A predecessor value XOR method for improving chaotic maps and its application in pseudo-random bit generators

With the increasing requirements for the quality of pseudo-random sequences in fields such as cryptography, researchers continue to propose new chaotic map improvement schemes to meet these needs. However, these schemes still have some limitations in terms of randomness, stability and security. In order to solve these problems, we propose a method named predecessor value XOR (PVX), and then use this method to improve chaotic maps and construct a pseudo-random bit generator (PRBG). The PVX method aims to select a delayed chaotic state, make a specific change to its bit sequence, and finally use the changed state to perform an XOR operation with the output value. This method does not destroy the original formulation of chaotic map and is universal. Numerous numerical experiments have confirmed the effectiveness of the PVX method. For example, when the computational precision was only 6 bits, the approximate entropy (1.799), permutation entropy (0.99), and cycle length (183,680) of the improved Logistic Map. Concurrently, the approximate entropy (2.042), permutation entropy (0.983), and cycle length (undetected) of the x-dimension sequence of the improved Hénon Map, all achieved excellent results. Additionally, the PRBG constructed by us is formed by a parallel connection of two improved Logistic Maps and one improved Hénon Map. Experimental results show that the proposed PRBG exhibits excellent randomness, good stability, and high security. It is worth noting that the improved chaotic maps using the PVX method outperform many recent improved schemes in several dimensions, especially in the low-precision computational scenarios, and the method effectively solves the problem of degradation of the chaotic map dynamics, and provides a more reliable technological support for cryptography and other fields.