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In this paper, we introduce a novel discrete chaotic map named zigzag mapthat demonstrates excellent chaotic behaviors and can be utilized in TrulyRandom Number Generators (TRNGs). We comprehensively investigate the map andexplore its critical chaotic characteristics and parameters. We further presenttwo circuit implementations for the zigzag map based on the switched currenttechnique as well as the current-mode affine interpolation of the breakpoints.In practice, implementation variations can deteriorate the quality of theoutput sequence as a result of variation of the chaotic map parameters. Inorder to quantify the impact of variations on the map performance, we model thevariations using a combination of theoretical analysis and Monte-Carlosimulations on the circuits. We demonstrate that even in the presence of themap variations, a TRNG based on the zigzag map passes all of the NIST 800-22statistical randomness tests using simple post processing of the output data.

Discrete-Time Chaotic-Map Truly Random Number Generators: Design, Implementation, and Variability Analysis of the Zigzag Map