Design and analysis of a secure image encryption algorithm using proposed non-linear RN chaotic system and ECC/HKDF key derivation with authentication support

Ensuring digital image security is critical in today's edge computing and networked communication environments. Chaotic systems offer powerful tools for lightweight, real-time encryption, but often suffer from limited chaotic ranges and weak key sensitivity. This paper introduces a robust nonlinear RN chaotic system, combining two chaotic maps to enhance unpredictability and expand the chaotic interval. A fast image encryption scheme is then developed by integrating this system with elliptic-curve Diffie-Hellman (ECDH) key exchange, hierarchical key derivation (HKDF), and dynamic chaotic S-box generation. The scheme ensures plaintext-independent key generation, authentication via ECDSA, and integrity through HMAC-SHA256, thereby preventing man-in-the-middle attacks and key leakage. Using the same set of security keys, this algorithm can produce a completely different encrypted image each time it is applied to the same original image. The proposed technique consistently achieves near-ideal entropy levels (~ 7.999), high NPCR (> 99.61%), and UACI above 32%, image complexity (with a keyspace equal to 10²⁵⁶), and resistance to security attacks, demonstrating outstanding sensitivity and randomness. The low PSNR values and limited correlation of the encrypted images further show strong resilience to statistical and differential assaults. The proposed approach outperforms existing methods in terms of computational reliability, encryption strength, and unpredictability. This work provides a dependable, portable, and efficient solution for secure image transfer in surveillance and multimedia applications.