New Composite Chaotic Map Applied to an Image Encryption Scheme in Cybersecurity Applications

Chaotic systems have long played a crucial role in cryptographic applications due to their inherent unpredictability and sensitivity to initial conditions. Building on this foundation, this paper introduces an Improved Composite Chaotic Map (ICCM), inspired by classical quadratic and cubic chaotic maps. The proposed ICCM is rigorously validated through Lyapunov exponents and bifurcation diagrams, demonstrating its enhanced dynamical complexity and suitability for secure applications. Designed to expand the chaotic range, ICCM incorporates an additional parameter that significantly enlarges the keyspace, thereby improving the robustness and adaptability of encryption methods. To demonstrate its practical utility, ICCM is integrated into a novel opto-digital encryption scheme aimed at enhancing sensitivity and ensuring superior encryption performance. The effectiveness of this scheme is evaluated using a comprehensive suite of tests, including sensitivity analysis, histogram analysis, the NIST statistical test suite ( $15/15$ passed), and key security metrics. A high mean square error (MSE) value ( $\gt 10^{4}$ ) indicates a significant difference between the original and encrypted images, while correlation coefficients ( $Cr \approx 0.0001$ to 0.0028) and a low peak signal-to-noise ratio (PSNR <10 dB) further confirm its robustness. Keyspace analysis ( $2^{674}$ ) ensures resilience against brute-force attacks. Simulation results reveal that the ICCM-based encryption scheme achieves a Lyapunov exponent of 21.42 (compared to 19 in prior works) and withstands data loss up to 50%. These findings position ICCM as a robust defense against statistical, differential, and chosen-plaintext attacks. In conclusion, the proposed ICCM and its integration into the opto-digital encryption scheme advance the security of encryption systems, setting a new benchmark for chaos-based cryptography. The results underscore the model’s potential to address modern data security challenges and inspire further research in this critical field.