Abstract
This paper presents an analytical study on the use of deterministic chaos as an entropy source for the generation of random numbers. The chaotic signal generated by a phase-locked loop (PLL) device is investigated using numerical simulations. Depending on the system parameters, the chaos originating from the PLL device can be either bounded or unbounded in the phase direction. Bounded and unbounded chaos differs in terms of the flatness of the power spectrum associated with the chaotic signal. Random bits are generated by regular sampling of the signal from bounded and unbounded chaos. A white Gaussian noise source is also sampled regularly to generate random bits. By varying the sampling frequency, and based on the autocorrelation and the approximate entropy analysis of the resulting bit sequences, a comparison is made between bounded chaos, unbounded chaos and Gaussian white noise as an entropy source for random number generators.
Highlights
Random number generators (RNGs) are fundamental components of cryptographic systems, as they are responsible for generating the unpredictable key values used in ciphering algorithms to protect the integrity, confidentiality and authenticity of the information [1]
The bounded and unbounded chaos is benchmarked against white imposes restrictions on the maximum allowable sampling frequency to maintain randomness in the Gaussian noise, which mightTo originate in athis stationary stochastic process
It is numerically shown that up to a certain frequency which is dependent on the phase-locked loop (PLL) system study on the application of bounded and unbounded chaos from a PLL device as an entropy source parameters, unbounded chaos approaches white Gaussian noise as an entropy source to generate for RNGrandom and thenumbers comparison deterministic bounded or unbounded chaosTo and by the of regular sampling of an irregular waveform method
Summary
Random number generators (RNGs) are fundamental components of cryptographic systems, as they are responsible for generating the unpredictable key values used in ciphering algorithms to protect the integrity, confidentiality and authenticity of the information [1]. The bounded and unbounded chaos is benchmarked against white imposes restrictions on the maximum allowable sampling frequency to maintain randomness in the Gaussian noise, which mightTo originate in athis stationary stochastic process Investigate phenomenon, the sampling frequency is graduallyshown that up to a certain which is dependent on the are PLL system parameters, unbounded elevated, andfrequency the randomness of the resulting bit streams assessed through the application of the chaos concepts of autocorrelation and approximate entropy. It is numerically shown that up to a certain frequency which is dependent on the PLL system study on the application of bounded and unbounded chaos from a PLL device as an entropy source parameters, unbounded chaos approaches white Gaussian noise as an entropy source to generate for RNGrandom and thenumbers comparison deterministic bounded or unbounded chaosTo and by the of regular sampling of an irregular waveform method.
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