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Construction method of three-dimensional multi-cavity chaotic system based on rotation method and method of obtaining pseudo-random sequence

A pseudo-random sequence and chaotic system technology, applied in the field of nonlinear systems and digital signals, can solve problems such as unfavorable engineering applications, and achieve the effect of excellent randomness

Active Publication Date: 2021-09-28
CENT SOUTH UNIV
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Problems solved by technology

However, the current discrete multi-cavity chaotic maps can only generate bipolar signals, which is not conducive to engineering applications

Method used

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  • Construction method of three-dimensional multi-cavity chaotic system based on rotation method and method of obtaining pseudo-random sequence
  • Construction method of three-dimensional multi-cavity chaotic system based on rotation method and method of obtaining pseudo-random sequence
  • Construction method of three-dimensional multi-cavity chaotic system based on rotation method and method of obtaining pseudo-random sequence

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Experimental program
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Embodiment 1

[0038] A three-dimensional multi-cavity chaotic system based on a rotation method, the establishment method of which includes the following steps:

[0039] The first step is to establish a one-dimensional chaotic system. The model of the chaotic system is Expression 1):

[0040] z(n+1)=h×sin(π×sin(c×z(n)))1);

[0041] Among them: z is the state variable; n is the number of iterations for the system to solve; h is the height of the chaotic system attractor; c is the internal disturbance frequency, and its value range is (0, +∞).

[0042] When c×h≤π is satisfied, the iterative sequence of expression 1) always maintains the same polarity as the initial value of the system, and the verification is as follows:

[0043] The first case: c>0, h>0, c×h≤π, -h≤z(0)<0;

[0044] n=0

[0045] -c×h≤c×z(0)<0

[0046] -π≤c×z(0)<0

[0047] -1≤sin(c×z(0))<0

[0048] -π≤π×sin(c×z(0))<0

[0049] -1≤sin(π×sin(c×z(0)))<0

[0050] -h≤h×sin(π×sin(c×z(0)))<0

[0051] -h≤z(1)<0

[0052] ·n=m(m...

Embodiment 2

[0100] A method for obtaining a pseudo-random sequence, the pseudo-random sequence is obtained based on the three-dimensional multi-cavity chaotic system obtained by the construction method disclosed in Embodiment 1.

[0101] The method for obtaining the pseudo-random sequence in this embodiment is: a chaotic sequence generated according to a certain dimension of the model expression 3); each state value in the chaotic sequence is enlarged by 10 6 times or 10 5 After multiplying, modulo 256 to obtain an integer sequence whose value varies between 0 and 255; convert each value in the integer sequence into an 8-bit binary number to obtain a pseudo-random sequence;

[0102] The pseudorandom sequence is Expression 4):

[0103]

[0104] Among them: PRBS is the generated pseudo-random series, floor is the round-down operation, mod is the modulo operation, x i is a chaotic sequence.

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Abstract

The invention discloses a method for constructing a three-dimensional multi-cavity chaotic system based on a rotation method. Firstly, a one-dimensional chaotic system whose iteration sequence always maintains the same polarity as the initial value of the system under specific conditions is established, and then based on the one-dimensional chaotic system Establish a three-dimensional hollow multi-cavity hyperchaotic system, and finally add filling items to the two dimensions on the basis of the three-dimensional hollow multi-cavity hyperchaotic system to obtain a three-dimensional solid multi-cavity hyperchaotic system. The establishment method is simple; the three-dimensional multi-cavity chaotic system has three-dimensional multi-cavity Cavity structure, controllable signal polarity, better performance (clear attractor phase diagram and rich dynamic characteristics) and other characteristics. The invention also discloses a method for obtaining a pseudo-random sequence, which is obtained based on the above-mentioned three-dimensional multi-cavity chaotic system. The pseudo-random sequence obtained in the invention has passed all tests, has excellent randomness, is suitable for encryption and other engineering fields, and is widely used.

Description

technical field [0001] The invention relates to the technical field of nonlinear systems and digital signals, in particular to a method for constructing a three-dimensional multi-cavity chaotic system based on a rotation method and a method for obtaining a pseudo-random sequence. Background technique [0002] Chaos is the unpredictable behavior of a deterministic system due to its extreme sensitivity to initial values ​​and parameters. Chaotic systems include continuous systems and discrete systems. Compared with continuous systems, discrete systems are simpler to implement, have less algorithm overhead, and can generate chaotic sequences with higher complexity, so they have better practicability. Chaotic systems can be divided into one-dimensional systems and high-dimensional systems. The one-dimensional chaotic system has a simple structure, few parameters, and a narrow chaotic range. Its phase space orbit is easy to predict, and it is difficult to resist attacks such as...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H04L9/00
CPCH04L9/001H04L2209/26
Inventor 孙克辉武晨阳
Owner CENT SOUTH UNIV
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