Manuscript received January 23, 2026; revised February 13, 2026; accepted March 27, 2026; published November 13, 2026.

Abstract—Image encryption technique is the procedure of converting an original image into an unreadable form to ensure privacy, security, and confidentiality during transmission. The Magic Square (MS) is a structured matrix in which all horizontal, vertical, and diagonal operations are applied to generate a deterministic, difficult pixel rearrangement pattern. However, the magic square and Elliptic Curve Cryptography (ECC)-based method do not perform well on color and high-resolution images, failing to achieve better integration between pixel-level and ECC-based key management, thereby minimizing the model’s encryption efficiency. To overcome these limitations, this research proposes the Elliptic Key-elliptic Curve Diffie-Hellman (EK-CDH) with MS for generating secure and effective key generation and key exchange mechanisms. The Elliptic Curve Diffie-Hellman (ECDH) provides strong, reliable shared keys for color and high-resolution images by connecting ECDH with a magic square, ensuring better coordination between the pixel-level and key management. The EK is generated by ECDH, which enables the sender and receiver to securely evaluate a shared secret key over an untrusted channel. The proposed EK-ECDH with MS achieves low encryption and decryption times of 0.24 s and 0.17 s, respectively, when compared with the enhanced Royat model with ECC.

Keywords—elliptic curve cryptography, elliptic curve Diffie-Hellman, image encryption, key exchange, magic square, pixel level

Cite: B. Vybhavi, K. Mani, V. Uma Devi, and S. Kumar Chandar, "Elliptic Key and Curve Diffie-Hellman with Magic Square for Secure Image Encryption," Journal of Image and Graphics, Vol. 14, No. 6, pp. 943-953, 2026.

Copyright © 2026 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).