CN109936436A - A kind of robust chaotic mapping system and its complexity optimal control method towards image data encryption - Google Patents
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Abstract
A kind of robust chaotic mapping system and its complexity optimal control method towards image data encryption, comprising the following steps: step 1: construction chaotic mapping system, computing system fixed point and its Eigenvalue expressions；Step 2: the influence by analysis system parameter to characteristic value determines constant lyapunov index characteristic of the mapped system in unlimited parameter area；Step 3: analysis parameter acts on the position modulation of mapping symmetry system having symmetry non-zero fixed point, determines signal amplitude with the changing rule of parameter；Step 4: writing Matlab program, draws lyapunov index spectrogram and bifurcation graphs about fork parameter, the robust chaotic characteristic and amplitude control feature of analysis system；Step 5: being defined based on iteration codomain matching condition and lyapunov index, is designed using lyapunov index as the complexity optimization control scheme of the robust chaotic mapping system of weighing criteria.
Description
Technical field
The present invention relates to a kind of robust chaotic mapping system towards image data encryption and its complexity optimal control sides
Method.
Background technique
The safe transmission of image data is the research hotspot in modern communications field, and Encryption Algorithm design is that image data is logical
Believe the important leverage of transmission security.Conventional encryption algorithm such as IDEA, DES, AES and RSA etc. are based on contents such as text informations
Property design data, encryption efficiency is low, and structure is complicated, and it is computationally intensive, it is unable to satisfy large information capacity High redundancy realtime graphic number
According to encryption requirements [1].Matrixing encryption, the encryption of SCAN language, point to deposit encryption, transform domain encryption and DNA encryption etc. dedicated plus
Close scheme can further improve the safety of image data encryption, but close in algorithm publicity (Kerckhoffs criterion), business
Code dependence, data expansion, arithmetic speed etc. Shortcomings, thus application range is restricted [2].
Pseudo-randomness, ergodic, Combination and the extreme sensitivity to primary condition and parameter of chaos system output signal
Property in contemporary cryptology the features such as to obscure, spread closely related [3].The stretching being converted by folding mechanism and Shannon of chaos
Mentioned scramble-diffusion encryption thought is even more to have wonderful [4] played the same tune on different musical instruments.Therefore, chaos is very suitable for image encryption system
Design.Compared with conventional cryptography mode, New chaotic image encryption is in algorithm security, scheme complexity, data operation ability etc.
Aspect has significant advantage [5].Nevertheless, existing Chaotic Encryption does not ensure that being perfectly safe for image information, mix
Ignorant code breaking algorithm is reported [6] successively.The safety issue of chaos cipher system depends mainly on the complexity of chaos sequence
The safety of property and Encryption Algorithm.It is generally believed that chaos sequence complexity and randomness are higher, it is more difficult to be attacked when applied to communication
It hits.And a kind of valid metric mode of chaos sequence complexity is Lyapunov index (lyapunov index), big positivity
Lyapunov index means that system has increasingly complex chaotic dynamics behavior.On the other hand, the one of Shannon proposition
A secondary close Encryption Algorithm (one-time pad, abbreviation OTP) is effective realization of security password system under unconditional security criterion
Form theoretically has perfect confidentiality [4].Since OTP encryption system requires key stream and encrypted information at least
It is isometric, for large information capacity image data, it is desirable that chaos system is capable of providing parameter key abundant enough, this is in reality
It is difficult to realize in operation.Thus, how design parameter key becomes as the key theory problem of OTP New chaotic image encryption system.
Document [7] carries out nonlinear combination to different One Dimensional Chaotic Maps, has obtained one kind by the mode of operation of modulus after being first added
Discrete system with wider chaotic parameter section, although the Lyapunov index of system is not in this way, increasing key space
Greatly, sequence complexity is not high.For this problem, document [8] is realized by carrying out cascade processing to multiple discrete chaotic systems
The purpose of increase system Lyapunov index, and cascade system extends the chaotic parameter section of system.Nevertheless, both
Method can not theoretically guarantee the single chaotic property (robust chaos) in parameter section.If the continuous chaotic parameter of system
Section is sufficiently wide, and this parameter is considered as encryption key, and a kind of feasible realization way can be provided for OTP image encryption system
Through.When the robustness of chaos system refers to that system parameter disturbs in a certain range, system still keeps chaos on the whole
Characteristic, i.e., in this parameter area, be not present periodic state or other states, chaos is unique state, and can join this
Number is known as the robust factor [9].Therefore, robust chaos system becomes naturally provides the reliable selection of abundant parameter key.Document
[10] corresponding about continuous chaotic system the study found that when certain system parameters change within the scope of entire real number
Lyapunov index is kept constant, that is, has stable robust chaotic characteristic, thus can provide infinitely great chaotic parameter section
With unlimited parameter key.But continuous chaotic system iterative algorithm is complicated, causes arithmetic speed slower, the sequence code rate of generation compared with
It is low.And discrete chaotic system iterative algorithm is relatively easy, thus arithmetic speed is fast, sequence code rate is high.Therefore, New chaotic image encryption
Preferred discrete chaotic system generates pseudo-random sequence in.However, the current chaos Robustness Study in relation to Discrete Mapping is only
It is limited to situation of the robust factor in limited parameter section, and cannot be guaranteed the stability and complexity [9] of chaos, thus it is inconvenient
In offer parameter key abundant enough.
To sum up, quickly image encryption mode can get efficiently using Discrete Chaotic Map system, but in order to obtain no item
OPT image encryption under part safety criterion communicates implementation, it is desirable that Discrete Mapping system (real number ginseng in unlimited parameter area
Number interval) there is complicated, robust chaotic characteristic.
It is the bibliography that applicant provides below:
[1]Deng C,Luo Y.An optimized RSA digital image encryption algorithm
and the analysis of its security.Manuf Autom.2010,32:40-43.
[2] Yu Simin, Lv Jinhu, Li Chengqing chaos cipher and its progress electronics applied in multimedia secret communication
With information journal .2016,38:735-752.
[3]Peng HP,Tian Y,Kurths J,Li LX,Yang YX,Wang DS.Secure and energy-
efficient data transmission system based on chaotic compressive sensing in
body-to-body networks.IEEE Trans Biomed Circuits Syst.2017,11:558-573.
[4]Shannon CE.Communication theory of secrecy systems.Bell Syst Tech
J.1949,
28:656-715.
[5]Jin X,Zhu S,Xiao C,Sun H,Li X,Zhao G,Ge S.3D textured model
encryption via 3D Lu chaotic mapping.Sci China Inform Sci.2017,60:122107.
[6]Li CQ,Liu Y,Xie T,Chen MZ.Breaking a novel image encryption scheme
based on improved hyperchaotic sequences.Nonlinear Dyn.2013,73:2083-2089.
[7]Zhou YC,Bao L,Chen CLP.A new 1D chaotic system for image
encryption.Signal processing.2014,97:172-182.
[8] Wang Guangyi, Yuan Fang Cascading Chaos and its Dynamical Characteristics Acta Physica Sinica .2013,62:020506.
[9] the design of the one-dimensional robust chaotic maps of Han Dandan, Min Lequan, Zhao Geng, Zhang Lijiao, Yan Shijie and S box
Electronic letters, vol .2015,9:1770-1775.
[10]Li CL,Wu L,Li HM,Tong YN.A novel chaotic system and its
topological horseshoe.NonlinearAnal Model Control.2013,18:66-77.
Summary of the invention
The present invention is to overcome above situation insufficient, it is desirable to provide can solve the technical solution of the above problem.
A kind of robust chaotic mapping system and its complexity optimal control method towards image data encryption, including it is following
Step:
Step 1: construction chaotic mapping system, computing system fixed point expression formula and system features value or characteristic equation table
Up to formula；
Step 2: shadow of the system parameter to system features value or characteristic equation by analyzing Discrete Chaotic Map system
It rings, so that it is determined that constant lyapunov index characteristic of the Discrete Chaotic Map system in unlimited parameter area, i.e. chaos Shandong
Stick；
Step 3: position tune of the system parameter to symmetrical non-zero fixed point by analyzing robust Discrete Chaotic Map system
Production is used, and determines influence of the system parameter to system signal amplitude, and then determines signal amplitude with the rule of Parameters variation；
Step 4: by writing Matlab program, the lyapunov index spectrogram about fork parameter is obtained, and pass through
It determines Poincare section, obtains the bifurcation graphs of the system parameter about amplitude-controllable robust Discrete Chaotic Map system, test respectively
The robust chaotic characteristic and amplitude control feature of card system；
Step 5: obtaining the robust chaotic characteristic and amplitude control feature of amplitude-controllable robust Discrete Chaotic Map system,
On this basis, it is defined based on iteration codomain matching condition and lyapunov index, design is weighing apparatus with lyapunov index
Measure the complexity optimization control scheme of the amplitude-controllable robust Discrete Chaotic Map system of criterion；
As a further solution of the present invention: in the step 1: the table of amplitude-controllable robust Discrete Chaotic Map system
Up to formula are as follows:
As a further solution of the present invention: in the step 5: amplitude-controllable robust Discrete Chaotic Map system is answered
Polygamy optimization control scheme the following steps are included:
Step 1: the sine-mapping in chaos state is set as xn+1=S (xn)=asin (π xn), amplitude-controllable robust chaos
It is mapped as f1(xn),f2(xn),…,fk(xn), to construct Compound Mappings system
xn+1=P (xn)=asin (π (f1(xn)+f2(xn)+…fk(xn)))
Step 2: Compound Mappings system is further represented as xn+1=P (xn)=P1(P2(xn)), wherein P1(xn)=S
(xn), P2(xn)=f1(xn)+f2(xn)+…fk(xn)；
Step 3: according to lyapunov index definition, the lyapunov index of composite system is indicated are as follows:
LES> 0 indicates the lyapunov index of sine-mapping,For amplitude-controllable robust chaotic mapping system
fiLyapunov index, thus, the lyapunov index of Compound Mappings system is greater than any one amplitude-controllable robust
The lyapunov index of chaotic maps subsystem, i.e. complexity increase, and kinetic characteristics are optimized；
Step 4: P is chosen2(xn)=kfi(xn) (k is real number), x can be obtainedn+1=P (xn)=P1(kfi(xn)), thusIn this way, system lyapunov index is changed with k by logarithmic parabola, as | k | >=
1,Due toTherefore LEPPerseverance is greater than 0.
As a further solution of the present invention: the calculating of the complexity optimization control scheme of the robust chaotic mapping system
As a result formula is
In the calculated result formula of the complexity optimization control scheme of robust chaotic mapping system, g1、g2Signal is controlled respectively
X, the amplitude of y, k1、k2By the lyapunov index size of logarithmic parabola control system.
Compared with prior art, the beneficial effects of the present invention are: realizing Discrete Chaotic Map system in unlimited parameter area
The chaos robustness of system, and optimize control by the complexity of the robust chaotic mapping system of weighing criteria of lyapunov index
System, so that the safety issue for chaos sequence complexity and two chaos cipher systems of Encryption Algorithm safety provides solution
Scheme, and communicate implementation for the OPT image encryption under unconditional security criterion and provide important entropy source and feasible realization way
Diameter.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Drawings in the following description are only some embodiments of the invention, for those of ordinary skill in the art,
Without any creative labor, it is also possible to obtain other drawings based on these drawings.
Fig. 1 is amplitude-controllable robust Discrete Chaotic Map system design scheme block diagram.
Fig. 2 is amplitude-controllable robust Discrete Chaotic Map system complexity optimization control scheme block diagram.
Fig. 3 is the bifurcation graphs and lyapunov index of amplitude-controllable robust Discrete Chaotic Map system when parameter a changes
Spectrum.
Fig. 4 is the bifurcation graphs and lyapunov index of amplitude-controllable robust Discrete Chaotic Map system when parameter c changes
Spectrum.
Fig. 5 is parameter k1The bifurcation graphs of complex discretization chaotic mapping system and lyapunov index spectrum when variation.
Fig. 6 is parameter k2The bifurcation graphs of complex discretization chaotic mapping system and lyapunov index spectrum when variation.
Fig. 7 is a kind of robust chaotic mapping system and its complexity optimal control method process towards image data encryption
Schematic diagram.
Specific embodiment
The technical scheme in the embodiments of the invention will be clearly and completely described below, it is clear that described implementation
Example is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, this field is common
Technical staff's every other embodiment obtained without making creative work belongs to the model that the present invention protects
It encloses.
Please refer to Fig. 1~6, in the embodiment of the present invention, a kind of robust chaotic mapping system towards image data encryption and
Its complexity optimal control method, comprising the following steps:
Step 1: construction chaotic mapping system, computing system fixed point expression formula and system features value or characteristic equation table
Up to formula；
Step 2: shadow of the system parameter to system features value or characteristic equation by analyzing Discrete Chaotic Map system
It rings, so that it is determined that constant lyapunov index characteristic of the Discrete Chaotic Map system in unlimited parameter area, i.e. chaos Shandong
Stick；
Step 3: position tune of the system parameter to symmetrical non-zero fixed point by analyzing robust Discrete Chaotic Map system
Production is used, and determines influence of the system parameter to system signal amplitude, and then determines signal amplitude with the rule of Parameters variation；
Step 4: by writing Matlab program, the lyapunov index spectrogram about fork parameter is obtained, and pass through
It determines Poincare section, obtains the bifurcation graphs of the system parameter about amplitude-controllable robust Discrete Chaotic Map system, test respectively
The robust chaotic characteristic and amplitude control feature of card system；
Step 5: obtaining the robust chaotic characteristic and amplitude control feature of amplitude-controllable robust Discrete Chaotic Map system,
On this basis, it is defined based on iteration codomain matching condition and lyapunov index, design is weighing apparatus with lyapunov index
Measure the complexity optimization control scheme of the amplitude-controllable robust Discrete Chaotic Map system of criterion；
As a further solution of the present invention: in the step 1: the table of amplitude-controllable robust Discrete Chaotic Map system
Up to formula are as follows:
Three fixed points of system are (0,0),Known to: non-zero is not
Dynamic point is symmetrical about x-axis；Parameter a does not influence the position of non-zero fixed point x-component, but presses (1/a)0.5It is motionless to control non-zero
The position of point y-component, therefore, parameter a can be by regular (1/a)0.5The amplitude of signal y is controlled, and the amplitude of signal x remains unchanged,
As shown in Fig. 3 (a), (b) bifurcation graphs (b=1.98, c=1.0)；Parameter c is controlled the position of non-zero fixed point x-component by 1/c, and
By (1/c)0.5The position of non-zero fixed point y-component is controlled, therefore, parameter c can be controlled the amplitude of signal x by regular 1/c, and be pressed
Regular (1/c)0.5The amplitude for controlling signal y, as shown in Fig. 4 (a), (b) bifurcation graphs (a=1, b=1.98).
The characteristic value of fixed point (0,0) is 0, b；Non-zero fixed pointOr's
Characteristic value isIt is found that parameter a, c does not influence the characteristic value dynamics of mapped system (1).
Therefore, with the variation of parameter a, c, the lyapunov index of mapped system is remained unchanged, i.e., with the chaotic characteristic of robust.
As shown in Fig. 3 (c), Fig. 4 (c).
As a further solution of the present invention: in the step 5: amplitude-controllable robust Discrete Chaotic Map system is answered
Polygamy optimization control scheme the following steps are included:
Step 1: the sine-mapping in chaos state is set as xn+1=S (xn)=asin (π xn), amplitude-controllable robust chaos
It is mapped as f1(xn),f2(xn),…,fk(xn), to construct Compound Mappings system
xn+1=P (xn)=asin (π (f1(xn)+f2(xn)+…fk(xn)))
Step 2: Compound Mappings system is further represented as xn+1=P (xn)=P1(P2(xn)), wherein P1(xn)=S
(xn), P2(xn)=f1(xn)+f2(xn)+…fk(xn)；
Step 3: according to lyapunov index definition, the lyapunov index of composite system is indicated are as follows:
LES> 0 indicates the lyapunov index of sine-mapping,For amplitude-controllable robust chaotic mapping system
fiLyapunov index.Thus, the lyapunov index of Compound Mappings system is greater than any one amplitude-controllable robust
The lyapunov index of chaotic maps subsystem, i.e. complexity increase, and kinetic characteristics are optimized；
Step 4: P is chosen2(xn)=kfi(xn) (k is real number), x can be obtainedn+1=P (xn)=P1(kfi(xn)), thusIn this way, system lyapunov index is as k is by logarithmic parabola variation.When | k | >=
1, LEP≥LES+LEfi, due toTherefore LEPPerseverance is greater than 0.
As a further solution of the present invention: the calculating of the complexity optimization control scheme of the robust chaotic mapping system
As a result formula is
In the calculated result formula of the complexity optimization control scheme of robust chaotic mapping system, g1、g2Signal is controlled respectively
X, the amplitude of y, k1、k2By the lyapunov index size of logarithmic parabola control system.
Work as a=1, b=1.98, c=1.0, g1=2, g2=2, k2=6, parameter k1Chaos fork figure and Liapunov
Exponential spectrum is as shown in Figure 5.Work as a=1, b=1.98, c=1.0, g1=2, g2=2, k1=6, parameter k2Chaos fork figure and Lee
Ya Punuofu exponential spectrum is as shown in Figure 6.Therefore, numerical simulation demonstrates theoretical analysis result well.
It is obvious to a person skilled in the art that invention is not limited to the details of the above exemplary embodiments, Er Qie
In the case where without departing substantially from spirit or essential attributes of the invention, the present invention can be realized in other specific forms.Therefore, no matter
From the point of view of which point, the present embodiments are to be considered as illustrative and not restrictive, and the scope of the present invention is by appended power
Benefit requires rather than above description limits, it is intended that all by what is fallen within the meaning and scope of the equivalent elements of the claims
Variation is included within the present invention.Any reference signs in the claims should not be construed as limiting the involved claims.
Claims (4)
1. a kind of robust chaotic mapping system and its complexity optimal control method, feature towards image data encryption exists
In: in unlimited parameter area, mapped system has the chaos robustness of constant or controllable lyapunov index spectrum；And parameter
The amplitude of controllable output chaotic signal, comprising the following steps:
Step 1: construction chaotic mapping system, computing system fixed point expression formula and system features value or characteristic equation expression formula；
Step 2: influence of the analysis system parameter to system features value or characteristic equation determines mapped system in unlimited parameter model
Enclose interior constant lyapunov index characteristic, i.e. chaos robustness；
Step 3: analysis parameter acts on the position modulation of the symmetrical non-zero fixed point of robust chaotic mapping system, determines system
Influence of the parameter to system signal amplitude, and then determine robust chaotic mapping system signal amplitude with the rule of Parameters variation；
Step 4: writing Matlab program, obtains the lyapunov index spectrogram about fork parameter, and suitable by determining
Poincare section, obtain the bifurcation graphs about system parameter, separately verify the robust chaotic characteristic of robust chaotic mapping system
And amplitude control feature；
Step 5: the robust chaotic characteristic and amplitude control feature of robust Discrete Chaotic Map system, on this basis, base are obtained
It is defined in iteration codomain matching condition and lyapunov index, design is mixed by the robust of weighing criteria of lyapunov index
The complexity optimization control scheme of ignorant mapped system.
2. a kind of robust chaotic mapping system and its complexity optimization towards image data encryption according to claim 1
Control method, which is characterized in that in unlimited parameter area, there is mapped system constant lyapunov index to compose, and join
The amplitudes of the controllable output chaotic signals of number, in the step 1: the robust chaotic mapping system expression formula of design are as follows:
Three fixed point expression formulas of system are (0,0),Non-zero fixed point
It is symmetrical about x-axis；Parameter a does not influence the position of non-zero fixed point x-component, but presses (1/a)0.5Control non-zero fixed point y points
The position of amount, therefore, parameter a can be by regular (1/a)0.5The amplitude of signal y is controlled, and the amplitude of signal x remains unchanged；Parameter c
By the position of 1/c control non-zero fixed point x-component, and press (1/c)0.5Control the position of non-zero fixed point y-component, therefore, parameter
C can be controlled the amplitude of signal x by regular 1/c, and by regular (1/c)0.5The amplitude of signal y is controlled,
The characteristic value of fixed point (0,0) is 0, b；Non-zero fixed pointOrFeature
Value isParameter a, c does not influence the characteristic value dynamics of mapped system, therefore, with ginseng
The variation of number a, c, the lyapunov index of mapped system remain unchanged, i.e., with the chaotic characteristic of robust.
3. a kind of robust chaotic mapping system and its complexity optimization towards image data encryption according to claim 1
Control method, which is characterized in that in unlimited parameter area, robust chaotic mapping system has controllable lyapunov index
Spectrum, in the step 5: the complexity optimization control scheme of robust chaotic mapping system the following steps are included:
Step 1: the sine-mapping in chaos state is set as xn+1=S (xn)=asin (π xn), amplitude-controllable robust chaotic maps
For f1(xn),f2(xn),…,fk(xn), to construct Compound Mappings system
xn+1=P (xn)=asin (π (f1(xn)+f2(xn)+…fk(xn)))
Step 2: Compound Mappings system is further represented as xn+1=P (xn)=P1(P2(xn)), wherein P1(xn)=S (xn), P2
(xn)=f1(xn)+f2(xn)+…fk(xn)；
Step 3: according to lyapunov index definition, the lyapunov index of composite system is indicated are as follows:
LES> 0 indicates the lyapunov index of sine-mapping,For amplitude-controllable robust chaotic mapping system fiLee
Ya Punuofu index, thus, the lyapunov index of Compound Mappings system is greater than any one amplitude-controllable robust chaos and reflects
The lyapunov index of subsystem is penetrated, i.e. complexity increases, and kinetic characteristics are optimized；
Step 4: P is chosen2(xn)=kfi(xn) (k is real number), x can be obtainedn+1=P (xn)=P1(kfi(xn)), thusIn this way, system lyapunov index is changed with k by logarithmic parabola, as | k | >=
1, LEP≥LES+LEfi, due toTherefore LEPPerseverance is greater than 0.
4. a kind of robust chaotic mapping system and its complexity optimization towards image data encryption according to claim 3
Control method, which is characterized in that under the premise of guaranteeing chaos robustness, parameter can be optimized within the scope of real number by logarithmic parabola
The lyapunov index of control chaotic mapped system is composed, the complexity optimization control scheme of the robust chaotic mapping system
Calculated result formula are as follows:
In the calculated result formula of robust chaotic mapping system complexity optimization control scheme, g1、g2Signal x, y are controlled respectively
Amplitude, k1、k2By the lyapunov index size of logarithmic parabola control system.
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