A Novel 1D Polynomial Chirp Based Chaotic Map and a Simple Application to PRNG

Chaotic maps have wide application areas due to their unpredictable behavior and sensitivity to initial conditions and control parameters. This paper presents a new chaotic map derived from polynomial chirp functions. The performance of the generated map is evaluated using bifurcation diagrams, phase portraits, Lyapunov exponents and sample entropy. To demonstrate the effectiveness of the map, random numbers are generated with a simple PRNG algorithm and analyzed with histogram, Shannon entropy, and NIST test. As a result of the evaluation, it is seen that both the proposed map has a wide chaotic range and a uniform distribution in the phase space and the numbers generated by the new map-based PRNG have perfect randomness.