CN109379510A - A kind of image encryption method based on two dimension Logistic chaotic system algorithm - Google Patents
A kind of image encryption method based on two dimension Logistic chaotic system algorithm Download PDFInfo
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- H—ELECTRICITY
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- H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
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Abstract
The invention discloses a kind of image encryption method based on two dimension Logistic chaotic system algorithm, this method is that first input needs the plaintext digital picture A encryptedm×nWith an arbitrary image Bm×n；Using logistic chaos system algorithm to plaintext digital picture Am×nIt carries out scramble and obtains scramble image Anew；Utilize matrix Q and scramble image AnewIt carries out XOR operation and obtains close figure SA；The close figure S that will be obtainedAEach pixel element improve, obtain improved SA(i, j), and it is loaded into image Bm×nIn, it obtains loading close figure SAPlaintext image Bnew；To plaintext image BnewIt carries out scramble and obtains Bk；Utilize exclusive or matrix E and scramble image BkIt carries out XOR operation and obtains image P1；Using shift transformation to image P1The binary shift operation for carrying out row and column carries out the processing of binary system step-by-step exclusive or with an equal amount of two-dimensional matrix that two dimension Logistic chaotic sequence is formed, obtains ciphertext image F.This method is safe and reliable, can preferably encrypt to digital picture.
Description
Technical field
The present invention relates to image encryption technology, specifically a kind of image based on two dimension Logistic chaotic system algorithm adds
Decryption method.
Background technique
With the development that science and technology is with rapid changepl. never-ending changes and improvements, information technology is widely used in people's daily life, together
When, the perfect combination of network technology and multimedia technology makes the application range of network obtain further widening, largely
Multimedia messages swap use by this medium of internet.Therefore, network information exchange is particularly important in today,
Important carrier of the digital picture as multimedia messages becomes the one of information security issue at this stage for the safe transmission of image
A important directions.By digital image information encryption, makes indistinguishable Secret Image this process and exist in recent years
The field has obtained extensive research, and the method for encryption mainly carries out transformation to the position of image slices vegetarian refreshments or to each picture
The pixel value of vegetarian refreshments is converted.
The aperiodicity continuous wide band frequency spectrum of chaotic signal, the characteristic of similar noise, makes it have natural concealment.Separately
Outside, chaotic signal is to the highly sensitive characterized by positive index of primary condition, even two identical chaos systems
Develop since almost the same primary condition, their track will become quickly irrelevant, this has chaotic signal
Very high complexity.Chaos system itself is deterministic again simultaneously, by the equation of nonlinear system, parameter and primary condition institute
It determines completely, therefore chaotic signal is made to be easy to generate and replicate again.Concealment, unpredictability, the high complexity of chaotic signal
It spends and is easily achieved etc. and be particularly applicable to secret communication.
Although stream cipher is mainly used for the national key departments such as government, military, and for the theory of these departments and
Technology is all secrecy, but since some mathematical tools such as algebra, number theory, probability etc. can be used for studying stream cipher, reason
By with technology in contrast comparative maturity.But there are many valuable open problems to need further to solve, such as motor synchronizing stream
The research of password, Chaotic stream cipher and the exploration of recent studies on method etc..
Chaos phenomenon is deterministic, the similar random process occurred in nonlinear dynamic system, and this process is non-
Period period endless in other words, does not restrain but bounded, and to initial value have tetchy dependence i.e. to process can not
It is predictive.Since chaos sequence has so excellent characteristic, from age Mo, chaos starts to be applied to secret communication field,
In be especially Chaotic stream cipher method by the attention of password educational circles.
Traditional cipher system is all based on so-called difficult problem, with the arrival and mankind computing capability of information age
It improves, people start to explore the physical code system for being not based on certain class difficult problem, and chaos encryption system is exactly one such
Nonlinear chaotic system is sensitive to primary condition and its iteration track and primary condition is made to have complicated non-linear relation, performance
Good pseudo-randomness is gone out and discrete chaos dynamic has been used for after constructing Encryption Algorithm earliest from year, the research of this respect is
Through attracting attention, what is proposed at present is some based on chaos system Encryption Algorithm, due to the defect of Encryption Algorithm itself
Or the generally all not high enough cryptosystem of the inherent characteristic safety of discrete chaotic system, actually one by key determine from
For plaintext space to the inverible transform of the cryptogram space, ideal stream cipher system should meet following condition: have very big close
Key space, with complicated non-linear cryptographic transformation, and the corresponding entirely different cryptographic transformation of different keys, in plain text with change
Information is changed to be fused together to form ciphertext well, be to reduce ciphertext to the leakage of information converting, the distribution of ciphertext it is uniform,
To obtain the big cryptogram space.
Since chaos system has randomness and for the sensibility of initial value, is widely used it in image encryption.
Many experts and scholars also obtain its research achievement in recent years, and 2009, Luo Jun was in " the digital picture based on chaos system of document 1
The method proposed in Encryption Algorithm " (computer engineering and design, 2009.08) be the real value sequence that is generated to Lorenz system into
Row pretreatment obtains pseudorandom integer sequence, then using pretreated integer sequence as key stream, to digital picture
The Magic Square Transformations taken turns and nonlinear transformation are carried out to realize the encryption of digital picture more.2006, Su Liping was " a kind of in document 2
By the picture of image in image encryption new algorithm based on Logistic chaos system " (computer and information technology, 2006.14 (5))
Plain value is scaled binary system, its a few bit map then are realized with encryption using chaos sequence.These methods are all relatively
It is simply easy the person of being decrypted to crack, key sensitivity volume is also more two-dimensional smaller.
Summary of the invention
In order to realize the safety of digital picture, the purpose of the present invention is to provide one kind to be based on Logistic chaos system
The image encryption method of algorithm, this method is safe and reliable, can preferably encrypt to digital picture.
Realizing the technical solution of the object of the invention is:
A kind of image encryption method based on two dimension Logistic chaotic system algorithm, includes the following steps:
(1) input needs the plaintext digital picture A encryptedm×nWith an arbitrary image Bm×n；
(2) line shuffle matrix M and column Scrambling Matrix N are obtained using logistic chaos system algorithm, to plaintext digitized map
As Am×nIt carries out scramble and obtains scramble image Anew, Anew=M × A × N；
(3) exclusive or matrix Q is obtained using logistic chaos system algorithm, utilizes matrix Q and scramble image AnewIt carries out different
Or operation obtains close figure SA；
(4) the close figure S for obtaining step (3)AEach pixel element improve as the following formula so that each pixel value
Less than 1, improved S is obtainedA(i, j),
SA(i, j)=SA×10-Q(i,j)
(5) by improved SA(i, j) is loaded into image Bm×nIn, it obtains loading close figure SAPlaintext image Bnew；
(6) line shuffle matrix H and column Scrambling Matrix L are obtained using logistic chaos system, to plaintext image BnewIt carries out
Scramble obtains Bk, Bk=H × Bnew×L；
(7) exclusive or matrix E is obtained using logistic chaos system, utilizes exclusive or matrix E and scramble image BkIt carries out different
Or operation obtains image P1；
(8) using shift transformation to image P1The binary shift operation for carrying out row and column, with two dimension Logistic chaotic
An equal amount of two-dimensional matrix that sequence is formed carries out the processing of binary system step-by-step exclusive or, obtains ciphertext image F.
Step (1) the plaintext digital picture Am×nWith image Bm×nIt is in the same size, and image pixel size is identical.
The step of step (6) the utilization logistic chaos system obtains line shuffle matrix H and column Scrambling Matrix L is such as
Under:
1) key is inputted, key is
Control parameter h, the initial value (x of two-dimentional Logistic system0,y0), the number of iterations (T0) value；
2) by initial value (x in step 1)0,y0), iteration T0Value after secondary brings two-dimentional logistic into as new initial value
System iteration n times again, and therefrom choose and obtain two chaos sequence { xi}、{yi}；
3) algorithm is utilized
To sequence { xi}、{yiProcessing operation is carried out, the integer that operation result is nearest is taken, new chaos sequence { X is generatedi}、
{Yi}；
4) from chaos sequence { Xi}、{YiIn extract continuous m, n sequence composition Scrambling Matrix respectively, that is, be respectively to go
Scrambling Matrix M and column Scrambling Matrix N.
The exclusive or matrix Q is from chaos sequence { Xi}、{YiIn extract continuous m, n sequence composition respectively again again
Exclusive or matrix Q.
The exclusive or matrix E is from chaos sequence { Xi}、{YiIn extract continuous m, n sequence composition respectively again again
Exclusive or matrix E.
The step of step (8) shift transformation to image P1 operates is as follows:
1) value of each pixel for the gray level image A that size is m × n is converted into binary system, then carries out moving by column
Position, i.e., by the 1st column step-by-step it is left circulation 1, by the 2nd column step-by-step it is left circulation 2, and so on, by the 7th column step-by-step it is left circulation 7
Position, since the 8th column, then successively left circulation 1, the left circulation 2 of the 9th column step-by-step obtain image B；
2) matrix for being m × n by the size generated by Logistic chaos sequence, is denoted as C, the value of C is converted into two
Image B after system, with cyclic shift carries out the processing of step-by-step exclusive or, obtains image D；
3) by image D carry out by row shift, i.e., by the 1st row step-by-step it is right circulation 1, by the 2nd column step-by-step it is right circulation 2, with
This analogizes, and by the right circulation 7 of the 7th column step-by-step, since the 8th column, then successively right circulation 1, the right circulation 2 of the 9th column step-by-step are obtained
To image E；
4) C and image E is subjected to the processing of step-by-step exclusive or, obtains ciphertext image F.
The two dimension Logistic chaotic sequence is
Wherein, 0 < r≤4,0 < Xn1,0 < Y of <n< 1, n are natural number, Xn,YnIt is traversed on section [0,1], due to figure
As specific pixel gray value convert between 0 to 255, and this chaos system generate ordered series of numbers value between 0 to 1, so
Need to expand each resulting ordered series of numbers value 1000 times then to 256 modulus.
The invention has the advantages that limitation of the present invention in view of traditional images encryption technology and low-dimensional chaos encryption technology,
Two-dimentional Logistic system is constructed, analyzes its chaotic characteristic, and it is combined with chaotic technology of digital images, iteration rail
Mark has better pseudo-randomness not only to primary condition sensibility, to provide one for construction cryptosystem
New way.
Detailed description of the invention
Fig. 1 is the method flow diagram of the embodiment of the present invention.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
Embodiment:
As shown in Figure 1, a kind of image encryption method based on two-dimentional logistic chaos system, includes the following steps:
Step a, input needs the plaintext digital picture A encryptedm×nWith an arbitrary image Bm×n；
Step b, line shuffle matrix M and column Scrambling Matrix N are obtained using two-dimentional logistic chaos system algorithm, in plain text
Digital picture Am×nIt carries out scramble and obtains scramble image Anew, Anew=M × A × N；
Step c, exclusive or matrix Q is obtained using two-dimentional logistic chaos system algorithm, utilizes matrix Q and scramble image
AnewIt carries out XOR operation and obtains close figure SA；
Step d, close figure SAIt hides and is loaded into image B:
Step d1, to close figure S obtained in step cAEach pixel element improve as the following formula so that each element
Value both less than 1, obtains improved SA(i, j),
SA(i, j)=SA×10-Q(i,j)
Step d2, improved SA(i, j) is loaded into image Bm×nIn, it obtains loading close figure SAPlaintext image Bnew；
Step e, line shuffle matrix H and column Scrambling Matrix L are obtained using two-dimentional logistic chaos system, to plaintext image
BnewScramble is carried out, B is obtainedk=H × Bnew×L；
Step f, exclusive or matrix E is obtained using two-dimentional logistic chaos system, utilizes exclusive or matrix E and scramble image Bk
It carries out XOR operation and obtains image P1；
Step g, using shift transformation to image P1The binary shift operation of row and column is carried out, it is mixed with two-dimentional Logistic
An equal amount of two-dimensional matrix that ignorant sequence is formed carries out the processing of binary system step-by-step exclusive or, obtains a completely new ciphertext image F,
To complete the final cryptographic operation of image.
The image Bm×nWith image Am×nIt is in the same size, guarantee Am×nWith Bm×nImage pixel size it is identical.Described
The step of line shuffle matrix M and column Scrambling Matrix N are obtained:
Step 1, input key, key are
Control parameter h, the initial value (x of two-dimentional Logistic system0,y0), the number of iterations (T0) value；
Step 2, by initial value (x in step 10,y0) iteration T0Value after secondary brings two dimension into as new initial value
Logistic system iteration n times again, and therefrom choose and obtain two chaos sequence { xi}、{yi}；
Step 3 utilizes algorithm
To sequence { xi}、{yiProcessing operation is carried out, the integer that operation result is nearest is taken, new chaos sequence { X is generatedi}、
{Yi}；
Step 4, from chaos sequence { Xi}、{YiIn extract continuous m, n sequence composition Scrambling Matrix respectively, respectively
Line shuffle matrix M and column Scrambling Matrix N.
The exclusive or matrix Q is from chaos sequence { Xi}、{YiIn extract continuous m, n sequence composition respectively again again
Exclusive or matrix Q.
The exclusive or matrix E is from chaos sequence { Xi}、{YiIn extract continuous m, n sequence composition respectively again again
Exclusive or matrix E.
It is as follows to the step concrete operations of the shift transformation operation of image P1:
The value of each pixel for the gray level image A that size is m × n is converted into binary system by step 1, then carry out by
Column displacement, i.e., by the 1st column step-by-step it is left circulation 1, by the 2nd column step-by-step it is left circulation 2, and so on, by the 7th left circulation of column step-by-step
7, since the 8th column, then successively left circulation 1, the left circulation 2 of the 9th column step-by-step obtain image B；
Step 2, the matrix for being m × n by the size generated by two dimension Logistic chaotic sequence, are denoted as C, by the value of C
It is converted into binary system, the processing of step-by-step exclusive or is carried out with the image B after cyclic shift, obtains image D；
Image D shift by row by step 3, i.e., by the right circulation 1 of the 1st row step-by-step, by the right circulation 2 of the 2nd column step-by-step
Position, and so on, by the right circulation 7 of the 7th column step-by-step, since the 8th column, then successively right circulation 1, the right circulation 2 of the 9th column step-by-step
Position, obtains image E；
C and image E is carried out the processing of step-by-step exclusive or by step 4, obtains image F.
Two dimension Logistic chaotic sequence of the present invention is
Wherein, 0 < r≤4,0 < Xn1,0 < Y of <n< 1, n are natural number, Xn,YnIt is traversed on section [0,1], due to figure
As specific pixel gray value convert between 0 to 255, and this chaos system generate ordered series of numbers value between 0 to 1, so
Need to expand each resulting ordered series of numbers value 1000 times then to 256 modulus.
Claims (7)
1. a kind of image encryption method based on two dimension Logistic chaotic system algorithm, it is characterized in that: including the following steps:
(1) input needs the plaintext digital picture A encryptedm×nWith an arbitrary image Bm×n；
(2) line shuffle matrix M and column Scrambling Matrix N are obtained using logistic chaos system algorithm, to plaintext digital picture Am×n
It carries out scramble and obtains scramble image Anew, Anew=M × A × N；
(3) exclusive or matrix Q is obtained using logistic chaos system algorithm, utilizes matrix Q and scramble image AnewCarry out exclusive or fortune
Calculation obtains close figure SA；
(4) the close figure S for obtaining step (3)AEach pixel element improve as the following formula, so that each pixel value is both less than 1,
Obtain improved SA(i, j),
SA(i, j)=SA×10-Q(i,j)
(5) by improved SA(i, j) is loaded into image Bm×nIn, it obtains loading close figure SAPlaintext image Bnew；
(6) line shuffle matrix H and column Scrambling Matrix L are obtained using logistic chaos system, to plaintext image BnewIt is set
Disorderly, B is obtainedk, Bk=H × Bnew×L；
(7) exclusive or matrix E is obtained using logistic chaos system, utilizes exclusive or matrix E and scramble image BkCarry out XOR operation
Obtain image P1；
(8) using shift transformation to image P1The binary shift operation for carrying out row and column, with two dimension Logistic chaotic sequence shape
At an equal amount of two-dimensional matrix carry out binary system step-by-step exclusive or processing, obtain ciphertext image F.
2. image encryption method according to claim 1, it is characterized in that: step (1) the plaintext digital picture Am×nAnd figure
As Bm×nIt is in the same size, and image pixel size is identical.
3. image encryption method according to claim 1, it is characterized in that: step (6) is described to utilize logistic chaos system
The step of system obtains line shuffle matrix H and column Scrambling Matrix L is as follows:
1) key is inputted, key is
Control parameter h, the initial value (x of two-dimentional Logistic system0,y0), the number of iterations (T0) value；
2) by initial value (x in step 1)0,y0), iteration T0Value after secondary brings two-dimentional logistic system into as new initial value
Again iteration n times, and therefrom choose and obtain two chaos sequence { xi}、{yi}；
3) algorithm is utilized
To sequence { xi}、{yiProcessing operation is carried out, the integer that operation result is nearest is taken, new chaos sequence { X is generatedi}、{Yi}；
4) from chaos sequence { Xi}、{YiIn extract continuous m, n sequence composition Scrambling Matrix, i.e. respectively line shuffle respectively
Matrix M and column Scrambling Matrix N.
4. image encryption method according to claim 1 or 3, it is characterized in that: the exclusive or matrix Q is from chaos sequence
{Xi}、{YiIn extract continuous m, n sequence composition exclusive or matrix Q respectively again again.
5. image encryption method according to claim 1 or 3, it is characterized in that: the exclusive or matrix E is from chaos sequence
{Xi}、{YiIn extract continuous m, n sequence composition exclusive or matrix E respectively again again.
6. image encryption method according to claim 1, it is characterized in that: step (8) shift transformation to image P1
The step of operation, is as follows:
1) value of each pixel for the gray level image A that size is m × n is converted into binary system, then carries out shifting by column, i.e.,
By the 1st column step-by-step it is left circulation 1, by the 2nd column step-by-step it is left circulation 2, and so on, by the 7th column step-by-step it is left circulation 7, from the 8th
Column start, then successively left circulation 1, and the left circulation 2 of the 9th column step-by-step obtains image B；
2) matrix for being m × n by the size generated by Logistic chaos sequence, is denoted as C, the value of C is converted into binary system,
The processing of step-by-step exclusive or is carried out with the image B after cyclic shift, obtains image D；
3) image D shift by row, i.e., by the right circulation 1 of the 1st row step-by-step, by the right circulation 2 of the 2nd column step-by-step, with such
It pushes away, by the right circulation 7 of the 7th column step-by-step, since the 8th column, then successively right circulation 1, the right circulation 2 of the 9th column step-by-step obtain figure
As E；
4) C and image E is subjected to the processing of step-by-step exclusive or, obtains ciphertext image F.
7. image encryption method according to claim 1, it is characterized in that: the two dimension Logistic chaotic sequence is
Wherein, 0 < r≤4,0 < Xn1,0 < Y of <n< 1, n are natural number, Xn,YnIt is traversed on section [0,1], since image has
The gray value of body image vegetarian refreshments converts between 0 to 255, and the ordered series of numbers value that this chaos system generates is between 0 to 1, so needing
Each resulting ordered series of numbers value is expanded 1000 times then to 256 modulus.
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| CN110069901A (en) * | 2019-04-24 | 2019-07-30 | 东北大学 | The more resume images of spatial domain based on chaos system |
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| US11734435B2 (en) | 2020-10-16 | 2023-08-22 | Qilu University Of Technology | Image encryption and decryption communication algorithm based on two-dimensional lag complex logistic map |
| CN112800444A (en) * | 2021-01-19 | 2021-05-14 | 桂林电子科技大学 | Color image encryption method based on two-dimensional chaotic mapping |
| CN112887075A (en) * | 2021-01-27 | 2021-06-01 | 长春理工大学 | Encryption method of similar full-connection network image based on plaintext correlation |
| CN112887075B (en) * | 2021-01-27 | 2022-06-24 | 长春理工大学 | Encryption method of similar full-connection network image based on plaintext correlation |
| CN115086058A (en) * | 2022-06-29 | 2022-09-20 | 中国工商银行股份有限公司 | Image encryption method and device, storage medium and electronic equipment |
| CN115086058B (en) * | 2022-06-29 | 2024-03-08 | 中国工商银行股份有限公司 | Image encryption method and device, storage medium and electronic equipment |
| CN115278181A (en) * | 2022-09-27 | 2022-11-01 | 中科金勃信(山东)科技有限公司 | Image processing method for intelligent security monitoring system |
| CN115278181B (en) * | 2022-09-27 | 2022-12-20 | 中科金勃信(山东)科技有限公司 | Image processing method for intelligent security monitoring system |
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