LC Map: A robust chaotic function for enhancing cryptographic security through key sensitivity and randomness analysis

Abstract

The security of digital image data has become increasingly critical in modern communication systems. While chaos-based cryptography offers a promising solution, many existing algorithms lack rigorous security validation. This paper introduces the Logistic-Circle Map (LC Map), a novel one-dimensional compound chaotic system designed to provide a robust and efficient foundation for image encryption. By composing the Logistic Map and the Circle Map, the LC Map exhibits a broader chaotic range and higher dynamical complexity. The performance and security of an LC Map-based encryption scheme are extensively validated using a comprehensive dataset of 24 digital images. Security analysis demonstrates that the algorithm is highly resistant to brute-force, statistical, and differential attacks. It provides a vast key space and demonstrates very strong key sensitivity, both confirmed through experimental evaluation. Test results show near-ideal performance on standard security metrics, with a Number of Pixels Change Rate (NPCR) approaching 99.6%, a Unified Average Changing Intensity (UACI) approaching 33.4%, and an information entropy value nearing the theoretical maximum of 8. Further quantitative comparative analysis demonstrates the superiority of the LC Map in balancing security and computational efficiency. Thus, the LC Map is presented as a rigorously validated component for the development of future image cryptosystems.