Secure image encryption and authentication using Gaussian elliptic curve and complex invertible matrix

Abstract

Image transmission in security-critical applications requires strong confidentiality, integrity, and key management. This paper proposes a Chaotic Complex Elliptic Curve-based Secure Image Encryption (CCEC-SIE) scheme operating in the Gaussian domain. By extending elliptic curve cryptography to Gaussian integers, the proposed framework significantly enlarges the cryptographic space without increasing the underlying prime size. Enhanced one-dimensional chaotic maps, including the Iterative Tent and Logistic Maps, are employed to construct a Complex Self-Invertible Key Matrix (CIKM), ensuring strong diffusion and high unpredictability. Pixel-level permutation is achieved via Arnold’s Cat Map, while asymmetric key exchange and image authentication are realized through Gaussian elliptic curve-based ElGamal encryption, and a complex-domain digital signature verified prior to decryption. Experimental results demonstrate robust security with near-ideal entropy, NPCR of 99.62%, UACI of 33.46%, near-zero-pixel correlation, and low computational overhead, confirming the suitability of the proposed scheme for efficient and secure real-time image transmission.