A Novel Discrete-Time Chaos-Function-Based Random-Number Generator: Design and Variability Analysis

Abstract

This paper presents a novel discrete-time (DT) chaotic map-based random-number generator (RNG), namely the Siponi map, which is a modification of the Logistic map. The Logistic map is usually applied to cryptosystems, mainly for the purposes of generating random numbers. In addition to being easy to implement, it has a better security level than other nonlinear functions. However, it can only process positive real-number inputs. Our proposed map is a deterministic function that can process positive and negative real values. We explored the map comprehensively and investigated its characteristics and parameters. We calculated the optimum parameter values using empirical and theoretical mathematical models to yield the maximum randomness of a sequence of bits. The limit variation of the maximum parameter value was determined based on a practical information measure. Empirical verification was performed for the Siponi map to generate bit sequences unrelated to the previous bit with high entropy values, and we found the extractor function threshold value to be 0.5, while the parameter control was −2 or 2. Using our proposed map, a simple RNG without post-processing passed DieHard statistical tests and all the tests on the NIST SP 800-22. Finally, we have implemented a Siponi map-based RNG on the FPGA board and demonstrated that the sources used are LUT = 4086, DSP = 62, and register = 2206.

Josephson junction oscillator embedded in the microcontroller: Pseudo-random number generation and combination synchronization

“…Chaotic signal generators are then used as the source of entropy to provide more randomness in the ciphering process. Generated random data are used to scramble the useful message and provide more security [36]. The chaos alone is a good source of randomness but when coupled with another source of entropy it results in robust and strong cryptographic processes.…”

“…The chaos alone is a good source of randomness but when coupled with another source of entropy it results in robust and strong cryptographic processes. In the literature, we can find chaos-based PRNG designed with continuous time chaotic maps [37][38][39], discrete chaotic maps [36,40], PWL chaotic maps [41,42], chaotic/hyperchaotic memristive systems [43][44][45] and artificial neural network based chaotic systems [45,46]. The post-processing units for these chaosbased PRNGs are: Ring oscillator [47], s-box [48], physical unclonable function [49][50][51], and LFSR [52][53][54].…”