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

TL;DR

This paper introduces a new discrete chaotic map called zigzag map for truly random number generation, provides circuit implementations, analyzes variability effects, and demonstrates its robustness through statistical testing.

Contribution

The paper presents the design, circuit implementation, and variability analysis of a novel zigzag chaotic map for TRNGs, showing its robustness despite parameter variations.

Findings

The zigzag map exhibits excellent chaotic behavior for TRNGs.

Circuit implementations successfully realize the zigzag map.

The TRNG passes all NIST 800-22 tests despite variations.

Abstract

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