A Number-Theoretic Generalization of the ElGamal Cryptosystem with Applications to Digital Signatures and Image Encryption

In this paper, we propose an image encryption and digital signature scheme based on a modification of ElGamal cryptosystem over a large modulus represented by 2pn, where p is a large prime number and n>2 is a dynamic exponent derived from a shared secret established by the communicating participants through a modification of the Diffie–Hellman Key Exchange Protocol. The proposed scheme combines a modified ElGamal framework with image encryption and digital signature mechanisms to support confidentiality, image authentication and integrity verification while preserving the standard security assumptions of discrete-logarithm-based cryptography. Empirical performance and image-statistical evaluations, including histogram analysis, entropy, correlation coefficients, NPCR and UACI, are conducted on applying the procedures of the proposed scheme on four standard images. The experimental results demonstrate the correctness and favorable empirical image-statistical behavior of the proposed scheme for grayscale image encryption and authentication under the classical DLP assumptions. Furthermore, comparisons with representative symmetric and asymmetric cryptographic schemes are provided to evaluate the performance of the proposed scheme.