A family of 1D modulo-based maps without equilibria and robust chaos: application to a PRBG

This work proposes a family of modulo-based one-dimensional maps with three control parameters. The input to the modulo function includes the addition of three terms, the map’s previous value, a scalar, and a multiple of a chosen seed function. Under certain conditions, the proposed maps will have no equilibria, which brings them into the category of maps with hidden attractors. Moreover, the maps can showcase wide parametric regions of uninterrupted chaotic behavior, indicative of robust chaos. The above properties are studied for a collection of different seed functions, inspired by well-known chaotic maps. The results are demonstrated by a series of numerical tools, like phase diagrams, bifurcation diagrams, Lyapunov exponent diagrams, and the 0–1 test. Finally, the maps are successfully applied to the design of a pseudo-random bit generator.