CN107770406B - Image encryption method and device based on the transformation of multi-parameter fractional order and semi-tensor product - Google Patents
Image encryption method and device based on the transformation of multi-parameter fractional order and semi-tensor product Download PDFInfo
- Publication number
- CN107770406B CN107770406B CN201711013258.5A CN201711013258A CN107770406B CN 107770406 B CN107770406 B CN 107770406B CN 201711013258 A CN201711013258 A CN 201711013258A CN 107770406 B CN107770406 B CN 107770406B
- Authority
- CN
- China
- Prior art keywords
- image
- matrix
- airspace
- dimension
- scramble
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- 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
-
- 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
-
- 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
-
- 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
- H04N1/44—Secrecy systems
- H04N1/448—Rendering the image unintelligible, e.g. scrambling
- H04N1/4486—Rendering the image unintelligible, e.g. scrambling using digital data encryption
Landscapes
- Engineering & Computer Science (AREA)
- Signal Processing (AREA)
- Multimedia (AREA)
- Computer Security & Cryptography (AREA)
- Computer Networks & Wireless Communication (AREA)
- Two-Way Televisions, Distribution Of Moving Picture Or The Like (AREA)
- Storage Device Security (AREA)
Abstract
The embodiment of the invention provides image encryption methods and device based on the transformation of multi-parameter fractional order and semi-tensor product.Method includes: to treat the pixel of encrypted image, changes the position of its pixel using Scrambling Matrix, obtains airspace scramble image；Phase code is carried out to the airspace scramble image according to preset rules and Multiple-Parameter Discrete Fractional rank converts, obtains changing image；The factor for the dimension that a dimension is the changing image and the square matrix not equal to 1 are generated, 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 with each submatrix to semi-tensor product operation respectively, obtains the operation result of each submatrix；The operation result of the multiple submatrix is integrated, encrypted image is obtained.Combination of embodiment of the present invention airspace scramble, score field transformation 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 technology fields, more particularly to based on the transformation of multi-parameter fractional order and semi-tensor product
Image encryption method and device.
Background technique
With the rapid development of Internet technology and image processing techniques, digital picture can be convenient, fast on network
Ground transmission, but this also brings image information security hidden trouble simultaneously.And it is 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.Number
Image encryption technology becomes a technology that is practical and urgently developing.
Existing image encryption method is broadly divided into two major classes: the Encryption Algorithm based on airspace and the encryption based on transform domain
Algorithm.
Resume image based on airspace is to generate a pseudo-random sequence by a kind of method, be based on the pseudorandom sequence
Column carry out disorder processing to digital picture, to obtain close figure；Image encryption method based on transform domain is to pass through a kind of mathematics
Digital service unit to be encrypted is a linear representation being made of one group of mutually orthogonal matrix, by the table by transformation
Up to pixel value of the coefficient as pixel each in encrypted image of matrix each in formula, to obtain encrypted image.
However, the existing image encryption method based on airspace only changes the position of pixel, original pixel is not changed
Value, causes safety often not high.Moreover, scramble obtained close figure in airspace is in transmission process 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
There are periodicity, leading to a kind of mathematic(al) manipulation mode, there are multiple decruption keys, while selectable mathematic(al) manipulation mode is less,
So that decryption figure is easy to be cracked, it is unable to ensure the safe transmission of digital picture.
Summary of the invention
The image encryption side of the embodiment of the present invention being designed to provide based on the transformation of multi-parameter fractional order and semi-tensor product
Method and device, to realize safely and effectively encrypting digital image.Specific technical solution is as follows:
Image encryption method provided by the invention based on the transformation of multi-parameter fractional order and semi-tensor product, the method packet
It includes:
The pixel for treating encrypted image changes the position of its pixel using Scrambling Matrix, obtains airspace scramble image；
Phase code is carried out to the airspace scramble image according to preset rules and Multiple-Parameter Discrete Fractional rank converts, is obtained
Changing image；
The factor that a dimension is the changing image dimension and the square matrix not equal to 1 are generated, 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 with each submatrix to semi-tensor product operation respectively, obtains the operation result of each submatrix；
The operation result of the multiple submatrix is integrated, encrypted image is obtained.
Further, described that phase code and discrete point of multi-parameter are carried out to the airspace scramble image according to preset rules
Number rank transformation, obtains changing image, comprising:
Dimension matrix equal with the dimension of the airspace scramble image is generated, as phase mask；
Length vector equal with the column dimension of the airspace scramble image is generated, and with each element of vector work
For parameter, Multiple-Parameter Discrete Fractional rank operator is generated；
Airspace scramble image is handled according to the following formula, obtains changing image:
Wherein I is the airspace 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, described that cipher key matrix is carried out with each submatrix to semi-tensor product operation respectively, obtain every sub- square
The operation result of battle array, comprising:
Cipher key matrix is carried out with each submatrix to semi-tensor product operation according to the following formula respectively, obtains the fortune of each submatrix
Calculate result:
S is the cipher key matrix in formula,For semi-tensor product operator, Q is the submatrix, Rowi(S) for matrix S's
I-th row, ColiIt (Q) is the i-th column of matrix Q, N is the column 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, further includes:
Using image to be encrypted four vertex pixel value to the four systems state variable of preset chaos system into
Row initialization；
Chaos system described in iteration saves the four systems of each iteration output 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；
Each pseudo-random sequence is generated by recording the size sequence of each element in the pseudo-random sequence
Pseudorandom address sequence；
By two of the generation pseudorandom address sequences, respectively as the row index sequence of Scrambling Matrix nonzero element
With column index series to generate a new Scrambling Matrix, until generating the second number Scrambling Matrix.
Further, described that phase code and discrete point of multi-parameter are carried out to the airspace scramble image according to preset rules
Number rank transformation, obtains changing image, further includes:
Generate two dimensions matrix equal with the dimension of the airspace scramble image, respectively as first phase exposure mask and
Second phase exposure mask；
Two length vector equal with the column dimension of the airspace 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 airspace scramble image using first phase exposure mask and the first Multiple-Parameter Discrete Fractional rank operator
Coding and the transformation of Multiple-Parameter Discrete Fractional rank, obtain transfer image acquisition；
Phase code is carried out to the transfer image acquisition using second phase exposure mask and the second Multiple-Parameter Discrete Fractional rank operator
It is converted with Multiple-Parameter Discrete Fractional rank, obtains changing image.
Image encrypting apparatus based on the transformation of multi-parameter fractional order and semi-tensor product, comprising:
Scramble module is changed the position of its pixel using Scrambling Matrix, obtains airspace for treating the pixel of encrypted image
Scramble image；
Conversion module, for carrying out phase code and Multiple-Parameter Discrete Fractional rank to the airspace scramble image according to default
Transformation, obtains changing image；
Cipher key module, for generating the square matrix that a dimension is the factor of the changing image dimension, as cipher key matrix；
Submatrix module, for being uniformly divided into multiple sub- squares according to the dimension of the cipher key matrix for the changing image
Battle array；
Semi-tensor volume module obtains each for cipher key matrix to be carried out with each submatrix to semi-tensor product operation respectively
The operation result of submatrix；
Module is integrated, the operation result of the multiple submatrix is integrated, encrypted image is obtained.
Further, the conversion module, comprising:
Mask cell, for generating dimension matrix equal with the dimension of the airspace scramble image, as phase
Exposure mask；
Operator unit, for generating length vector equal with the dimension of the airspace scramble image, and with this to
The each element of amount generates Multiple-Parameter Discrete Fractional rank operator as parameter；
Converter unit according to the following formula handles airspace scramble image, obtains changing image:
I is the airspace 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 with each submatrix to semi-tensor product operation according to the following formula respectively, obtains the fortune of each submatrix
Calculate result:
S is the cipher key matrix in formula,For semi-tensor product operator, Q is the submatrix, Rowi(S) for matrix S's
I-th row, ColiIt (Q) is the i-th column of matrix Q, N is the column dimension of the submatrix, and M is the dimension of the cipher key matrix.
Further, described device, further includes:
Initialization module, the pixel value for four vertex using image to be encrypted is to four of preset chaos system
System state variables are initialized；
Iteration module saves each iteration output for chaos system described in iteration since present count contents iteration
The four systems state variable numerical value；
Pseudo-random sequence module, for generating the pseudorandom of the first number preset length using the numerical value saved
Sequence；
Address sequence module is used 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, two pseudorandom address sequences for that will generate are non-respectively as Scrambling Matrix
The row index sequence and column index series of neutral element are to generate a new Scrambling Matrix, until generating the second number scramble square
Battle array.
Further, the conversion module, comprising:
Phase mask unit, for generating two length matrix equal with the dimension of the airspace scramble image, respectively
As first phase exposure mask and second phase exposure mask；
It is equal with the column dimension of the airspace scramble image to generate two length for Multiple-Parameter Discrete Fractional rank operator module
Vector is utilized respectively the element in two vectors 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 exposure mask and the first Multiple-Parameter Discrete Fractional rank operator to the airspace scramble
Image carries out phase code and the transformation of Multiple-Parameter Discrete Fractional rank, obtains transfer image acquisition；
Conversion module, for utilizing second phase exposure mask and the second Multiple-Parameter Discrete Fractional rank operator to the transfer image acquisition
Phase code and the transformation of Multiple-Parameter Discrete Fractional rank are carried out, changing image is obtained.
Image encryption method and device provided in an embodiment of the present invention based on the transformation of multi-parameter fractional order and semi-tensor product,
It can be by phase code and semi-tensor product operation, so that the information of each pixel is divided into multiple portions in image to be encrypted
It is stored in all pixels point in close figure respectively, even if interference or lost part pixel of the close figure by noise signal, shadow
It rings on all pixels point that can be also shared in decryption figure after decryption, enhances close figure and anti-noise signal and pixel are lost
Ability.Image encryption after the scramble of airspace is projected into score field, and combines semi-tensor product operation, has been widened in ciphering process
The space of parameter selection avoids the periodicity of score field transformation, increases the ability of decrypted image confrontation statistical attack, improves
The safety of Digital Image Transmission.Certainly, implement any of the products of the present invention or method must be not necessarily required to reach simultaneously with
Upper all advantages.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is the image encryption method provided in an embodiment of the present invention based on the transformation of multi-parameter fractional order and semi-tensor product
A kind of flow diagram；
Fig. 2 is a kind of flow diagram 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 transformation of multi-parameter fractional order and semi-tensor product
A kind of structural schematic diagram；
Fig. 4 a is the pixel distribution histogram of sample picture A；
Fig. 4 b is the pixel distribution histogram of sample picture B；
Fig. 4 c is the pixel distribution histogram for the encrypted image that sample picture A is obtained after the embodiment of the present invention encrypts；
Fig. 4 d is the pixel distribution histogram for the encrypted image that sample picture B is obtained after the embodiment of the present invention encrypts；
The horizontal pixel that Fig. 5 a is sample picture C is distributed scatter plot；
Fig. 5 b is that the horizontal pixel for the encrypted image that sample picture C is obtained after the embodiment of the present invention encrypts is distributed scatterplot
Figure；
Fig. 5 c is longitudinal pixel distribution scatter plot of sample picture C；
Fig. 5 d is the longitudinal pixel distribution scatterplot for the encrypted image that sample picture C is obtained after the embodiment of the present invention encrypts
Figure；
Fig. 5 e is the diagonal pixel distribution scatter plot of sample picture C；
Fig. 5 f is the diagonal pixel point for the encrypted image that sample picture C is obtained after the embodiment of the present invention encrypts
Cloth scatter plot.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The figure provided in an embodiment of the present invention based on the transformation of multi-parameter fractional order and semi-tensor product is shown referring to Fig. 1, Fig. 1
As a kind of flow diagram of encryption method, may comprise steps of:
S101 treats the pixel of encrypted image, changes the position of its pixel using Scrambling Matrix, obtains airspace scramble figure
Picture.
Wherein, which can be the matrix of preset one or a set of fixation, or pass through specific method
The one or a set of matrix generated.The position for being changed its pixel using Scrambling Matrix can be to change in image to be encrypted and 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 matrix, by adding frame to image to be encrypted
Mode is changed into square matrix.
In a kind of preferred implementation, the pixel of encrypted image is treated, changes the position of its pixel using Scrambling Matrix
It sets, obtains airspace scramble image, comprising:
The pixel for treating every a line of encrypted image, is changed the position of its pixel using different Scrambling Matrixes, is obtained
Cross scramble image；To the pixel of each column of transition scramble image, changes the position of its pixel using different Scrambling Matrixes, obtain
To airspace scramble image.
The implementation is selected, can fully change the position of each pixel of image to be encrypted, increase encrypted image
Complexity improves decryption difficulty.
S102 carries out phase code to the airspace scramble image according to preset rules and Multiple-Parameter Discrete Fractional rank becomes
It changes, obtains changing image.
In an optional implementation manner, phase code and is carried out more to the airspace scramble image according to preset rules
The transformation of parameter discrete fractional order, comprising:
Dimension matrix equal with the dimension of the airspace scramble image is generated, as phase mask α；Generate one
The length vector equal with the column dimension of the airspace scramble image, and using each element of the vector as parameter, generate more ginsengs
Number Discrete Fractional operatorAirspace scramble image is handled according to the following formula, obtains changing image:
I is airspace scramble image in formula, and O is changing image, and j is complex unit, and π is pi.
In a kind of preferred implementation, phase code and is carried out more to the airspace scramble image according to preset rules
The transformation of parameter discrete fractional order, comprising:
Two dimensions matrix equal with the dimension of airspace scramble image is generated, respectively as first phase exposure mask α1With
Two phase exposure mask α2；Two length vector equal with the column dimension of airspace 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 operatorBenefit
Use α1WithPhase code is carried out to airspace 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 code and Multiple-Parameter Discrete Fractional rank are converted according to the following formula, obtained
To changing image O:
The implementation is selected, 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 divided into multiple portions and is stored in respectively all in changing image by more uniform in image
In pixel, the correlation in encrypted image between pixel is reduced.
S103 generates the factor that a dimension is the changing image dimension, and is not equal to 1 square matrix, 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.
Illustratively, it is assumed that changing image is the square matrix of 64 ranks, remove in 64 factor 1 and 64 there are also 2,4,8,
16,32, cipher key matrix can be one of 2 ranks, 4 ranks, 8 ranks, 16 ranks, 32 rank square matrixes square matrix.
The changing image is uniformly divided into multiple submatrixs according to the dimension of the cipher key matrix by S104.
In the present embodiment, changing image is uniformly divided into square submatrix of the dimension of cipher key matrix.
Illustratively, it is assumed that changing image is a 4 rank square matrixes, and cipher key matrix is 2 rank square matrixes, by changing image according to such as
Mode shown in lower is evenly dividing as 4 submatrixs:
Cipher key matrix is carried out semi-tensor product operation with each submatrix respectively, obtains the operation of each submatrix by S105
As a result.
In the present embodiment, cipher key matrix is carried out with each submatrix to semi-tensor product operation according to the following formula respectively, is obtained
Result after each submatrix operation:
S is cipher key matrix in formula,For semi-tensor product operator, Q is submatrix, Rowi(S) the i-th row for being matrix S,
ColiIt (Q) is the i-th column of matrix Q, N is the column dimension of submatrix, and M is the dimension of cipher key matrix.
The operation result of the multiple submatrix is integrated, obtains encrypted image by S106.
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.
Illustratively, it is assumed that one shares the operation result of 16 submatrixs, respectively A1、A2、A3…A16, by 16 operations
As a result encrypted image is combined into according to mode as follows:
It can specifically be used for 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, including the following steps:
S201, the pixel value using four vertex of image to be encrypted become the four systems state of preset chaos system
Amount is initialized.
In the present embodiment, chaos system as follows is selected:
Wherein a, b, c, r are the control parameter of system, x, y, z, the state variable that w is system.It is described to utilize figure to be encrypted
The pixel value on four vertex of picture initializes the four systems state variable of preset chaos system, can be four
The pixel value on vertex is directly respectively as x, y, z, the initial value of w, or can be the pixel value on four vertex after treatment
Respectively as x, y, z, the initial value of w.
Illustratively, it is assumed that the width of image to be encrypted is K, and the pixel value on four vertex is respectively P1、P2、 P3、P4, can
Directly to enable x0=P1,、y0=P2、z0=P3、w0=P4To initialize the chaos system, or x can also be enabled0=P1,/K、y0
=P2/K、z0=P3/K、w0=P4/ K is to initialize the chaos system.
S202, chaos system described in iteration save described the four of each iteration output since present count contents iteration
The numerical value of a system state variables.
Since the output result of the iteration of the previous fixed number contents of the chaos system has periodically, in order to avoid the period
Property influence the ability that encrypted image resists statistical attack, the iteration that the present invention is only saved since present count contents iteration is defeated
Out.
In the present embodiment, x, y, z, the value of w of each iteration output since default contents iteration save respectively
In vector X, Y, Z, W.
S203 generates the pseudo-random sequence of the first number preset length using the numerical value of preservation, 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
A element will not repeatedly be chosen.It to each element selected, is handled according to the following formula, using obtained result as sequence
Element generates pseudo-random sequence:
ti=((| ei|-|_i_|×1016)modL
Wherein eiFor i-th of element of selection, _i_ for choose i-th of element integer part, L is preset length, ti
For the result obtained after i-th of element processing of selection.
Illustratively, it is assumed that preset length 3 selects 3 elements 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, it generates 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.
Illustratively, 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, and so on, obtain address sequence { 4,2,3,5,1 }.
S205 refers to two of the generation pseudorandom address sequences respectively as the row of Scrambling Matrix nonzero element
Sequence and column index series are marked to generate a new Scrambling Matrix, until generating the second number Scrambling Matrix.
Illustratively, 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 the corresponding element of these footmarks is set as 1,
Other all elements are set as 0, available following Scrambling Matrix:
Using embodiment illustrated in fig. 2 of the present invention, chaos system can use to generate Scrambling Matrix, so that generated set
Random matrix has good pseudo-randomness and complexity, simultaneously because chaos system there is very high sensibility to make initial value
The sensibility of encrypted image improves, and increases the difficulty of decryption, guarantees the safety of encrypted image.
The figure provided in an embodiment of the present invention based on the transformation of multi-parameter fractional order and semi-tensor product is shown referring to Fig. 3, Fig. 3
May include with lower module as a kind of structural schematic diagram of encryption device:
Scramble module 301 is changed the position of its pixel using Scrambling Matrix, obtained for treating the pixel of encrypted image
Airspace scramble image；
Conversion module 302, for according to preset rules to the airspace scramble image carry out phase code and multi-parameter from
Fractional order transformation is dissipated, changing image is obtained；
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 being uniformly divided into multiple sons according to the dimension of the cipher key matrix for the changing image
Matrix；
Semi-tensor volume module 305 obtains every for cipher key matrix to be carried out with each submatrix to semi-tensor product operation respectively
The operation result of a submatrix；
Module 306 is integrated, for integrating the operation result of the multiple submatrix, obtains encrypted image.
Further, the conversion module 302 may include:
Mask cell, for generating dimension matrix equal with the dimension of the airspace scramble image, as phase
Exposure mask；
Operator unit, for generating length vector equal with the column dimension of the airspace scramble image, and with this
The each element of vector generates Multiple-Parameter Discrete Fractional rank operator as parameter；
Converter unit according to the following formula handles airspace scramble image, obtains changing image:
I is the airspace 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 with each submatrix to semi-tensor product operation according to the following formula respectively, obtains the fortune of each submatrix
Calculate result:
S is the cipher key matrix in formula,For semi-tensor product operator, Q is the submatrix, Rowi(S) for matrix S's
I-th row, ColiIt (Q) is the i-th column of matrix Q, N is the column dimension of the submatrix, and M is the dimension of the cipher key matrix.
Further, above-mentioned image encrypting apparatus, further includes following module:
Initialization module 307, the pixel value for four vertex using image to be encrypted is to preset chaos system
Four systems state variable is initialized.
Iteration module 308, is used for chaos system described in iteration, and it is defeated to save each iteration since present count contents iteration
The numerical value of the four systems state variable out.
Pseudo-random sequence module 309, for using save the numerical value, generate the first number preset length puppet with
Machine sequence.
Address sequence module 310 is used for each pseudo-random sequence, each in the pseudo-random sequence by recording
The size sequence of element generates pseudorandom address sequence.
Scrambling Matrix module 311, two pseudorandom address sequences for that will generate, respectively as Scrambling Matrix
The row index sequence and column index series of nonzero element are to generate a new Scrambling Matrix, until generating the second number scramble
Matrix.
Further, the conversion module 302 may include:
Mask cell, for generating two dimensions matrix equal with the dimension of the airspace scramble image, respectively as
First phase exposure mask and second phase exposure mask；
Operator unit, it is sharp respectively for generating two length vector equal with the column dimension of the airspace scramble image
It uses the element in two vectors as parameter, generates the first Multiple-Parameter Discrete Fractional rank operator and the second Multiple-Parameter Discrete Fractional rank
Operator；
Transition element, for utilizing first phase exposure mask and the first Multiple-Parameter Discrete Fractional rank operator to the airspace scramble
Image carries out phase code and the transformation of Multiple-Parameter Discrete Fractional rank, obtains transfer image acquisition；
Converter unit carries out the transfer image acquisition using second phase exposure mask and the second Multiple-Parameter Discrete Fractional rank operator
Phase code and the transformation of Multiple-Parameter Discrete Fractional rank, obtain changing image.
Fig. 4 a, Fig. 4 b are the pixel distribution histogram of sample picture A and sample picture B respectively, and abscissa indicates picture in figure
Element value, ordinate indicate the number of pixel.As shown, pixel distribution difference is obvious in two histograms, it is easy 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 encrypts respectively
The pixel distribution histogram of picture, as shown, 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 by the safety of the encrypted encrypted image of the embodiment of the present invention
Property.
Fig. 5 a, Fig. 5 c, Fig. 5 e are the pixel distribution scatter plot of the lateral of sample picture C, longitudinal direction, diagonal respectively,
Abscissa respectively represents pixel in lateral, longitudinal, diagonally adjacent coordinate in figure, and ordinate represents pixel value, such as schemes
Shown, for sample picture C in the scatter plot in three directions, the distribution of pixel is similar to linear distribution, and correlation is larger.
Fig. 5 b, Fig. 5 d, Fig. 5 f are the encrypted image of sample picture C obtained after the embodiment of the present invention encrypts respectively
Transverse direction, longitudinal direction, diagonal correlation scatter plot.As shown, sample picture C is obtained after the embodiment of the present invention encrypts
To encrypted image scatter plot in three directions in, the distribution of pixel is similar to be uniformly distributed, and there's almost no phase
Guan Xing.The correlation in the encrypted image that the embodiment of the present invention eliminates between neighbor pixel is demonstrated, ensure that and add
The safety of close image.
Using image encrypting apparatus shown in Fig. 3 of the present invention, chaos system can use to generate Scrambling Matrix, so that giving birth to
At Scrambling Matrix have good pseudo-randomness and complexity, simultaneously because chaos system to initial value have very high sensitivity
Property improves the sensibility of encrypted image, increases the difficulty of decryption, guarantees the safety of encrypted image.
It should be noted that, in this document, relational terms such as first and second and the like are used merely to a reality
Body or operation are distinguished with another entity or operation, are deposited without necessarily requiring or implying between these entities or operation
In any actual relationship or order or sequence.Moreover, the terms "include", "comprise" or its any other variant are intended to
Non-exclusive inclusion, so that the process, method, article or equipment including a series of elements is not only wanted including those
Element, but also including other elements that are not explicitly listed, or further include for this process, method, article or equipment
Intrinsic element.In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that
There is also other identical elements in process, method, article or equipment including the element.
Each embodiment in this specification is all made of relevant mode and describes, same and similar portion between each embodiment
Dividing may refer to each other, and each embodiment focuses on the differences from other embodiments.Especially for device reality
For applying example, since it is substantially similar to the method embodiment, so being described relatively simple, related place 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 replacement, improvement and so within the spirit and principles in the present invention, are all contained in protection scope of the present invention
It is interior.
Claims (10)
1. the image encryption method based on the transformation of multi-parameter fractional order and semi-tensor product characterized by comprising
The pixel for treating encrypted image changes the position of its pixel using Scrambling Matrix, obtains airspace scramble image；
Phase code is carried out to the airspace scramble image according to preset rules and Multiple-Parameter Discrete Fractional rank converts, is converted
Image；
The factor for the dimension that a dimension is the changing image and the square matrix not equal to 1 are generated, 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 with each submatrix to semi-tensor product operation respectively, obtains the operation result of each submatrix；
The operation result of the multiple submatrix is integrated, encrypted image is obtained.
2. the method according to claim 1, wherein it is described according to preset rules to the airspace scramble image into
Row phase code and the transformation of Multiple-Parameter Discrete Fractional rank, obtain changing image, comprising:
Dimension matrix equal with the dimension of the airspace scramble image is generated, as phase mask；
Length vector equal with the column dimension of the airspace scramble image is generated, and using each element of the vector as ginseng
Number generates Multiple-Parameter Discrete Fractional rank operator；
Airspace scramble image is handled according to the following formula, obtains changing image:
I is the airspace scramble image in formula, and O is the changing image, and j is complex unit, and π is pi, and α is the phase
Exposure mask,For Multiple-Parameter Discrete Fractional rank operator.
3. the method according to claim 1, wherein described carry out half with each submatrix respectively for cipher key matrix
Tensor product operation obtains the operation result of each submatrix, comprising:
Cipher key matrix is carried out with each submatrix to semi-tensor product operation according to the following formula respectively, obtains the operation knot of each submatrix
Fruit:
S is the cipher key matrix in formula,For semi-tensor product operator, Q is the submatrix, RowiIt (S) is the i-th of matrix S
Row, ColiIt (Q) is the i-th column of matrix Q, N is the column dimension of the submatrix, and M is the dimension of the cipher key matrix.
4. being changed the method according to claim 1, wherein treating encrypted image described using Scrambling Matrix
Before the position of its pixel, further includes:
The four systems state variable of preset chaos system is carried out just using the pixel value on four vertex of image to be encrypted
Beginningization；
Chaos system described in iteration saves the four systems state of each iteration output 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, generate it is pseudo- with
The address sequence of machine；
By two of the generation pseudorandom address sequences, respectively as the row index sequence and column of Scrambling Matrix nonzero element
Index series is to generate a new Scrambling Matrix, until generating the second number Scrambling Matrix.
5. the method according to claim 1, wherein it is described according to preset rules to the airspace scramble image into
Row phase code and the transformation of Multiple-Parameter Discrete Fractional rank, obtain changing image, comprising:
Two dimensions matrix equal with the dimension of the airspace scramble image is generated, respectively as first phase exposure mask and second
Phase mask；
Generate two length vector equal with the column dimension of the airspace 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 airspace scramble image using first phase exposure mask and the first Multiple-Parameter Discrete Fractional rank operator
It is converted with Multiple-Parameter Discrete Fractional rank, obtains transfer image acquisition；
Phase code and is carried out more to the transfer image acquisition using second phase exposure mask and the second Multiple-Parameter Discrete Fractional rank operator
The transformation of parameter discrete fractional order, obtains changing image.
6. the image encrypting apparatus based on the transformation of multi-parameter fractional order and semi-tensor product characterized by comprising
Scramble module changes the position of its pixel using Scrambling Matrix for treating the pixel of encrypted image, obtains airspace scramble
Image；
Conversion module, for carrying out phase code and Multiple-Parameter Discrete Fractional rank to the airspace scramble image according to preset rules
Transformation, obtains changing image；
Cipher key module, for generating the factor that a dimension is the changing image dimension, and the square matrix not equal to 1, as close
Key matrix；
Submatrix module, for being uniformly divided into multiple submatrixs according to the dimension of the cipher key matrix for the changing image；
Semi-tensor volume module obtains every sub- square for cipher key matrix to be carried out with each submatrix to semi-tensor product operation respectively
The operation result of battle array；
Module is integrated, the operation result of the multiple submatrix is integrated, encrypted image is obtained.
7. device according to claim 6, which is characterized in that the conversion module, comprising:
Mask cell, for generating dimension matrix equal with the dimension of the airspace scramble image, as phase mask；
Operator unit, for generating length vector equal with the column dimension of the airspace scramble image, and with the vector
Each element as parameter, generate Multiple-Parameter Discrete Fractional rank operator；
Converter unit according to the following formula handles airspace scramble image, obtains changing image:
I is the airspace scramble image in formula, and O is the changing image, and j is complex unit, and π is pi, and α is the phase
Exposure mask,For Multiple-Parameter Discrete Fractional rank operator.
8. device according to claim 6, which is characterized in that the semi-tensor volume module is specifically used for:
Cipher key matrix is carried out with each submatrix to semi-tensor product operation according to the following formula respectively, obtains the operation knot of each submatrix
Fruit:
S is the cipher key matrix in formula,For semi-tensor product operator, Q is the submatrix, RowiIt (S) is the i-th of matrix S
Row, ColiIt (Q) is the i-th column of matrix Q, N is the column dimension of the submatrix, and M is the dimension of the cipher key matrix.
9. device according to claim 6, which is characterized in that described device, further includes:
Initialization module, the pixel value for four vertex using image to be encrypted is to the four systems of preset chaos system
State variable is initialized；
Iteration module saves the institute of each iteration output for chaos system described in iteration since present count contents iteration
State the numerical value of four systems state variable；
Pseudo-random sequence module, for generating the pseudo-random sequence of the first number preset length using the numerical value saved；
Address sequence module is used for each pseudo-random sequence, by recording each element in the pseudo-random sequence
Size sequence generates pseudorandom address sequence；
Scrambling Matrix module, two pseudorandom address sequences for that will generate, respectively as Scrambling Matrix non-zero entry
The row index and column index series of element are to generate a new Scrambling Matrix, until generating the second number Scrambling Matrix.
10. device according to claim 6, which is characterized in that the conversion module, comprising:
Mask cell, for generating two dimensions matrix equal with the dimension of the airspace scramble image, respectively as first
Phase mask and second phase exposure mask；
Operator unit is utilized respectively two for generating two length vector equal with the column dimension of the airspace scramble image
Element in a 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 exposure mask and the first Multiple-Parameter Discrete Fractional rank operator to the airspace scramble image
Phase code and the transformation of Multiple-Parameter Discrete Fractional rank are carried out, transfer image acquisition is obtained；
Converter unit carries out phase to the transfer image acquisition using second phase exposure mask and the second Multiple-Parameter Discrete Fractional rank operator
Coding and the transformation of Multiple-Parameter Discrete Fractional rank, obtain changing image.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711013258.5A CN107770406B (en) | 2017-10-26 | 2017-10-26 | Image encryption method and device based on the transformation of multi-parameter fractional order and semi-tensor product |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711013258.5A CN107770406B (en) | 2017-10-26 | 2017-10-26 | Image encryption method and device based on the transformation of multi-parameter fractional order and semi-tensor product |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107770406A CN107770406A (en) | 2018-03-06 |
| CN107770406B true CN107770406B (en) | 2019-06-21 |
Family
ID=61271644
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201711013258.5A Active CN107770406B (en) | 2017-10-26 | 2017-10-26 | Image encryption method and device based on the transformation of multi-parameter fractional order and semi-tensor product |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107770406B (en) |
Families Citing this family (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108717683B (en) * | 2018-05-16 | 2022-03-29 | 陕西师范大学 | Secret pattern camouflage recovery method combining secret key and random orthogonal tensor base |
| WO2020149913A2 (en) * | 2018-10-26 | 2020-07-23 | Visa International Service Association | Computing key rotation period for block cipher-based encryption schemes system and method |
| CN111476865B (en) * | 2020-03-24 | 2023-07-07 | 北京国信云服科技有限公司 | Image protection method for image recognition based on deep learning neural network |
| CN111800251B (en) * | 2020-05-21 | 2021-11-12 | 北京邮电大学 | Image compressed sensing encryption and decryption method, device and system based on chaotic source |
| CN112529586B (en) * | 2020-12-15 | 2023-07-28 | 深圳市快付通金融网络科技服务有限公司 | Transaction information management method, device, equipment and storage medium |
| CN112788197B (en) * | 2021-01-27 | 2023-04-07 | 长春理工大学 | Color image encryption method based on chaos selection scrambling and half tensor product diffusion |
| CN113852827B (en) * | 2021-08-18 | 2023-10-17 | 河海大学 | Image encryption method based on partial block matching and half tensor product |
| CN113689321B (en) * | 2021-08-23 | 2023-12-22 | 深圳普汇智为科技有限公司 | Image information transmission method and device based on stereoscopic projection encryption |
| CN115834790B (en) * | 2023-01-09 | 2023-04-28 | 徐工汉云技术股份有限公司 | Information encryption transmission method and information decryption transmission method based on pixel movement |
| CN117240604B (en) * | 2023-11-10 | 2024-02-27 | 深圳市互盟科技股份有限公司 | Cloud computing-based data safe storage and energy saving optimization method |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009159365A (en) * | 2007-12-27 | 2009-07-16 | Fujitsu Ltd | Image data verification program, image data verification method and image data verification system |
| CN104778652A (en) * | 2015-04-21 | 2015-07-15 | 广东日正实业有限公司 | Double-image encryption and decryption method |
| CN105447396A (en) * | 2015-12-15 | 2016-03-30 | 西安电子科技大学 | Fractional domain image encryption method based on Arnold transformation and compound chaos |
| CN107292805A (en) * | 2017-06-02 | 2017-10-24 | 重庆邮电大学 | A kind of image encryption method based on the discrete Tchebichef conversion of multi-parameter fractional order |
-
2017
- 2017-10-26 CN CN201711013258.5A patent/CN107770406B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009159365A (en) * | 2007-12-27 | 2009-07-16 | Fujitsu Ltd | Image data verification program, image data verification method and image data verification system |
| CN104778652A (en) * | 2015-04-21 | 2015-07-15 | 广东日正实业有限公司 | Double-image encryption and decryption method |
| CN105447396A (en) * | 2015-12-15 | 2016-03-30 | 西安电子科技大学 | Fractional domain image encryption method based on Arnold transformation and compound chaos |
| CN107292805A (en) * | 2017-06-02 | 2017-10-24 | 重庆邮电大学 | A kind of image encryption method based on the discrete Tchebichef conversion of multi-parameter fractional order |
Non-Patent Citations (2)
| Title |
|---|
| 基于小波稀疏表示的压缩感知与分数阶变换的图像压缩加密;杨建平;《万方数据》;20170428;全文 |
| 李恩全;基于压缩感知技术的图像水印算法研究;《万方数据》;20140225;全文 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107770406A (en) | 2018-03-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107770406B (en) | Image encryption method and device based on the transformation of multi-parameter fractional order and semi-tensor product | |
| François et al. | A new image encryption scheme based on a chaotic function | |
| CN104680476B (en) | The lossless encryption method of coloured image based on two-dimensional discrete wavelet conversion and space-time chaos | |
| You et al. | A novel parallel image encryption algorithm based on hybrid chaotic maps with OpenCL implementation | |
| Tanveer et al. | Multi-images encryption scheme based on 3D chaotic map and substitution box | |
| Liu et al. | A novel image encryption algorithm based on improved 3D chaotic cat map | |
| Ghebleh et al. | A novel image encryption algorithm based on piecewise linear chaotic maps and least squares approximation | |
| CN108537716A (en) | A kind of color image encryption embedding grammar based on discrete domain | |
| Kaur et al. | Fourier–Mellin moment-based intertwining map for image encryption | |
| CN108122188A (en) | A kind of image encryption method | |
| Machkour et al. | A novel image encryption algorithm based on the two-dimensional logistic map and the latin square image cipher | |
| Hu et al. | A uniform chaotic system with extended parameter range for image encryption | |
| Fu et al. | A new fast color image encryption scheme using chen chaotic system | |
| Nkandeu et al. | Image encryption algorithm based on synchronized parallel diffusion and new combinations of 1D discrete maps | |
| Zhao et al. | Image encryption algorithm based on a novel improper fractional-order attractor and a wavelet function map | |
| Munir et al. | Cryptanalysis and improvement of novel image encryption technique using hybrid method of discrete dynamical chaotic maps and brownian motion | |
| Iqbal et al. | An efficient grayscale image encryption scheme based on variable length row-column swapping operations | |
| Ramírez-Torres et al. | Image encryption with an improved cryptosystem based on a matrix approach | |
| Mehdi et al. | Image encryption based on the novel 5D hyper-chaotic system via improved AES algorithm | |
| CN114022339A (en) | Image encryption method based on fractional order Lorenz chaotic system and storage medium | |
| Zhang et al. | Joint image encryption and compression scheme based on a new hyperchaotic system and curvelet transform | |
| Granboulan et al. | Perfect block ciphers with small blocks | |
| Abdul-Kareem et al. | Hybrid image encryption algorithm based on compressive sensing, gray wolf optimization, and chaos | |
| Agarwal | A fractal based image cipher using Knuth shuffle method and dynamic diffusion | |
| CN109639423A (en) | A kind of constituent apparatus of Encryption Algorithm and the constituent apparatus of decipherment algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |