
In pixel, the correlation between pixel in encrypted image is reduced.
S103, one dimension of generation are the factor of the changing image dimension, and are not equal to 1 square formation, as key square
Battle array.
In the present embodiment, from the factor of the dimension of the changing image in addition to the dimension of 1 and changing image itself, choosing
One dimension as the cipher key matrix.
It is exemplary, it is assumed that changing image is the square formation of 64 ranks, removed in 64 factor 1 and 64 also have 2,4,8,
16th, 32, cipher key matrix can be a kind of square formation in 2 ranks, 4 ranks, 8 ranks, 16 ranks, 32 rank square formations.
S104, by the changing image, uniformly it is divided into multiple submatrixs according to the dimension of the cipher key matrix.
In the present embodiment, changing image is uniformly divided into a square submatrix for the dimension of cipher key matrix.
Exemplary, it is assumed that changing image is a 4 rank square formations, and cipher key matrix is 2 rank square formations, by changing image according to such as
Mode shown in lower is evenly dividing as 4 submatrixs：
S105, cipher key matrix is carried out to semi-tensor product computing with each submatrix respectively, obtains the computing of each submatrix
As a result.
In the present embodiment, cipher key matrix is carried out to semi-tensor product computing according to the following formula with each submatrix respectively, obtained
Result after each submatrix computing：
S is cipher key matrix in formula,Operator is accumulated for semi-tensor, Q is submatrix, Rowi(S) the i-th row for being matrix S,
Coli(Q) it is matrix Q the i-th row, N is the row dimension of submatrix, and M is the dimension of cipher key matrix.
S106, the operation result of the multiple submatrix is integrated, obtains encrypted image.
In the present embodiment, the operation result of the multiple submatrix is integrated, obtains encrypted image, referred to：Will
Submatrix of the operation result of all submatrixs as encrypted image, is combined into encrypted image.
Exemplary, it is assumed that one shares the operation result of 16 submatrixs, respectively A1、A2、A3…A16, by 16 computings
As a result it is combined into encrypted image according to mode as follows：
It can specifically be used for the Scrambling Matrix used in above-mentioned embodiment illustrated in fig. 1, in the embodiment of the present invention as follows
Mode obtains, as shown in Fig. 2 comprising the following steps：
S201, the pixel value using four summits of image to be encrypted become to the four systemses state of default chaos system
Amount is initialized.
In the present embodiment, from chaos system as follows：
Wherein a, b, c, r be system control parameter, x, y, z, w be system state variable.It is described to utilize figure to be encrypted
The pixel value on four summits of picture initializes to the four systemses state variable of default chaos system, can be by four
The pixel value on summit directly respectively as x, y, z, w initial value, or can be the pixel value on four summits after treatment
Respectively as x, y, z, w initial value.
Exemplary, it is assumed that the width of image to be encrypted is K, and the pixel value on four summits is respectively P1、P2、 P3、P4, can
Directly to make x0=P1,、y0=P2、z0=P3、w0=P4To initialize the chaos system, or x can also be made0=P1,/K、y0
=P2/K、z0=P3/K、w0=P4/ K is to initialize the chaos system.
S202, chaos system described in iteration, described the four of each iteration output is preserved since present count contents iteration
The numerical value of individual system state variables.
Because the output result of the iteration of the previous fixed number contents of the chaos system has periodically, in order to avoid the cycle
Property influence the ability of encrypted image resistance statistical attack, the iteration that only preserves since present count contents iteration of the present invention is defeated
Go out.
In the present embodiment, x, y, z, w value that each iteration since default contents iteration is exported, preserve respectively
In vectorial X, Y, Z, W.
S203, using the numerical value of preservation, the pseudo-random sequence of the first number preset length is generated, stops iteration.
In the present embodiment, the number element equal with preset length is selected from tetra- vectors of X, Y, Z, W every time, it is same
Individual element will not repeatedly be chosen.To each element selected, handled according to the following formula, using obtained result as sequence
Element, generate pseudo-random sequence：
ti=((| ei|-|_i_|×1016)modL
Wherein eiFor i-th of element of selection, _i_ for the integer part for i-th of the element chosen, L is preset length, ti
For the result obtained after i-th of element processing of selection.
Exemplary, it is assumed that preset length 3,3 elements are selected from tetra- vectors of X, Z, Y, W, it is assumed that be respectively
{ 1.33, -2.34,3.35 }, then have t1=((1.33-1) × 1016) mod3=0, t2=((2.34-2) × 1016) mod3=1,
t3=((3.35-3 × 1016) mod3=2, generation pseudo-random sequence { 0,1,2 }.
S204, to each pseudo-random sequence, by recording the size sequence of each element in the pseudo-random sequence,
Generate pseudorandom address sequence.
Exemplary, it is assumed that pseudo-random sequence is { 15,22,18,11,24 }, using descending sort, the size time of element 15
Sequence is 4, and the size sequence of element 22 is 2, the like, obtain address sequence { 4,2,3,5,1 }.
S205, two of the generation pseudorandom address sequences refer to respectively as the row of Scrambling Matrix nonzero element
Sequence and row index series are marked to generate a new Scrambling Matrix, until the second number Scrambling Matrix of generation.
Exemplary, it is assumed that two pseudorandom address sequences of generation are respectively { 3,1,2 } and { 1,3,2 }, then scramble
(3,1), (1,3), (2,2) are followed successively by for the footmark of nonzero element in matrix, the value of element corresponding to these footmarks is set to 1,
Other all elements are set to 0, can obtain following Scrambling Matrix：
Using embodiment illustrated in fig. 2 of the present invention, Scrambling Matrix can be generated using chaos system so that what is generated puts
Random matrix has good pseudo-randomness and complexity, simultaneously because chaos system there is very high sensitiveness to cause initial value
The sensitiveness of encrypted image improves, and adds the difficulty of decryption, ensures the security of encrypted image.
Referring to Fig. 3, Fig. 3 show the figure provided in an embodiment of the present invention based on the conversion of multi-parameter fractional order and semi-tensor product
As a kind of structural representation of encryption device, can include with lower module：
Scramble module 301, for treating the pixel of encrypted image, change the position of its pixel using Scrambling Matrix, obtain
Spatial domain scramble image；
Conversion module 302, for the spatial domain scramble image is carried out according to preset rules phase code and multi-parameter from
Fractional order conversion is dissipated, obtains changing image；
Cipher key module 303, for generating the factor that a dimension is the changing image dimension, and the side not equal to 1
Battle array, as cipher key matrix；
Submatrix module 304, for by the changing image, being uniformly divided into more height according to the dimension of the cipher key matrix
Matrix；
Semi-tensor volume module 305, for cipher key matrix to be carried out to semi-tensor product computing with each submatrix respectively, obtain every
The operation result of individual submatrix；
Module 306 is integrated, for the operation result of the multiple submatrix to be integrated, obtains encrypted image.
Further, the conversion module 302, can include：
Mask cell, the matrix equal with the dimension of the spatial domain scramble image for generating a dimension, as phase
Mask；
Operator unit, the vector equal with the row dimension of the spatial domain scramble image for generating a length, and with this
The each element of vector generates Multiple-Parameter Discrete Fractional rank operator as parameter；
Converter unit, spatial domain scramble image is handled according to the following formula, obtains changing image：
I is the spatial domain scramble image in formula, and O is the changing image, and j is complex unit, and π is pi, and α is described
Phase mask,For Multiple-Parameter Discrete Fractional rank operator.
Further, the semi-tensor volume module 305, is specifically used for：
Cipher key matrix is carried out to semi-tensor product computing according to the following formula with each submatrix respectively, obtains the fortune of each submatrix
Calculate result：
S is the cipher key matrix in formula,Operator is accumulated for semi-tensor, Q is the submatrix, Rowi(S) for matrix S's
I-th row, Coli(Q) it is matrix Q the i-th row, N is the row dimension of the submatrix, and M is the dimension of the cipher key matrix.
Further, above-mentioned image encrypting apparatus, in addition to following module：
Initialization module 307, the pixel value for four summits using image to be encrypted is to default chaos system
Four systemses state variable is initialized.
Iteration module 308, for chaos system described in iteration, it is defeated since present count contents iteration to preserve each iteration
The numerical value of the four systemses state variable gone out.
Pseudo-random sequence module 309, for using preserve the numerical value, generation the first number preset length puppet with
Machine sequence.
Address sequence module 310, it is each in the pseudo-random sequence by recording for each pseudo-random sequence
The size sequence of element, generate pseudorandom address sequence.
Scrambling Matrix module 311, for by two of the generation pseudorandom address sequences, respectively as Scrambling Matrix
The row index sequence and row index series of nonzero element are to generate a new Scrambling Matrix, until the second number scramble of generation
Matrix.
Further, the conversion module 302, can include：
Mask cell, the matrix equal with the dimension of the spatial domain scramble image for generating two dimensions, respectively as
First phase mask and second phase mask；
Operator unit, the vector equal with the row dimension of the spatial domain scramble image for generating two length are sharp respectively
By the use of the element in two vectors as parameter, the first Multiple-Parameter Discrete Fractional rank operator and the second Multiple-Parameter Discrete Fractional rank are generated
Operator；
Transition element, for utilizing first phase mask and the first Multiple-Parameter Discrete Fractional rank operator to the spatial domain scramble
Image carries out phase code and the conversion of Multiple-Parameter Discrete Fractional rank, obtains transfer image acquisition；
Converter unit, the transfer image acquisition is carried out using second phase mask and the second Multiple-Parameter Discrete Fractional rank operator
Phase code and the conversion of Multiple-Parameter Discrete Fractional rank, obtain changing image.
Fig. 4 a, Fig. 4 b are sample picture A and sample picture B pixel distribution histogram respectively, and abscissa represents picture in figure
Element value, ordinate represent the number of pixel.As illustrated, pixel distribution difference is obvious in two histograms, easily according to straight
Two width pictures are distinguished in the distribution of pixel in square figure.
Fig. 4 c, Fig. 4 d are the encryption figure that sample picture A and sample picture B are obtained after the embodiment of the present invention is encrypted respectively
The pixel distribution histogram of picture, as illustrated, the distribution presentation of pixel is approximately uniformly distributed in two histograms, it is difficult to according to
Pixel distribution in encrypted image distinguishes two width pictures, it was demonstrated that the safety of the encrypted image after the embodiment of the present invention is encrypted
Property.
Fig. 5 a, Fig. 5 c, Fig. 5 e are the pixel distribution scatter diagram of the horizontal of sample picture C, longitudinal direction, diagonal respectively,
Abscissa represents pixel and represents pixel value in horizontal, longitudinal, diagonally adjacent coordinate, ordinate respectively in figure, such as schemes
Shown, sample picture C is in the scatter diagram in three directions, and the distribution of pixel is similar to linear distribution, and correlation is larger.
Fig. 5 b, Fig. 5 d, Fig. 5 f are the sample picture C encrypted image obtained after the embodiment of the present invention is encrypted respectively
Transverse direction, longitudinal direction, the correlation scatter diagram of diagonal.As illustrated, sample picture C is obtained after the embodiment of the present invention is encrypted
To encrypted image scatter diagram in three directions in, the distribution of pixel is similar to be uniformly distributed, and there's almost no phase
Guan Xing.Demonstrate the embodiment of the present invention and eliminate correlation in obtained encrypted image between neighbor pixel, ensure that plus
The security of close image.
Using image encrypting apparatus shown in Fig. 3 of the present invention, Scrambling Matrix can be generated using chaos system so that give birth to
Into Scrambling Matrix there is good pseudo-randomness and complexity, simultaneously because chaos system has very high sensitivity to initial value
Property make it that the sensitiveness of encrypted image improves, and adds the difficulty of decryption, ensures the security of encrypted image.
It should be noted that herein, such as first and second or the like relational terms are used merely to a reality
Body or operation make a distinction with another entity or operation, and not necessarily require or imply and deposited between these entities or operation
In any this actual relation or order.Moreover, term " comprising ", "comprising" or its any other variant are intended to
Nonexcludability includes, so that process, method, article or equipment including a series of elements not only will including those
Element, but also the other element including being not expressly set out, or it is this process, method, article or equipment also to include
Intrinsic key element.In the absence of more restrictions, the key element limited by sentence "including a ...", it is not excluded that
Other identical element also be present in process, method, article or equipment including the key element.
Each embodiment in this specification is described by the way of related, identical similar portion between each embodiment
Divide mutually referring to what each embodiment stressed is the difference with other embodiment.It is real especially for device
For applying example, because it is substantially similar to embodiment of the method, so description is fairly simple, related part is referring to embodiment of the method
Part explanation.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the scope of the present invention.It is all
Any modification, equivalent substitution and improvements made within the spirit and principles in the present invention etc., are all contained in protection scope of the present invention
It is interior.
Claims (10)
1. the image encryption method based on the conversion of multi-parameter fractional order and semi-tensor product, it is characterised in that including：
The pixel of encrypted image is treated, changes the position of its pixel using Scrambling Matrix, obtains spatial domain scramble image；
Phase code is carried out to the spatial domain scramble image according to preset rules and Multiple-Parameter Discrete Fractional rank converts, is converted
Image；
One dimension of generation is the factor of the dimension of the changing image and the square formation not equal to 1, as cipher key matrix；
By the changing image, uniformly it is divided into multiple submatrixs according to the dimension of the cipher key matrix；
Cipher key matrix is carried out to semi-tensor product computing with each submatrix respectively, obtains the operation result of each submatrix；
The operation result of the multiple submatrix is integrated, obtains encrypted image.
2. according to the method for claim 1, it is characterised in that described that the spatial domain scramble image is entered according to preset rules
Row phase code and the conversion of Multiple-Parameter Discrete Fractional rank, obtain changing image, including：
The dimension matrix equal with the dimension of the spatial domain scramble image is generated, as phase mask；
The length vector equal with the row dimension of the spatial domain scramble image is generated, and ginseng is used as using the vectorial each element
Number, generate Multiple-Parameter Discrete Fractional rank operator；
Spatial domain scramble image is handled according to the following formula, obtains changing image：
<mrow>
<mi>O</mi>
<mo>=</mo>
<msup>
<mi>C</mi>
<mover>
<mi>a</mi>
<mo>&OverBar;</mo>
</mover>
</msup>
<mo>{</mo>
<mi>I</mi>
<mo>&CircleTimes;</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>j</mi>
<mi>&pi;</mi>
<mi>&alpha;</mi>
<mo>)</mo>
</mrow>
<mo>}</mo>
</mrow>
I is the spatial domain scramble image in formula, and O is the changing image, and j is complex unit, and π is pi, and α is the phase
Mask,For Multiple-Parameter Discrete Fractional rank operator.
3. according to the method for claim 1, it is characterised in that described that cipher key matrix is carried out half with each submatrix respectively
Tensor product computing, the operation result of each submatrix is obtained, including：
Cipher key matrix is carried out to semi-tensor product computing according to the following formula with each submatrix respectively, obtains the computing knot of each submatrix
Fruit：
S is the cipher key matrix in formula,Operator is accumulated for semi-tensor, Q is the submatrix, Rowi(S) the i-th row for being matrix S,
Coli(Q) it is matrix Q the i-th row, N is the row dimension of the submatrix, and M is the dimension of the cipher key matrix.
4. according to the method for claim 1, it is characterised in that treat encrypted image described, changed using Scrambling Matrix
Before the position of its pixel, in addition to：
The four systemses state variable of default chaos system is carried out just using the pixel value on four summits of image to be encrypted
Beginningization；
Chaos system described in iteration, the four systemses state of each iteration output is preserved since present count contents iteration
The numerical value of variable；
Using the numerical value of preservation, the pseudo-random sequence of the first number preset length is generated, stops iteration；
To each pseudo-random sequence, by recording the size sequence of each element in the pseudo-random sequence, generation it is pseudo- with
The address sequence of machine；
By two of the generation pseudorandom address sequences, respectively as the row index sequence and row of Scrambling Matrix nonzero element
Index series is to generate a new Scrambling Matrix, until the second number Scrambling Matrix of generation.
5. according to the method for claim 1, it is characterised in that described that the spatial domain scramble image is entered according to preset rules
Row phase code and the conversion of Multiple-Parameter Discrete Fractional rank, obtain changing image, including：
Two dimensions matrix equal with the dimension of the spatial domain scramble image is generated, respectively as first phase mask and second
Phase mask；
Generate two length vector equal with the row dimension of the spatial domain scramble image, the element being utilized respectively in two vectors
As parameter, the first Multiple-Parameter Discrete Fractional rank operator and the second Multiple-Parameter Discrete Fractional rank operator are generated；
Phase code is carried out to the spatial domain scramble image using first phase mask and the first Multiple-Parameter Discrete Fractional rank operator
Converted with Multiple-Parameter Discrete Fractional rank, obtain transfer image acquisition；
Phase code and more is carried out to the transfer image acquisition using second phase mask and the second Multiple-Parameter Discrete Fractional rank operator
Parameter discrete fractional order converts, and obtains changing image.
6. the image encrypting apparatus based on the conversion of multi-parameter fractional order and semi-tensor product, it is characterised in that including：
Scramble module, for treating the pixel of encrypted image, change the position of its pixel using Scrambling Matrix, obtain spatial domain scramble
Image；
Conversion module, for carrying out phase code and Multiple-Parameter Discrete Fractional rank to the spatial domain scramble image according to preset rules
Conversion, obtains changing image；
Cipher key module, for generating the factor that a dimension is the changing image dimension, and the square formation not equal to 1, as close
Key matrix；
Submatrix module, for by the changing image, being uniformly divided into multiple submatrixs according to the dimension of the cipher key matrix；
Semi-tensor volume module, for cipher key matrix to be carried out to semi-tensor product computing with each submatrix respectively, obtain every sub- square
The operation result of battle array；
Module is integrated, the operation result of the multiple submatrix is integrated, obtains encrypted image.
7. device according to claim 6, it is characterised in that the conversion module, including：
Mask cell, the matrix equal with the dimension of the spatial domain scramble image for generating a dimension, as phase mask；
Operator unit, the vector equal with the row dimension of the spatial domain scramble image for generating a length, and with the vector
Each element as parameter, generate Multiple-Parameter Discrete Fractional rank operator；
Converter unit, spatial domain scramble image is handled according to the following formula, obtains changing image：
<mrow>
<mi>O</mi>
<mo>=</mo>
<msup>
<mi>C</mi>
<mover>
<mi>a</mi>
<mo>&OverBar;</mo>
</mover>
</msup>
<mo>{</mo>
<mi>I</mi>
<mo>&CircleTimes;</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>j</mi>
<mi>&pi;</mi>
<mi>&alpha;</mi>
<mo>)</mo>
</mrow>
<mo>}</mo>
</mrow>
I is the spatial domain scramble image in formula, and O is the changing image, and j is complex unit, and π is pi, and α is the phase
Mask,For Multiple-Parameter Discrete Fractional rank operator.
8. device according to claim 6, it is characterised in that the semi-tensor volume module, be specifically used for：
Cipher key matrix is carried out to semi-tensor product computing according to the following formula with each submatrix respectively, obtains the computing knot of each submatrix
Fruit：
S is the cipher key matrix in formula,Operator is accumulated for semi-tensor, Q is the submatrix, Rowi(S) the i-th row for being matrix S,
Coli(Q) it is matrix Q the i-th row, N is the row dimension of the submatrix, and M is the dimension of the cipher key matrix.
9. device according to claim 6, it is characterised in that described device, in addition to：
Initialization module, the pixel value for four summits using image to be encrypted is to the four systemses of default chaos system
State variable is initialized；
Iteration module, for chaos system described in iteration, the institute that each iteration exports is preserved since present count contents iteration
State the numerical value of four systemses state variable；
Pseudo-random sequence module, for utilizing the numerical value preserved, the pseudo-random sequence of the first number preset length of generation；
Address sequence module, for each pseudo-random sequence, by recording each element in the pseudo-random sequence
Size sequence, generate pseudorandom address sequence；
Scrambling Matrix module, for by two of the generation pseudorandom address sequences, respectively as Scrambling Matrix non-zero entry
The row index and row index series of element are to generate a new Scrambling Matrix, until the second number Scrambling Matrix of generation.
10. device according to claim 6, it is characterised in that the conversion module, including：
Mask cell, the matrix equal with the dimension of the spatial domain scramble image for generating two dimensions, respectively as first
Phase mask and second phase mask；
Operator unit, the vector equal with the row dimension of the spatial domain scramble image for generating two length, is utilized respectively two
Element in individual vector generates the first Multiple-Parameter Discrete Fractional rank operator and the second Multiple-Parameter Discrete Fractional rank is calculated as parameter
Son；
Transition element, for utilizing first phase mask and the first Multiple-Parameter Discrete Fractional rank operator to the spatial domain scramble image
Phase code and the conversion of Multiple-Parameter Discrete Fractional rank are carried out, obtains transfer image acquisition；
Converter unit, phase is carried out to the transfer image acquisition using second phase mask and the second Multiple-Parameter Discrete Fractional rank operator
Coding and the conversion of Multiple-Parameter Discrete Fractional rank, obtain changing image.
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