Split-Slope Chaotic Map Providing High Entropy Across Wide Range

Partha Sarathi Paul1, Maisha Sadia1, Anurag Dhungel1, Parker Hardy1, Md Sakib Hasan2
1Graduate Student, 2Assistant Professor


In this paper, we have presented a novel one-dimensional discrete-time chaotic map. This chaotic map has a uni-modal transfer characteristic. Unlike common practices, the mechanism of generating the positive slope and the negative slope of the uni-modal transfer characteristic are split in this map circuit. In this way, a stiffer transfer characteristic is achieved which results in a more complex chaotic behavior compared to already published one-dimensional maps. The design methodology of this split-slope chaotic map is presented with the help of the stability analysis of fixed points in non-linear dynamics. The design methodology is generally applicable to a wide variety of non-linear circuits. The chaotic complexity of the proposed circuit is analyzed with bifurcation plot, correlation-coefficient, and Lyapunov Exponent. The results are compared with reported works to demonstrate a significant improvement that is achieved from the proposed design. Along with high chaotic complexity, this split-slope chaotic map provides a wide chaotic range covering 100\% of the region of operation with a low-overhead CMOS circuit. The high chaotic complexity and wide chaotic range of the proposed circuit can be applicable for hardware-security applications including, random number generation, chaotic logic circuits, and so on for resource-constrained devices.