Split-Slope Chaotic Map Providing High Entropy Across Wide Range

This paper presents a novel one-dimensional discrete-time chaotic map. A significantly improved chaotic behavior, compared to already published one-dimensional maps, is achieved in the proposed design by virtue of this non-linear map’s stiffer transfer characteristics. The novelty of the work comes from the proposed methodology of splitting upward and downward slopping mechanisms to gain a stiffer slope in the uni-modal nonlinear circuit. The design methodology is presented with the help of the stability analysis of fixed points, which is generally applicable to a wide variety of nonlinear circuits. The chaotic complexity of the proposed circuit is analyzed with the bifurcation plot, correlation coefficient, and Lyapunov Exponent. The results are compared with reported works to demonstrate a significant improvement. Along with high chaotic complexity, this split-slope chaotic map provides a wide chaotic range covering 100% of the overall region of operation. The high chaotic complexity across a wide chaotic range is achieved with a remarkably low transistor-count circuit which is suitable in many hardware-security applications including, random number generation, chaotic logic circuits, and so on, for resource-constrained devices.