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An Analysis of Deterministic Chaos as an Entropy Source for Random Number Generators
1TÜBİTAK-Informatics and Information Security Research Center, 41470 Gebze, Kocaeli, Turkey.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Deterministic chaos from phase-locked loops (PLLs) can generate random numbers. Both bounded and unbounded chaos show potential as entropy sources, comparable to Gaussian white noise for random bit generation.
Area of Science:
- Chaos theory
- Information theory
- Signal processing
Background:
- Deterministic chaos is explored as a source for random number generation.
- Phase-locked loop (PLL) devices can exhibit chaotic behavior.
- Assessing the quality of random numbers is crucial for cryptography and simulations.
Purpose of the Study:
- To analytically study deterministic chaos from PLLs as an entropy source.
- To compare bounded and unbounded chaos against Gaussian white noise for random bit generation.
- To evaluate the impact of sampling frequency on the randomness of generated bits.
Main Methods:
- Numerical simulations of chaotic signals from a PLL device.
- Analysis of bounded and unbounded chaos properties, including power spectrum flatness.
- Generation of random bits by sampling chaotic signals and Gaussian white noise.
- Autocorrelation and approximate entropy analysis of generated bit sequences.
Main Results:
- Bounded and unbounded chaos exhibit distinct power spectrum characteristics.
- Random bit sequences were generated from both chaotic signals and Gaussian noise.
- Varying sampling frequencies influenced the randomness of the generated bits.
- Chaos-derived random numbers showed comparable quality to Gaussian white noise.
Conclusions:
- Deterministic chaos from PLLs is a viable entropy source for random number generators.
- Bounded and unbounded chaos offer different properties that can be leveraged for randomness.
- The study provides insights into optimizing random bit generation using chaotic systems.
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