KR20000013680A - Vertical and/or horizontal synchronization method for chaos system - Google Patents

Abstract

PURPOSE: A vertical and/or horizontal synchronization method is provided to synchronize a plurality of chaos system pairs sequentially or simultaneously modulating a nest stage of a chaos system by use of a chaos signal of a previous chaos system. CONSTITUTION: In the control method of a chaos system which has a plurality of chaos system pairs each consisting of a main chaos system and a subordinary chaos system identical to the main chaos system, one or more variables of a main chaos system of a first chaos system pair is modulated to a noise or independent chaos signal, and a variable of a subordinary chaos system corresponding to the main chaos system of the first chaos system pair is modulated into the noise or independent chaos signal to synchronize the first chaos system pair. One or more variables of a main chaos system of a second chaos system pair is modulated into a variable signal of the main chaos system of the first chaos system pair thus synchronized, and a variable of a subordinary chaos system of the second chaos system corresponding to the main chaos system of the second chaos system pair is modulated into a variable signal corresponding to a modulation signal of the main chaos system of the first chaos system pair to synchronize the second chaos system pair. Other chaos system pairs are sequentially synchronized by the above-described procedure.

Description

Vertical and / or horizontal synchronization method of chaotic system

The present invention relates to a plurality of systems (hereinafter, abbreviated as 'chaos system') for generating a signal having chaos characteristics (hereinafter, referred to as 'chaos signal'). The present invention relates to a vertical and / or horizontal synchronization method of a chaotic system in which each chaotic pair generates the same chaotic signal.

Recently, as the interest in "chaos" has been concentrated, researches for actively applying it to various fields of the industry have been actively conducted.

Here, chaos is one of the complex physical phenomena that occur in nonlinear physical systems, as it is widely known. Even though two chaotic systems with the same configuration show very different initial conditions even though they differ slightly over time, It has a property that becomes unpredictable. The sensitivity of the chaotic system to the initial conditions (a sensitivity to initial conditions) is also referred to as the 'butterfly effect'.

Synchronization of the chaos system means that the state variables of each chaos device are identical to each other in a chaos system composed of at least two identical chaos devices having several state variables.

In other words, if there are two chaos devices of the same configuration with the same state variables (one of which is called the main chaos and the other is called the dependent chaos), as described above, Each chaotic system is a completely independent chaos system because each unsynchronized chaos system shows a completely different time trajectory.

However, if any one state variable of the main chaos device is passed to the dependent chaotic device, and the dependent chaotic device properly uses this state variable, and the dependent chaotic device is synchronized to the main chaotic device, all the state variables of the main chaotic device and the dependent chaotic device are dependent. All state variables of the chaos device are equally variable and equal.

This chaotic synchronization technology can be applied to various fields of the industry, and particularly suitable for secret communication.

The method of synchronizing 'Pakkora and Carol' according to the prior art for controlling and synchronizing such chaotic systems is called PHYSICAL REVIEW LETTERS.p821 under the heading 'Synchronization in chaotic systems'. And a paper published by the same person in the 1991 IEEE Journal (IEEE TRANSACTIONS CIRCUIT AND SYSTEMS. P453 (Apr. 1991)) entitled 'synchronizing chaotic circuits'. And US Patent No. 5,245,660 (Pecora and Carroll. "System for Producing Synchronized Signals" US Pattent Number 5,245,660, Issued Date; 1993.14.14), which they acquired in 1993.

In addition, a technique for applying chaos to secret communication using such a method of synchronizing the chaos system is disclosed in U.S. Patent Nos. 5,291,555 (KM Coumo and AV Oppenheim, "Communication Using Synchronized Chaotic Systems" US Pat No. 5,291,555). Issued Dste; 1994.3.1).

That is, US Patent No. According to the method of synchronizing Pacora and Carol published in US Pat. No. 5,245,660, as shown in FIG. 1, after dividing one chaos (driving unit) 10 into the first and second subsystems 11 and 12, The response unit 10 'is formed of the third subsystem 12' having the same structure as the second subsystem 12 to form one chaotic system.

In addition, the driving signal X4 generated by the first sub-system 11 of the divided driving unit 10 is transmitted to the second sub-system 12 and the response unit 10 'so that the driving unit 10 generates chaos. The signals X1, X2, X3, X4 and the chaotic signals X1 ', X2', X3 ', and X4' generated by the response unit 10 'are synchronized.

In other words, if the description of the synchronization method proposed by Pacora and Carol, the main chaos device 10 for generating signals of X1, X2, X3, X4 variables, the first sub-system 11 for generating signals according to the X4 variable, After subdividing the signal according to the variables X1, X2, X3 into the second subsystem 12, X1 ', X2 corresponding to X1, X2, X3 of the main chaos 10 Implemented as a third sub-system 12 'that generates a signal according to the', X3 'variable, and receives the X4 signal of the main chaos device 10 as a drive signal, the main chaos device 10 and the dependent chaos device 10'. ) Is synchronized.

Thus, the synchronization method proposed by Pacora and Carol is to synchronize the main chaos system with the subordinate chaos system by replacing (substituting) one variable of the subordinate chaos system with a variable of the main chaos system.

In this case, the condition that the main chaotic system and the subordinate chaotic system are synchronized is when the Lyapunov Exponent of the subsystem is both negative.

On the other hand, US Pat. The communication system disclosed in 5,291,555 is composed of a drive signal generator 21, an adder 22, a drive signal regenerator 23, and a subtractor 24, as shown in FIG. The information m (t) is loaded on the chaotic signal u (t) generated by the generator 21 and transmitted, and at the receiver, the chaos signal of the drive signal generator 21 is transmitted from the drive signal regenerator 23. After generating the synchronized chaos signal u '(t), the chaos signal is removed from the received signal u (t) + m (t) to reproduce the information m' (t).

The chaos system synchronization method according to the prior art divides each chaos system into two sub-systems to synchronize the main chaos system and the subordinate chaos system, and then the driving signal of the driver unit is divided into a packora and a carol in the response unit. This proposed synchronization condition, i.e., the condition that the Lyapunov exponents of the subsystems are all negative, simply synchronizes one chaos system consisting of the main chaos system and the dependent chaos system. There is a problem that cannot be synchronized.

In addition, since a plurality of chaotic systems cannot be synchronized continuously, not only multi-channel communication is difficult, but also there is a difficulty in stratifying users.

Accordingly, the present invention has been made in order to solve the problems of the prior art, in a continuous chaos system by modulating the chaos system of the next stage by a constant chaos signal of the preceding chaos system by sequentially or chaos system consisting of a plurality of chaos system It is an object of the present invention to provide a vertical and / or horizontal synchronization method of a chaotic system for simultaneous synchronization at the same time.

1 is a schematic conceptual diagram illustrating a synchronization principle of a chaotic system according to the prior art proposed by Pacora and Carol,

2 is a block diagram illustrating a communication system implemented using a synchronization principle according to the prior art;

3 is a conceptual diagram illustrating a vertical synchronization method of a chaotic system according to the present invention;

4 is a view showing a synchronization method of a chaotic system composed of a low lens chaos system and a duffing chaos system according to the present invention;

5A is a noise signal for synchronization, FIG. 5B is a variable signal of a main chaos device of a low lens chaos system, FIG. 5C is a signal waveform showing a variable difference between a main chaos device of a low lens chaos system and a dependent chaotic device corresponding thereto; FIG. 5D is an arbitrary variable signal of the synchronized low lens chaos system, FIG. 5E is a signal waveform of the duffing chaotic system created by adding an arbitrary variable signal of the low lens chaotic system (FIG. 5D) to the variable signal of the duffing chaotic system, FIG. 5F. Is a signal waveform diagram showing the variable difference between the main chaotic device of the duffing chaotic system and the corresponding chaotic device corresponding thereto;

6 is a conceptual diagram illustrating a multi-channel secret communication system according to the present invention;

FIG. 7A is a correlation diagram of the noise signal itself, FIG. 7B is a correlation diagram of the z variable itself of the low lens chaos system before synchronization with the noise signal, and FIG. 7C is a z variable of the low lens chaos system synchronized by the noise signal. 7D is a cross-correlation diagram of a noise signal and a chaotic signal synchronized with the noise signal,

8 is a schematic diagram illustrating a horizontal synchronization method of the chaotic system according to the present invention.

♣ Explanation of symbols for main part of drawing ♣

30-1 to 30-N: first to Nth chaotic apparatus

30-1 'to 30-N': first to Nth chaotic device

40-1 to 40-N: first to Nth main synchronization unit

40-1 'to 40-N': 1st to Nth passivating unit

41-1: First scaling unit 42-1: Subtractor

43-1: second scaling unit 44-1: adder

The vertical synchronization method of the chaos system according to the present invention is a control method of a chaos system in which a plurality of chaos system pairs are formed in a main chaos system and a subordinate chaos system identical to the main chaos system. First chaos by modulating one or a plurality of variables of the main chaos system of the pair into a noise or independent chaos signal, and a variable of the chaos system corresponding to the main chaos system of the first chaos system pair by a noise or independent chaos signal Synchronizing the system pairs, modulating one or a plurality of variables of the main chaos system of the second chaos system pair of the plurality of continuous chaos systems into an arbitrary variable signal of the main chaos system of the synchronized first chaos system pair, Any variable of the dependent chaos system of the second chaotic pair corresponding to the main chaotic system of the two chaotic pairs corresponds to any variable signal of the main chaotic system of the first chaotic pair. Modulating the second chaotic pair by modulating the variable signal, modulating one or a plurality of variables of the main chaotic series of the next chaotic pair with an arbitrary variable signal of the main chaotic series of the synchronized second chaotic pair, 2 A variable of a dependent chaos system corresponding to an arbitrary variable signal of a main chaos system of a chaotic pair, and modulating a variable of a dependent chaos system corresponding to an arbitrary variable signal of a main chaotic system of a next chaotic system pair, Iteratively, it is characterized by sequentially synchronizing a plurality of chaotic pairs.

The horizontal synchronization method of the chaos system according to the present invention is a control method of a chaos system composed of an upper chaos system pair and a plurality of lower chaos system pairs included in the upper chaos system. Synchronize the upper chaotic pairs according to the output variable signal, and one or more variables of the main chaotic pair of the first lower chaotic pair among the plurality of lower chaotic pairs. Modulating the variable into a variable signal of a dependent chaos system corresponding to an arbitrary variable signal of the main chaos system of the upper chaos pair and the variable of the dependent chaos system corresponding to the main chaos system of the first lower chaos system pair. Synchronize one lower chaotic pair and replace any one or more variables of the main chaotic pair of the second lower chaotic pair among the plurality of lower chaotic pairs. Synchronize the subordinate chaos device of the second subordinate chaotic pair with the subordinate chaotic variable in the first lower chaotic pair corresponding to the variable signal modulating the variable signal of the chaotic system and the variable signal modulating the variable of the second lower chaotic pair In addition, the method is repeatedly performed to simultaneously synchronize a plurality of lower chaotic pairs.

The vertical and horizontal synchronization method of the chaos system according to the present invention includes main chaos systems, a plurality of higher chaos systems in which the same chaos systems as the main chaos systems are paired, main chaos systems and subordinate chaos systems. A method of controlling a chaotic system consisting of a plurality of lower chaos systems which are included in an upper chaos system, wherein the random chaos system of the first chaos system pair of the upper chaos system and the corresponding subordinate chaos system Or by synchronizing with another chaotic signal and synchronizing any variable signal of the main chaotic system of the synchronized upper chaotic system pair and the variable signal of the dependent chaotic system corresponding to the main chaotic system and subordinate of the next higher chaotic system pair Modulation is added to any variable in the chaos system so that multiple upper chaos pairs can be synchronized sequentially, and higher levels of the schedule synchronized with the higher chaos pairs. By synchronizing a plurality of sub-chaos pairs simultaneously by adding different variable signals of main chaos and subordinate chaos of a chaotic pair to each of the main chaos and subordinate chaos of a plurality of sub-chaos pairs. There is a characteristic.

Hereinafter, a preferred embodiment of the vertical and / or horizontal synchronization method of the chaos system according to the present invention will be described in detail with reference to the accompanying drawings.

The present invention adds noise or chaos signals to the variables of the main chaos and subordinate chaos of each chaotic system to modulate the variables or synchronizes the main chaos and subordinate chaos of the chaos system. In addition to the coefficients of the device to modulate the coefficients by using a method of synchronizing to synchronize a plurality of chaos system as described with reference to Figure 3 as follows.

3 is a conceptual diagram illustrating a vertical synchronization method of the chaos system according to the present invention. When there are N chaos systems paired with the main chaos device and the subordinate chaos device, the main chaos device and the subordinate chaos device of each chaos system are It has any number of variables, where the variables of the first chaotic system 30-1 of the first chaotic system are x ₁ , y ₁ , z ₁ , ..., and the first main chaotic device 30-1. ) And the variables of the first dependent chaotic device 30-1 ′, which are the same chaotic system pairs, correspond to x ₁ ′, y ₁ ′, z ₁ ′,. The variables of the second main chaos device 30-2 of the second chaotic system are x ₂ , y ₂ , z ₂ ,..., And a second corresponding to the second main chaos device 30-2. The variables of the dependent chaos device 30-2 'are composed of pairs of x ₂ ', y ₂ ', z ₂ ', ..., in this way the main chaos device and the dependent chaos device of each chaos system. Are given, so that the variables of the Nth chaotic apparatus 30-N of the Nth chaotic system are x _N , y _N , z _N , ... and correspond to each other with the Nth chaotic apparatus 30-N. The variable of the Nth chaotic device 30-N ', which is the same chaotic system pair, is such that the chaotic system composed of N chaotic systems paired with x _N ', y _N ', z _N ', ... Synchronize to generate chaos.

In more detail with reference to Figure 3, when there are N chaos system consisting of the main chaos device and the dependent chaos device, there is a synchronization unit for synchronizing the N chaos system, respectively, First to Nth main synchronization units 40-1, 40-2, ..., for synchronizing the first to Nth main chaos devices 30-1, 30-2, ..., 30-N 40-N and first through Nth passivators 40-1 for synchronizing the first through Nth chaotic devices 30-1 ', 30-2', ..., 30-N '. ', 40-2', ..., 40-N ').

Here, the first to N-th master synchronization units 40-1, 40-2, ..., 40-N may generate a random chaos signal for synchronizing each chaos system with the first scaling factor β ₁ , β _2. First scaling units 41-1, 41-2, ..., 41-N scaling with..., β _N ), and first scaling units 41-1, 41-2. A subtractor 42-subtracting the scaled chaotic signal in .., 41-N and any variable value of the first to Nth main chaotic devices 30-1, 30-2, ..., 30-N. 1,42-2, ..., 42-N), a subtractor (42-1,42-2, ..., 42-N ) the output signal the second scaling factor (α _1, α _2, of. second scaling units 43-1, 43-2,..., 43 -N scaling with .., α _N ), and second scaling units 43-1, 43-2,. -N) and the first to n-th main chaos device 30 by adding arbitrary variable values of the first to N-th main chaos devices 30-1, 30-2, ..., 30-N. And adders 44-1, 44-2, ..., 44-N that feed back to -1,30-2, ..., 30-N).

In addition, the first to Nth passivation units 40-1 ', 40-2', ..., 40-N 'may generate any chaotic signals for synchronization with the first scaling factor β ₁ , β ₂ ,. .., β _N) a third scaling section (41-1 ', 41-2', ... , 41-N ') , a third scaler (41-1', 41-2 'for scaling a, ... subtracted from the scaled chaotic signal at < RTI ID = 0.0 > 41-N 'and < / RTI > Subtracter 42-1 ', 42-1', ..., 42-N 'and output signals of the subtractors 42-1', 42-1 ', ..., 42-N'. A fourth scaling unit 43-1'43-2 ', ..., 43-N' that scales by two scaling coefficients α ₁ , α ₂ ,..., Α _N , and a fourth scaling unit ( 43-1'43-2 ', ..., 43-N') and the first to Nth chaotic devices 30-1 ', 30-2', ..., 30-N ' Adders 44-1 ', 44-2' that feed back to the first to Nth chaotic devices 30-1 ', 30-2', ..., 30-N 'by adding arbitrary variable values , ..., 44-N ').

In this case, the first scaling factor β ₁ , β ₂ , .., β _N and the second scaling factor α ₁ , α ₂ , ..., α _N are both negative or positive values. Can be.

In general, chaos devices are very sensitive to initial values, so if the N chaos systems operate independently of each other, the variables xi (t) and xi '(t of the i chaos and dependent chaos of the i chaos system ), yi (t) and yi '(t), and the zi (t) and zi' (t) trajectories are very different. Therefore, the first to Nth main synchronization units 40-1, 40-2,..., 40 -N and the first to Nth passivators for synchronizing the N chaotic systems shown in FIG. Without 40-1 ', 40-2', ..., 40-N '), the signals from each chaotic system will move in different trajectories.

Therefore, in order to continuously synchronize the N chaotic systems, first, a kind of variable corresponding to each other in the first main chaotic device 30-1 and the first subordinate chaotic device 30-1 '(for example, x ₁ (t) and x ₁ '(t)) or more variables and select the same noise or chaos signal (ξ (t)) for the first main chaos 30-1 and the first subordinate chaos 30 -1 ') and add it to the variables (x ₁ (t) and x ₁ ' (t)) respectively. In more detail, the size of the noise or chaos signal ξ (t) is scaled by β ₁ times, and the first main chaos device 30-1 in the scaled noise or chaos signal β ₁ ξ (t). And subtract the variables x ₁ (t) and x ₁ '(t) of the first dependent chaotic device 30-1', respectively, and then scale them by α ₁ times so that the first main chaotic device and the dependent chaotic device 30- 1,30-1 ') to the variables x ₁ (t) and x ₁ ' (t), respectively, to the first main chaos device 30-1 and the first dependent chaos device 30-1 '. When fed back, the first chaotic system is synchronized with each other, and the corresponding variables are drawn with the same trajectory, whereby the synchronized main chaotic device and the dependent chaotic device are represented by Equations 1 and 2 below. Accordingly, the first main chaos device 30-1 and the first slave chaos device 30-1 'of the first chaotic system are connected to the first main synchronization unit and the floating unit 40-1 and 40-1'. Synchronized by x ₁ (t) = x ₁ '(t), y ₁ (t) = y ₁ ' (t) and z ₁ (t) = z ₁ '(t). That is, all state variable values of the first main chaos device 30-1 and all state variable values of the first subordinate chaotic device 30-1 ′ are equal to each other so that the spatiotemporal change is the same.

Here, the reason for synchronizing the first main chaos 30-1 and the first subordinate chaos 30-1 'of the first chaos system with noise or chaos will be described below.

The noise or chaos signal for synchronizing the chaos system paired with the main chaos device and the subordinate chaotic device is modulated in addition to the variables of the main chaotic device and the subordinate chaotic device corresponding thereto. The new nonlinear difference equation formed by the difference produces on-off intermittence, which causes the length of the average laminar to be infinitely long due to the on-off intermittence resulting in a critical condition that the difference between the two chaotic devices converges to zero. Within this critical condition, the new chaotic signal formed by the difference between the two chaotic devices immediately converges to zero, and the difference becomes zero, indicating that the same chaotic signals are outputted without the trajectory difference between the two chaotic devices.

Subsequently, any variable signal of the first main chaotic device 30-1 and the first subordinate chaotic device 30-1 'of the first chaotic system synchronized by the synchronization principle described above (for example, y ₁ ( t) and y ₁ ′ (t) are scaled by β ₂ times, and the second main chaotic device 30-2 in the scaled variable signals β ₂ y ₁ (t) and β ₂ y ₁ ′ (t) And subtracting arbitrary variables (e.g., y ₁ (t) and y ₁ '(t)) of the second and second dependent chaos device 30-2', respectively, and then scaling them by α ₂ times. Adding to the variables y ₁ (t) and y ₁ '(t) of (30-2,30-2'), respectively, to the second main chaos device 30-2 and the second dependent chaos device 30-2. The second chaos system is synchronized according to the synchronization principle described above, so that the variables of the second main chaos device 30-2 and the second subordinate chaos device 30-2 'are represented by Equation 3 and Equation 2. Appears as 4.

In this manner, the Nth main chaos 30-N and the Nth subordinate chaos 30-N 'of the Nth chaotic system are also synchronized, which are represented by Equations 5 and 6.

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In this case, each of the first to Nth chaotic pairs is a function of f, g, h and the like.

Here, in addition to the method of modulating the chaos signal for the synchronization of the chaos system consisting of a plurality of chaos system pairs to the variables of each chaos system pair, the chaos signal for synchronization is added to the coefficients of each chaos system pair We can synchronize each chaotic system by modulating its coefficients.

The case of applying the vertical synchronization method of the chaos system according to the present invention described above with reference to FIG. 4 will now be described.

In general, the chaotic system includes a differential equation system and a differential equation system. The differential equation system is a Lorentz system, a Rossler system, and a duffing system. ) Systems are widely known, and a logistic map or the like is known as a system of difference equations.

4 is a view showing a synchronization method of a chaotic system composed of a low lens chaos system and a duffing chaos system according to the present invention.

Referring to FIG. 4, the first chaotic system pair is composed of a low lens main chaos device 50, which is given as a low lens chaos system, and the same low lens subordinate chaos device 50 ′ corresponding thereto. The pair consists of a duffing main chaos device 60, which is given as a duffing chaos system, and a corresponding duffing subordinate chaos device 60 'corresponding to the first and second synchronization units 70 and 70 for synchronizing the low lens chaos system. ') And third and fourth synchronization units 80 and 80' for synchronizing the duffing chaos system.

Here, the first synchronization unit 70 is a bandpass filter (71) for filtering the noise or chaos signal (ξ (t)) applied from the outside, the filtered noise or chaos signal and low lens main chaos A subtractor 72 which subtracts any variable of the device 70 (e.g., y (t) here), a scaling unit 73 that scales the output signal of the subtractor 72 by α times, and scaled noise or chaos And an adder 74 that adds a signal and an arbitrary variable y (t) of the low lens main chaos device 70. In this case, the second synchronization unit 70 'includes a band pass filter 71', a subtractor 72 ', a scaling unit 73' and an adder 74 '.

In addition, the third synchronization unit 80 for synchronizing the duffing chaotic system pair may include a first scaling unit γ-scaling an arbitrary variable (eg, x (t)) signal input from the low lens chaotic system pair ( 81), a subtractor 82 which subtracts the scaled variable signal and any variable signal u (t) of the main chaotic device 60 of the duffing chaotic system, and β times the signal output from the subtractor 82. And a second scaling unit 83 to scale, and an adder 84 that adds the scaled signal and an arbitrary variable signal u (t). In this case, the fourth synchronization unit 80 'includes a first scaling unit 81', a subtractor 82 ', a second scaling unit 83', and an adder 84 '.

The synchronization method of the chaotic system configured as described above is as follows.

First, the noise or chaos signal for synchronizing the low lens chaos system pair is prevented by any other user by the band pass filter 71, and then any arbitrary low lens main chaotic device 70 and subordinate chaotic device 70 '. Subtract the variable y (t) of and multiply it by α times, and apply the signal to the variables y (t) and y (t) 'of the low lens main chaos 70 and the subordinate chaos 70'. As the feedback is added to each other, the low lens main chaos device 70 and the subordinate chaos device 70 'are synchronized, which are represented by Equations 7 and 8.

In this case, in Equations 7 and 8 Is a parameter.

Then, the arbitrary variable signals (x (t), x (t) ') of the main chaotic device 70 and the dependent chaotic device 70' of the synchronized low lens chaos system pair are scaled by γ times, and the signal is scaled. Subtracts any of the variables (u (t), u (t) ') of the main chaos device 60 and the dependent chaos device 60' of the duffing chaotic system pair and scales the subtracted signal by β times (u (t), u (t) ') is added to each of the feedback and synchronized, the main chaos device and the chaotic device of the synchronized duffing chaos system is shown in equation (9) and (10).

In this case, in Equations 9 to 10, B is an amplitude and Ω is a frequency.

As shown in Equation 7 to Equation 10, the signal of the chaos system that appears when the chaos system in which the low lens chaos system pair and the duffing chaos system pair are continuously synchronized is described with reference to FIG. 5.

FIG. 5A is a noise signal for synchronization, FIG. 5B is a variable signal of a main chaos device of a low lens chaos system, and FIG. 5C is a signal representing a variable difference between a main chaos device of a low lens chaos system and a corresponding chaotic device corresponding thereto. Waveform. 5D is an arbitrary variable signal of a synchronized low lens chaos system, and FIG. 5E is a signal waveform of a duffing chaotic system created by adding an arbitrary variable signal of the low lens chaotic system (FIG. 5D) to a variable signal of a duffing chaotic system. 5F is a signal waveform showing a variable difference between a main chaotic device of a duffing chaotic system and a dependent chaotic device corresponding thereto.

Here, the noise signal of Figure 5a ξ (t) = Acos (ωt) Where A = 0.5 + 10.0ζ (where ζ is a random number between 0 and 1) and ω = 2πν (ν = 8.0 × (0.5 + ζ)), and this noise signal is added to the low lens chaos meter. When the chaotic device 50 and the dependent chaotic device 50 'are synchronized, the main chaotic device variable and the variable of the chaotic device as shown in FIG. 5B have the same temporal shape. Therefore, it can be seen that the difference between the two chaotic device variables converges to zero as shown in FIG. 5C. In this case, signals having a value of 0 for two chaotic devices frequently appear because of on-off intermittent characteristics.

5D is an arbitrary variable signal of the low lens chaotic pair for synchronizing the duffing chaotic pairs, the signal of each of the main chaotic device 60 and the dependent chaotic device 60 'of the duffing chaotic pair. When the synchronization is performed in addition to the variable signal, the variable signal of the main chaotic device is output as shown in FIG. 5D, and the signals of the two chaotic devices coincide to have the same temporal shape. Therefore, as shown in FIG. 5F, the difference between the variables of the two chaotic devices converges to zero.

Accordingly, the present invention can sequentially synchronize N chaotic pairs independent of each other, as described above. Any variable signal outputted to synchronize the chaotic system of the rear stage in the synchronized front chaotic system is the front chaos system. The branch chaos system can be synchronized by a new chaotic signal generated by adding, subtracting, multiplying, or dividing a plurality of variable signals. That is, the random chaos signal output to synchronize the chaos pairs of the rear end in the front chaos pair is to synchronize the chaos pairs of the rear end by a new chaos signal generated by arithmetic operation of the variable signal of the front chaos system. .

Next, an example of application to a multi-channel secret communication system using the synchronization method of the chaos system according to the present invention as described above will be described.

In a secret communication system, first, when the main chaos device and the sub chaotic device are synchronized with each other at the transmitting end, a random signal of the main chaotic device is used as a masking signal, and the voice is much smaller than the power spectrum of the chaotic signal generated in the main chaotic device. The signal, the information signal, is mixed and transmitted along with the noise or another chaos signal for synchronization.

In addition, when the receiver uses noise or another chaotic signal as a synchronization signal, obtains a signal from the dependent chaotic device, and obtains a difference between the main chaotic device and the information signal mixed together, the original information signal is restored.

This is because, in the absence of an information signal, if the main chaotic device and the subordinate chaotic device are synchronized with each other, the two chaotic devices are completely identical to each other. At this time, since the chaos signal from the chaos system after synchronization is very disordered, it is impossible to know how the chaos device is actually made by using the equation, and thus the signal from the chaos device can be found by various methods such as chaos prediction. There is a merit that the confidentiality is very high.

The multi-channel secret communication method using a plurality of chaotic pairs synchronized by the vertical synchronization method of the present invention by such a secret communication method will be described with reference to FIG.

FIG. 6 illustrates a concept for explaining a multi-channel secret communication system according to the present invention, wherein the adders 100-1, 100-2, ..., in the synchronization device of the chaos system of FIG. 100-N) and a decryption unit consisting of subtractors 110-1, 110-2, ..., 110-N.

Referring to FIG. 6, a plurality of adders 100-1, 100-2,..., 100 at the transmitting end of the chaos system in which N consecutive pairs of chaos systems are synchronized by the vertical synchronization method of the chaos system according to the present invention described in FIG. -N is the information signal m ₁ , m ₂ , ..., m to any variable of the main chaos device 30-1,30-2, ..., 30-N of each chaotic system pair. _N ) is added and transmitted to the receiver. At the receiving end, the plurality of subtractors 110-1, 110-2, ..., 110-N is applied to the variables of the main chaos devices 30-1, 30-2, ..., 30-N from the received signal. Restore the information signals m ₁ , m ₂ , ..., m _N by subtracting the variables of the respective dependent chaotic devices 30-1 ', 30-2', ..., 30-N '. .

In other words, the first slave chaos device 30-1 'is loaded with a weak voice signal, that is, an information signal m ₁ , to be transmitted by the first main chaos device 30-1 of the first chaos system pair. Send to). Then, the first subordinate chaos 30-1 'receives the transmitted signal and the noise or another chaotic signal and corresponds to the variable from the first main chaotic device 30-1 with this noise or another chaotic signal. Synchronize with the synchronization method of the present invention in addition to the variable.

In this manner, the first subordinate chaotic device 30-1 'has a trajectory difference corresponding to the difference of the transmitted information signal. That is, the original information signal from which the signal obtained by subtracting the variable of the first main chaotic device 30-1 and the information signal m ₁ from the variable of the first dependent chaotic device 30-1 'is immediately decoded. It is

Similar to the secret communication method of the first chaotic pair described above, the second chaotic pair carries a weak voice signal, that is, an information signal m ₂ , to be transmitted by the second main chaotic apparatus 30-2. 2 slave chaos device 30-2 'receives second variable chaos device 30-2' and receives a random variable signal of the first chaos system pair synchronized with the transmitted signal. The synchronization method according to the present invention adds an arbitrary variable signal to a variable corresponding to the variable from the second main chaotic device 30-2. At this time, a method of synchronizing each chaotic system pair of the chaotic system may be used to modulate a noise signal or the like in addition to the coefficients of the main chaotic device and the dependent chaotic device.

In this way, a multi-channel secret communication is performed using a chaos system composed of N chaotic pairs.

As described above, in order to perform multi-channel secret communication using the vertical synchronization method of the chaos system according to the present invention, each communication channel should not have any relationship with each other, for example, the first lens of the lens chaos system of the chaos system in FIG. Looking at the correlation with reference to Figure 7 as follows.

That is, FIG. 7A shows correlations such as the δ-function as the correlation of the noise signal itself, and FIG. 7B shows the correlation of the z-variable itself of the low lens chaos system before synchronizing with the noise signal. You can see the big picture. In addition, it can be seen from FIG. 7c that the self-correlation of the z-variable of the low-lens chaos system synchronized by the noise signal has a correlation similar to that of the noise signal in the δ function. It can be seen that it has characteristics similar to noise. In addition, when the information signal is transmitted, the noise signal and the chaotic signal synchronized with the noise signal are also transmitted. In this case, the third party should not know the information signal hidden inside the chaotic signal using the two signals. The cross-correlation between and the chaotic signal synchronized with the noise signal is similar to the self-correlation of the noise signal, indicating that there is little correlation between the two signals. Therefore, since these two signals have nothing to do with each other, the secret communication using the synchronization method of the present invention not only effectively hides the transmitted information signal, but also the relationship between the chaotic signals between each channel. Almost no effective secret communication is possible.

In addition, the method of sequentially synchronizing the N chaotic pairs of the present invention can be applied to the hierarchization between secret users. That is, as shown in FIG. 6, the noise signal for synchronizing the first chaotic system pair is shared by all users, but the signal output from the first chaotic system pair synchronized by the noise signal shares the first chaotic system pair. Only a user who knows the information signal communicated using the first chaos pair. Therefore, a user having only the first chaotic pair cannot know the contents of the information signal transmitted and received in the second chaotic pair, and thus a higher layer having both the lower layer having only the first chaotic pair and the first and second chaotic pairs. The multilayering of information is possible between users of the hierarchy. That is, the upper layer can know all of the information of the lower layer, but the lower layer can not know the information of the upper layer, it is possible to fundamentally block the leakage of high-level information.

Meanwhile, a horizontal synchronization method of the chaotic system according to the present invention will be described with reference to FIG. 8.

8 is a schematic diagram illustrating a horizontal synchronization method of a chaotic system according to the present invention.

Here, horizontal synchronization of a chaotic system composed of a plurality of chaotic pairs refers to simultaneously synchronizing a plurality of independent lower layers of the same layer included in the upper layer by an arbitrary chaotic signal output from the chaotic system of the upper layer. .

That is, referring to Fig. 8, the upper main chaos device having variables such as x, y, z, u, ..., which are previously synchronized by any chaotic signal or noise signal of the synchronized chaotic system at the front end thereof. (200), the lower main chaos (210-1, 210-2, ...) of the same layer, and the lower main chaos (210) by a random chaos signal respectively output from the upper main chaos (200) It consists of a plurality of synchronization unit (220-1,220-2, ..) for synchronizing -1,210-2, ...). Here, the first synchronization unit 220-1 includes a first scaling unit 221, a subtractor 222, a second scaling unit 223, and an adder 224. Other synchronization units have the same configuration.

The horizontal synchronization method of the present invention configured as described above is as follows.

First, the upper main chaos 200 is pre-synchronized by the noise signal ξ (t) or any chaotic signals output from the synchronized upper main chaos (not shown) and synchronized upper An arbitrary variable signal (eg, u (t) here) of the main chaos device 200 is output. The first synchronization unit 220-1 for synchronizing the A lower main chaotic device 210-1 scales the arbitrary variable signal u (t) by α ₁ times, and the A lower main chaotic device 210-1. The subtracted signal is subtracted from an arbitrary variable of (210-1), and the subtracted signal is scaled β ₁ times and then added to each of the random variables to be fed back to synchronize.

And, in order to synchronize the B lower main chaos device 210-2, the upper main chaos device 200 may generate a variable signal other than any variable for synchronizing the A lower chaos device 210-1 (for example, z ( t)) The arbitrary variable signal for synchronizing the B lower main chaotic device 210-2 is α ₂ times scaled, and the signal is subtracted from any variable of the B lower main chaotic device 210-2 and subtracted. After scaling to β ₂ times and adding to each of the random feedback to be synchronized, the plurality of lower main chaos device is synchronized by this method. Here, the synchronization of the subordinate chaos described is the same.

In this manner, a plurality of chaotic pairs of the same layer are synchronized, and the chaotic pairs of the same lower layer are synchronized with each other because they are synchronized by different variable signals of the upper layer chaotic system. Therefore, when secret communication is performed by the horizontal synchronization method as in the secret communication method using the vertical synchronization described above, the information signals encrypted in the same plurality of lower layer chaos systems are encrypted by different signals, so that the different lower layer chaos It is impossible to restore the system's password.

Therefore, when secret communication is performed using the vertical and horizontal synchronization method of the chaos system according to the present invention, the user can be layered by the range including the chaos system to maintain confidentiality by sharing and blocking information signals. Will be.

In addition, by the vertical and horizontal synchronization method of the chaos system according to the present invention is composed of a plurality of upper chaos system as shown in Figure 3 and a plurality of lower chaos system contained in a certain upper chaos system as shown in FIG. The chaos system simultaneously synchronizes a plurality of lower chaos systems included therein by different variable signals of the upper chaos system synchronized with the vertical synchronization in which the plurality of upper chaos systems are sequentially synchronized.

As described above, the vertical synchronization method of the chaos system according to the present invention is a variable of the second chaos system pair or a random signal output from the first chaos system pair synchronized by the external noise or another chaos signal In addition to the modulated modulator, the chaotic system composed of a plurality of chaotic pairs is vertically and continuously synchronized by a method of synchronizing, and an information signal is loaded on an arbitrary chaotic signal output from the plurality of chaotic pairs and the receiver is synchronized with the present invention. The multi-channel secret communication is performed by generating a chaotic signal identical to the chaotic signal of the transmitting end, subtracting the signal, and restoring the information signal.

In addition, the horizontal synchronization method of the chaos system according to the present invention modulates each variable signal output from the upper chaos system synchronized by the upper chaos system pair of the previous stage in addition to the variables or coefficients of the plurality of lower chaos systems. As a result, a plurality of lower chaos systems are synchronized at the same time.

Further, in the chaos system composed of a plurality of upper chaos systems and a plurality of lower chaos systems included in any upper chaos system, the synchronization of the plurality of upper chaos systems is sequentially performed by the vertical synchronization method of the present invention. Along with the synchronization of the chaos system, a plurality of lower chaos systems are simultaneously synchronized by the horizontal synchronization method of the present invention.

The vertical and / or horizontal synchronization method of the chaos system according to the present invention modulates any variable signal output from the synchronized chaos pair of the previous stage in addition to any variable or coefficient of the chaos pair of the next stage, Random variable signals of the chaos system of the hierarchy are modulated in addition to the variables or coefficients of the lower-layer chaos system included in the upper-level chaos system, so that a plurality of chaotic pairs can be easily synchronized continuously.

In addition, the synchronization of the chaos system of the present invention because the plurality of chaos system is continuously synchronized, there is also an effect that the multi-channel secret communication using a plurality of synchronized chaos system can be easily made.

In addition, it is possible to increase the confidentiality, etc., because the hierarchical layer between users according to the range including the vertical or horizontal synchronized chaos system can be shared and blocked between users.

Claims (15)

In the control method of the chaos system in which there are a plurality of chaos system pairs composed of a main chaos system and a slave chaos system identical to the main chaos system, (a) modulating one or a plurality of variables of the main chaotic system of the first chaotic system pair among the plurality of chaotic system pairs with noise or an independent chaotic signal, and subordinate chaos corresponding to the main chaotic system of the first chaotic system pair Synchronizing the first chaotic pairs by modulating the system parameters with the noise or independent chaotic signals, (b) modulating one or a plurality of variables of the main chaotic system of the second chaotic system pair among the plurality of chaotic system pairs into arbitrary variable signals of the main chaotic system of the first chaotic system pair synchronized; Any variable signal of the dependent chaotic system corresponding to any variable signal of the main chaotic system of the second chaotic system pair corresponding to the main chaotic system of the chaotic system pair To modulate the second chaotic pair, (c) modulating one or a plurality of variables of the main chaos of the next chaotic pair with any variable signal of the main chaos of the second chaotic pair, Modulating a variable of the dependent chaotic system corresponding to an arbitrary variable signal of the main chaotic system of the next chaotic system pair with a variable of the chaotic system corresponding to an arbitrary variable signal, (d) The method of vertically synchronizing the chaos system, characterized in that by sequentially performing the above method to synchronize the plurality of chaotic pairs sequentially. The method of claim 1, wherein one or a plurality of coefficients of each chaotic system pair are modulated and synchronized by a variable signal for synchronizing the plurality of chaotic systems. 2. The method of claim 1, wherein the variable signal for synchronizing the chaotic system uses a new signal that is arithmetic of a plurality of variable signals of a synchronized chaos system pair. The vertical synchronization method of claim 1, wherein the noise of the chaotic system is modulated by filtering the noise or independent chaotic signal and the variable signal for synchronizing the chaotic system pairs. 5. The method of claim 4, wherein the noise or independent chaotic signal and the variable signal for synchronizing each chaotic system pair are filtered using a bandpass filter. The main chaos system of claim 1, wherein each information signal is added to and transmitted from one or more chaos signals generated in each main chaos system of the synchronized chaos system, and the chaos system of each chaos system pair mixed with the transmitted information signals. A chaotic signal identical to the chaotic signal of is generated in each dependent chaotic system corresponding to each main chaotic system, and the information signal and the chaotic signal of each main chaotic system are mixed to transmit the chaotic signal of the dependent chaotic system. A vertical synchronization method of a chaotic system, characterized in that for performing subchannel multi-channel communication to restore the information signal by subtracting. 7. The method of claim 6, wherein the information signal is shared and blocked according to a range including the chaotic pair by encryption of the information signal by the multi-channel secret communication. 2. The method of claim 1, wherein the chaotic system comprises a chaotic system given by a differential equation and a chaotic system given by a differential equation. In the chaos system control method comprising an upper chaos system pair and a plurality of lower chaos system pairs included in the upper chaos system, (a) synchronizing the upper chaos pairs by a variable signal output from the upper chaos system of the previous stage in the chaos system; (b) modulating one or a plurality of variables of the main chaotic system of the first lower chaotic pair of the plurality of lower chaotic pairs into any variable of the main chaotic system in the synchronized upper chaotic pair, The first lower chaos pair is modulated by a variable signal of a subordinate chaos system corresponding to an arbitrary variable signal of the main chaos system of the upper chaos system pair to a variable of the chaos system corresponding to the main chaos system of the lower chaos system pair. To synchronize (c) modulating any one or a plurality of variables of the main chaotic system of the second lower chaotic pair of the plurality of lower chaotic pairs into variable signals of the main chaotic system of the upper chaotic pair, Synchronizing the subordinate chaos of the second subordinate chaotic pair with the subordinate chaotic variable in the first subordinate chaotic based pair corresponding to the variable signal for modulating the variable of the chaotic pair, (d) horizontally synchronizing the chaotic system, characterized in that by performing the above method repeatedly to synchronize the plurality of lower chaos pairs at the same time. 10. The method of claim 9, wherein one or more coefficients of each of the lower chaotic pairs are modulated and synchronized by a variable signal for synchronizing the plurality of lower chaotic pairs. 10. The horizontal synchronization method of claim 9, wherein the variable signal for synchronizing the plurality of lower chaotic pairs uses a new signal obtained by arithmetic operation of the plurality of variable signals of the upper chaotic pair. 10. The method of claim 9, wherein the variable signal for synchronizing the lower chaotic pairs is filtered to modulate the variables of each chaotic pair. 13. The method of claim 12, wherein the variable signal for synchronizing the lower chaotic pairs is filtered using a bandpass filter. 10. The method of claim 9, wherein the leakage of the information signal between the lower chaos pairs is blocked by the encryption of the information signals using the synchronization of the lower chaos pairs simultaneously. A plurality of lower chaos included in the upper chaos system composed of main chaos systems, a plurality of higher chaos systems paired with the same chaos systems as the main chaos systems, and the main chaos systems and the dependent chaos systems In the control method of the chaotic system composed of a system, (a) modulating and synchronizing any variable of the main chaotic system of the first chaotic system pair of the upper chaotic system with a corresponding chaotic system by noise or another chaotic signal, (b) Arbitrary variable signals of the main chaotic system of the synchronized upper chaotic system pairs and variable signal of the dependent chaotic system corresponding to the main chaos system and the dependent chaotic system of the next higher chaotic system pair In addition, it modulates a plurality of higher chaos pairs sequentially, (c) The main chaotic system and the subordinate chaotic system of the plurality of lower chaotic system pairs with different variable signals of the main chaotic system and the subordinate chaotic system of the synchronized constant upper chaotic system pair with synchronization of the upper chaotic system pair; And synchronizing the plurality of lower chaos pairs simultaneously in addition to each of the arbitrary parameters of the chaotic system.