Periodicity of Timeseries Generated by Logistic Map: Part II

The paper investigates the impact of limited computational precision on chaotic systems used in cryptography, focusing on how floating-point arithmetic influences the periodicity and degradation of chaotic timeseries. The study analyses the behaviour of logistic map, revealing that different initial conditions and parameters lead to varying cycle lengths, which are critical for maintaining chaos in encryption algorithms. The order of arithmetic operations and the choice of coupling methods between maps are shown to significantly affect the system's dynamics. The efficiency of using floating-point and fixed-point arithmetic is compared, demonstrating that precision limitations can lead to the degradation of chaos, thereby compromising the effectiveness of some chaos-based ciphers. The research provides insights into the behaviour of chaotic systems under computational constraints, aiming to improve the reliability and security of chaotic encryption techniques.