Pseudo-Random Number Generator Based on Logistic Chaotic System
<p>Parameter generation of normal chaotic system.</p> "> Figure 2
<p>Iteration times of the normal chaotic system.</p> "> Figure 3
<p>(<b>a</b>) Logistic bifurcation diagram; (<b>b</b>) Lyapunov exponent of Logistic mapping.</p> "> Figure 4
<p>Dynamic behavior under different seed parameters.</p> "> Figure 5
<p>Comparison of distribution: (<b>a</b>) Distribution after rearranging once; (<b>b</b>) Distribution after rearranging twice; (<b>c</b>) Distribution after improved.</p> "> Figure 6
<p>Histogram of integer value sequence: (<b>a</b>) Histogram of integer value sequence of sample 1; (<b>b</b>) Histogram of integer value sequence of sample 2; (<b>c</b>) Histogram of integer value sequence of sample 3; (<b>d</b>) Histogram of integer value sequence of sample 4.</p> "> Figure 6 Cont.
<p>Histogram of integer value sequence: (<b>a</b>) Histogram of integer value sequence of sample 1; (<b>b</b>) Histogram of integer value sequence of sample 2; (<b>c</b>) Histogram of integer value sequence of sample 3; (<b>d</b>) Histogram of integer value sequence of sample 4.</p> ">
Abstract
:1. Introduction
2. Pseudo-Random Sequence Generator Algorithm
2.1. Generation of Initial Pseudo-Random Sequences
2.2. Generation of Normal Pseudo-Random Sequences (Taking the Nth Times as an Example)
3. Performance Analysis
3.1. Logistic Chaotic System
3.2. Sequence Analysis
3.2.1. Rearrangement Analysis
- In the 15 digital sequence generated by chaotic sequence, a single real number iterates many times and more than one number iterates many times.
- The different numbers between the rearranged sequence and the original sequence are less than 12.
3.2.2. Extraction Analysis
3.2.3. Modular Operation Analysis
3.2.4. Analysis of Pseudo-Random Sequences
3.3. Safety Analysis
3.3.1. The Key Space
3.3.2. Resistance to Attack
- Attack the seed parameters
- Attack the sequence generated by the chaotic system
- Attack the sequence after rearrangement
3.3.3. NIST Analysis
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Iterations | |||||
---|---|---|---|---|---|
0.9120 | 0.3050 | 0.4341 | 0.7967 | 0.1947 | |
0.9121 | 0.3047 | 0.5385 | 0.6639 | 0.2505 | |
0.9122 | 0.3045 | 0.6726 | 0.9110 | 0.9343 |
System Parameters | Initial Value | Number of Iterations | 16 Floating Point Numbers Generated |
---|---|---|---|
3.8001 | 0.4000 | 100 | 0.272365554369460 |
3.8002 | 0.4001 | 110 | 0.641375560291393 |
3.8003 | 0.4002 | 120 | 0.939999673380606 |
3.8003 | 0.4003 | 120 | 0.419646260514604 |
3.8004 | 0.4003 | 120 | 0.935574949032498 |
3.8004 | 0.4004 | 120 | 0.246683325821152 |
3.8004 | 0.4004 | 121 | 0.706230850080309 |
Extraction Method | Extraction Times | |||
---|---|---|---|---|
(1, 2, 3, 4) | 10.4222 | 10.4224 | 10.4221 | 10.4222 |
(5, 6, 7, 8) | 10.4220 | 10.4218 | 10.4223 | 10.4222 |
(9, 10, 11, 12) | 10.4220 | 10.4224 | 10.4218 | 10.4220 |
(1, 5, 9, 13) | 10.4221 | 10.4220 | 10.4219 | 10.4223 |
(2, 6, 10, 14) | 10.4222 | 10.4221 | 10.4221 | 10.4221 |
(3, 7, 11, 15) | 10.4223 | 10.4214 | 10.4222 | 10.4219 |
Sample | |||
---|---|---|---|
Sample1 | 3.8000 | 0.5000 | 1000 |
Sample2 | 3.9748 | 0.9734 | 6376 |
Sample3 | 3.6779 | 0.6942 | 8459 |
Sample4 | 3.7166 | 0.1674 | 7348 |
Sample | Standard Deviation |
---|---|
Sample 1 | 0.000488336 |
Sample 2 | 0. 000308604 |
Sample 3 | 0.000435827 |
Sample 4 | 0.000373529 |
Sample | Numbers of Sample Extracted | ||||||
---|---|---|---|---|---|---|---|
10000 | 20000 | 40000 | 60000 | 80000 | 100000 | 200000 | |
Sample 1 | 7.9682 | 7.9681 | 7.9695 | 7.9692 | 7.9688 | 7.9692 | 7.9692 |
Sample 2 | 7.9939 | 7.9947 | 7.9951 | 7.9952 | 7.9951 | 7.9956 | 7.9955 |
Sample 3 | 7.9896 | 7.9911 | 7.9911 | 7.9911 | 7.9913 | 7.9911 | 7.9913 |
Sample 4 | 7.9922 | 7.9929 | 7.9933 | 7.9936 | 7.9936 | 7.9933 | 7.9934 |
51.9231 | ||
42.3077 | ||
51.9231 | ||
43.2692 | ||
44.2308 |
Test Name | p_Value | Result |
---|---|---|
Approximate Entropy | 0.287458 | SUCCESS |
Block Frequency | 0.578344 | SUCCESS |
Cumulative Sums | 0.691934 | SUCCESS |
FFT | 0.402675 | SUCCESS |
Frequency | 0.556298 | SUCCESS |
Linear Complexity | 0.651363 | SUCCESS |
Longest Run | 0.084999 | SUCCESS |
NonOverlapping Template | 0.457732 | SUCCESS |
Overlapping Template | 0.210308 | SUCCESS |
Random Excursions | 0.347548 | SUCCESS |
Random Excursions Variant | 0.219526 | SUCCESS |
Rank | 0.670342 | SUCCESS |
Runs | 0.510265 | SUCCESS |
Serial(1) | 0.512756 | SUCCESS |
Serial(2) | 0.595549 | SUCCESS |
Universal | 0.784275 | SUCCESS |
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Wang, L.; Cheng, H. Pseudo-Random Number Generator Based on Logistic Chaotic System. Entropy 2019, 21, 960. https://doi.org/10.3390/e21100960
Wang L, Cheng H. Pseudo-Random Number Generator Based on Logistic Chaotic System. Entropy. 2019; 21(10):960. https://doi.org/10.3390/e21100960
Chicago/Turabian StyleWang, Luyao, and Hai Cheng. 2019. "Pseudo-Random Number Generator Based on Logistic Chaotic System" Entropy 21, no. 10: 960. https://doi.org/10.3390/e21100960