CN110098917A - The building method of new type of chaotic system based on fractal algorithm - Google Patents
The building method of new type of chaotic system based on fractal algorithm Download PDFInfo
- Publication number
- CN110098917A CN110098917A CN201910398330.3A CN201910398330A CN110098917A CN 110098917 A CN110098917 A CN 110098917A CN 201910398330 A CN201910398330 A CN 201910398330A CN 110098917 A CN110098917 A CN 110098917A
- Authority
- CN
- China
- Prior art keywords
- fractal algorithm
- fractal
- chaos
- algorithm
- new type
- 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.)
- Granted
Links
Classifications
-
- 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
Landscapes
- Engineering & Computer Science (AREA)
- Computer Security & Cryptography (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Air Conditioning Control Device (AREA)
- Feedback Control In General (AREA)
- Complex Calculations (AREA)
Abstract
List entries the invention discloses a kind of building method of new type of chaotic system based on fractal algorithm, including the chaos sequence that selects three-dimensional chaotic system and generated as fractal algorithm；The chaos sequence that will acquire is used to ternary fractal algorithm to obtain novel point of final shape chaos system.The building method of this new type of chaotic system based on fractal algorithm provided by the invention, by selecting different chaos subsystem and increase to divide shape number, many different chaos systems can be constructed, the key space of system can not only be improved, and strong applicability, flexibility are high.
Description
Technical field
The invention belongs to electronic communication fields, and in particular to a kind of construction side of the new type of chaotic system based on fractal algorithm
Method.
Background technique
With the development of economic technology, chaos science more and more receives all circles as a kind of nonlinear kinetics
Study the concern of personage.The good randomness of chaotic signal, ergodic, unpredictability, suffer from very in information security field
High application value.Meanwhile in order to more preferably improve chaos system kinetic characteristics, people are dedicated to research and strengthen chaos system.
From single scrollwork, single wing chaos system to multiple scrolls, more wing chaos systems, from the low-dimensional for possessing a positive Lyapunov index
Chaos system is provided to obtain performance and preferably strengthens chaos system to the hyperchaotic system for possessing multiple positive Lyapunov indexes
System.
From it is in the past different from the internal system construction mechanism building research of new accountant rule, fractal algorithm is from external mechanism
Hand extends the Construction Methods of chaos system modeling.New accountant rule based on fractal algorithm has more complicated dynamics
Behavior has bigger application prospect in chaotic secret communication.Therefore, the chaos system modeling based on fractal algorithm is chaos reason
By the hot spot with application study.
But currently based on the chaos system construction process of fractal algorithm, applicability is poor, and flexibility is poor,
Constrain the universal of the algorithm.
Summary of the invention
The high new chaotic system based on fractal algorithm of good and flexibility the purpose of the present invention is to provide a kind of applicability
The building method of system.
The building method of this new type of chaotic system based on fractal algorithm provided by the invention, includes the following steps:
S1. three-dimensional chaotic system model is selected, and the chaos sequence that the system is generated is as the input sequence of fractal algorithm
Column；
S2. chaos sequence step S1 obtained is used to ternary fractal algorithm, so that it is mixed to obtain novel point of final shape
Ignorant system.
The chaos sequence for obtaining step S1 described in step S2 is used to ternary fractal algorithm, is specially calculated using following
Formula uses chaos sequence to ternary fractal algorithm:
X in formulan,yn,znFor chaos sequence；Rn、QnAnd SnTo export fractal sequences；Δ1And Δ2For the fractal algorithm of setting
Variable Factors.
Fractal algorithm Variable Factors Δ1And Δ2Value are as follows: Δ1=xn, Δ2=yn。
The building method of this new type of chaotic system based on fractal algorithm provided by the invention, by selecting different mix
Ignorant subsystem and increase divide shape number, can construct many different chaos systems, can not only improve the key of system
Space, and strong applicability, flexibility are high.
Detailed description of the invention
Fig. 1 is the method flow schematic diagram of the method for the present invention.
Fig. 2 is that the method for the present invention uses the attractor that divides shape before and after of the Lorenz system as three-dimensional chaotic system model when
Phasor.
Fig. 3 is that the method for the present invention uses the fork that divides shape before and after of the Lorenz system as three-dimensional chaotic system model when
Figure.
Fig. 4 is the frequency spectrum point divided before and after shape when the method for the present invention uses Lorenz system as three-dimensional chaotic system model
Cloth characteristic schematic diagram.
Fig. 5 is that the method for the present invention uses the complexity divided shape before and after of the Lorenz system as three-dimensional chaotic system model when
Schematic diagram.
Specific embodiment
It is as shown in Figure 1 the method flow schematic diagram of the method for the present invention: provided by the invention this based on fractal algorithm
The building method of new type of chaotic system, includes the following steps:
S1. three-dimensional chaotic system model is selected, and the chaos sequence that the system is generated is as the input sequence of fractal algorithm
Column；
S2. chaos sequence step S1 obtained is used to ternary fractal algorithm, so that it is mixed to obtain novel point of final shape
Ignorant system；Specially chaos sequence is used to ternary fractal algorithm using following formula:
X in formulan,yn,znFor three-dimensional chaos sequence；Rn、QnAnd SnTo export fractal sequences；Δ1And Δ2Divide shape for setting
The algorithmic variable factor.
In the specific implementation, fractal algorithm Variable Factors Δ1And Δ2Value a kind of preferred embodiment are as follows: Δ1=xn, Δ2
=yn。
Below by taking Lorenz system as an example, it is based on ternary fractal algorithm, constructs fractal L orenz system.Pass through attractor
Phasor, bifurcation graphs, arrangement entropy and frequency spectrum point etc., the kinetic characteristics of analysis system, to verify the validity of this method.In conjunction with
The present invention is described in further detail for attached drawing and technical solution, and the implementation of the invention by preferred example in detail
Mode.
Example: fractal L orenz system, specific configuration are as follows:
Step 1: select Lorenz system as the system model of point shape, system equation are as follows:
Step 2: continuous chaotic system is solved to obtain three of them subsequence, and using subsequence as three-dimensional fractal algorithm
List entries, take Δ1=xn, Δ2=yn；
Step 3: using attractor phasor, bifurcation graphs, spectrum distribution and the kinetic characteristics for arranging entropy analysis system.
The kinetic characteristics of chaos system are often assessed with attractor phasor, bifurcation graphs, spectrum distribution and arrangement entropy.
Fig. 2 (a)-(d) be respectively Lorenz system, primary point shape after, the attractor phase after secondary point of shape, three times after point shape
Figure.Obviously, compared to Lorenz system, fractal algorithm can effectively be replicated original system phasor.Every process once divides shape,
The number of cavities of new system increases one times compared to the last time.Ternary fractal algorithm has continued the characteristics of binary fractal algorithm,
In this way, undoubtedly increase the building of multi-cavity system a kind of by way of.Simultaneously as the flexibility of fractal algorithm, discrete system
System or even common time series are equally applicable in.Fig. 3 (a)-(d) be respectively Lorenz system, primary point shape after, secondary point of shape
Afterwards, divide the bifurcation diagram after shape three times.As it can be seen that many period windows present in Lorenz system, become after excessive shape operation
At chaos state.Fig. 4 (a)-(d) be respectively Lorenz system, primary point shape after, the frequency after secondary point of shape, three times after point shape
Spectral structure Character Comparison.
Fig. 2 (a)-(d) be respectively Lorenz system, primary point shape after, the attractor phase after secondary point of shape, three times after point shape
Figure.Obviously, compared to Lorenz system, fractal algorithm can effectively be replicated original system cavity.Every process once divides shape,
The number of cavities of new system increases one times compared to the last time.Ternary fractal algorithm has continued the characteristics of binary point shape, but right
The characteristic of raising system is advantageously.In this way, undoubtedly increase the building of multi-cavity system a kind of by way of.Simultaneously as
The flexibility of fractal algorithm, discrete system or even common time series are equally applicable in.
The dynamic behavior of chaos system can be assessed with bifurcation graphs.Fig. 3 (a)-(d) be respectively Lorenz system, primary
After point shape, after secondary point of shape, divide the bifurcation diagram after shape three times.As it can be seen that many period windows present in Lorenz system, warp
After excessive shape operation, become chaos state in fractal L orenz system.Chaos system modeling based on ternary fractal algorithm,
It being capable of effective lifting system chaos performance.
Fig. 4 (a)-(d) illustrates the frequency spectrum distribution characteristics before and after Lorenz system point shape.For general frequency spectrum, point
The cloth the uniform, illustrates that distribution character is better.Contrast simulation result, it is apparent that the distribution of Lorenz system itself more
It concentrates, and is more uniformly spread based on the fractal L orenz system after ternary fractal algorithm.Therefore, based on ternary fractal algorithm
Chaos system modeling, can effectively promote chaos system distribution character.
In cryptographic applications, the randomness that chaos system generates time series is better, and the safety of cryptographic system is also
It is higher.And the randomness of sequence can be measured by product complexity theory, wherein arrangement entropy (Permutation entropy,
PE) algorithm is widely used because realizing simply.In this experiment, arrangement plan method is selected to come computation complexity, simulation result
As shown in Figure 5.As seen from the figure, the arrangement entropy complexity peak of Lorenz system only has 0.25, and after once dividing shape
Fractal L orenz system arrangement entropy complexity has reached 0.75, and the fractal L orenz system arrangement entropy complexity after point shape mentions three times
It is raised to 0.98.Therefore, which can effectively improve the complexity of chaos system.
Claims (3)
1. a kind of building method of the new type of chaotic system based on fractal algorithm, includes the following steps:
S1. three-dimensional chaotic system is selected, and the chaos sequence that the system is generated is as the list entries of fractal algorithm；
S2. chaos sequence step S1 obtained is used to ternary fractal algorithm, to obtain novel point of final shape chaos system
System.
2. the building method of the new type of chaotic system according to claim 1 based on fractal algorithm, it is characterised in that step
The chaos sequence for obtaining step S1 described in S2 is used to ternary fractal algorithm, is specially transported subsequence using following formula
With to ternary fractal algorithm:
X in formulan,yn,znFor three-dimensional chaos sequence；Rn、QnAnd SnTo export fractal sequences；Δ1And Δ2For the fractal algorithm of setting
Variable Factors.
3. the building method of the new type of chaotic system according to claim 1 or 2 based on fractal algorithm, it is characterised in that point
Shape algorithmic variable factor Δ1And Δ2Value are as follows: Δ1=xn, Δ2=yn。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910398330.3A CN110098917B (en) | 2019-05-14 | 2019-05-14 | Construction method of novel chaotic system based on fractal algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910398330.3A CN110098917B (en) | 2019-05-14 | 2019-05-14 | Construction method of novel chaotic system based on fractal algorithm |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110098917A true CN110098917A (en) | 2019-08-06 |
| CN110098917B CN110098917B (en) | 2021-07-02 |
Family
ID=67447978
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910398330.3A Active CN110098917B (en) | 2019-05-14 | 2019-05-14 | Construction method of novel chaotic system based on fractal algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110098917B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113259085A (en) * | 2021-06-17 | 2021-08-13 | 中南大学 | Three-dimensional multi-cavity chaotic system construction method based on rotation method and pseudo-random sequence generator |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100031039A1 (en) * | 2008-02-14 | 2010-02-04 | Mathieu Ciet | Method and apparatus for data protection system using geometry of fractals or other chaotic systems |
| CN103957026A (en) * | 2014-04-14 | 2014-07-30 | 武汉大学 | Code hopping spread spectrum communication system based on chaos sequence |
| CN106330425A (en) * | 2015-06-18 | 2017-01-11 | 中国科学院深圳先进技术研究院 | One-dimensional shift multiplication-based chaos sequence generating method |
| CN108075732A (en) * | 2017-11-07 | 2018-05-25 | 西安电子科技大学 | A kind of new three-dimensional chaos model of high-order and its circuit |
| CN109257159A (en) * | 2018-11-07 | 2019-01-22 | 中南大学 | The building method of novel higher-dimension hyperchaotic system |
-
2019
- 2019-05-14 CN CN201910398330.3A patent/CN110098917B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100031039A1 (en) * | 2008-02-14 | 2010-02-04 | Mathieu Ciet | Method and apparatus for data protection system using geometry of fractals or other chaotic systems |
| CN103957026A (en) * | 2014-04-14 | 2014-07-30 | 武汉大学 | Code hopping spread spectrum communication system based on chaos sequence |
| CN106330425A (en) * | 2015-06-18 | 2017-01-11 | 中国科学院深圳先进技术研究院 | One-dimensional shift multiplication-based chaos sequence generating method |
| CN108075732A (en) * | 2017-11-07 | 2018-05-25 | 西安电子科技大学 | A kind of new three-dimensional chaos model of high-order and its circuit |
| CN109257159A (en) * | 2018-11-07 | 2019-01-22 | 中南大学 | The building method of novel higher-dimension hyperchaotic system |
Non-Patent Citations (1)
| Title |
|---|
| SHENGQIU DAI ET AL.: "Complex Chaotic Attractor via Fractal Transformation", 《ENTROPY 2019》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113259085A (en) * | 2021-06-17 | 2021-08-13 | 中南大学 | Three-dimensional multi-cavity chaotic system construction method based on rotation method and pseudo-random sequence generator |
| CN113259085B (en) * | 2021-06-17 | 2021-09-28 | 中南大学 | Three-dimensional multi-cavity chaotic system construction method based on rotation method and pseudo-random sequence acquisition method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110098917B (en) | 2021-07-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Lai et al. | Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors | |
| Peng et al. | Dynamics of a higher dimensional fractional-order chaotic map | |
| CN101237320B (en) | Method for password protection for constructing unidirectional hash function based on infinite dimension ultra-chaos | |
| CN105681026B (en) | Dynamic S-box building method and system suitable for lightweight encryption algorithm | |
| CN103020891A (en) | Color image encryption method based on compound chaotic sequence and shifting | |
| CN104333447A (en) | SM4 method capable of resisting energy analysis attack | |
| CN103019648A (en) | True random number generator with digital post-processing circuit | |
| CN106357380A (en) | Mask method and mask device for SM4 algorithm | |
| CN102957536A (en) | Identifier-based certificate authentication system CFL | |
| Alamodi et al. | Design new chaotic maps based on dimension expansion | |
| Ye et al. | A self-cited pixel summation based image encryption algorithm | |
| Zhang et al. | A memristive autapse-synapse neural network: application to image encryption | |
| Ma et al. | A multi‐wing butterfly chaotic system and its implementation | |
| CN110098917A (en) | The building method of new type of chaotic system based on fractal algorithm | |
| CN104410490A (en) | Method for protecting cryptographic S-box (substitution-box) through nonlinear extrusion | |
| CN103997401B (en) | Multi-scroll chaotic signal generating device and method based on Jerk circuit form | |
| Cao et al. | A Simple memristive chaotic system with complex dynamics and ITS image encryption application | |
| CN103701591B (en) | A kind of sequential cipher realization method and key stream generate method and device | |
| Wu | A chaos-based hash function | |
| Yuan et al. | Parameter control methods for discrete memristive maps with network structure | |
| CN106160997B (en) | A kind of New Grid sine chamber hyperchaotic map system | |
| CN105119929A (en) | Safe mode index outsourcing method and system under single malicious cloud server | |
| CN104301090A (en) | Four-dimensional chaotic system circuit with time-lag items | |
| CN106201435A (en) | Pseudo-random number generation method based on cell neural network | |
| CN107276743A (en) | The building method of novel reinforced chaos system |
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 |