Enhancing logistic chaotic map for improved cryptographic security in random number generation

Abstract

The use of chaotic maps for cryptography is advantageous due to their desirable characteristics, including complexity, unpredictability, sensitivity to initial values and control parameters, and ergodicity. However, most chaos-based systems have limitations that make them impractical, such as low efficiency, insufficient security, and small keyspace. To overcome these challenges, this paper proposes an enhanced logistic map (ELM), a one-dimensional digital chaotic map based on the logistic map and anterior perturbation method. The ELM map leverages perturbations of chaotic states, leading to enhanced randomness, data distribution, and low correlation, with improved security properties. The ELM map is simple yet capable of generating large chaotic behavior. The findings show that the ELM map is highly secure and can be used in various cryptographic applications. A new pseudorandom number generator (PRNG) is also proposed based on a combination of ELM chaotic maps. The resulting PRNG is highly dependent on the chaotic properties of the maps and the combination rule. Statistical analysis shows that the proposed method is statistically secure, highlighting the potential of the ELM map for other cryptographic applications.