Self-Parameterized Chaotic Map for Low-Cost Robust Chaos

This paper presents a general method, called “self-parameterization”, for designing one-dimensional (1-D) chaotic maps that provide wider regions compared to existing 1-D maps. A wide region is desirable property, as it helps robust performance by enlarging the design space in many hardware-security applications, including reconfigurable logic and encryption. The proposed self-parameterization scheme uses only one map, referred seed simple transformation block. effective control parameter of map treated an intermediate variable derived from input self-parameterized under some constraints, achieve desired functionality. widening after adding first demonstrated on three ideal functions: Logistic; Tent; Sine. digitized version was developed realized field-programmable gate array (FPGA) implementation. An analog with very low transistor-count topologies hardware-constrained integrated circuit (IC) both digital implementations evaluated bifurcation plots four established entropy metrics: Lyapunov Exponent; Correlation Coefficient; Dimension; Approximate Entropy. application random number generator design, statistical randomness generated sequence verified NIST test.