A modified ElGamal-like cryptosystem

The ElGamal cryptosystem stands as one of the foremost public key encryption methods and represents a probabilistic algorithm, originating from the framework of the Diffie-Hellman key exchange protocol. Diverging from the Diffie-Hellman approach, ElGamal cryptosystem constitutes a comprehensive encryption-decryption scheme hinging on the discrete logarithm problem for its security. Its robustness is rooted in the formidable challenge of computing the discrete logarithm modulo a substantially large prime number. In this study, a variation of the ElGamal algorithm was introduced using matrices. The key generation of the new system is different from that of the standard ElGamal Cryptosystem. Here, our generator is a 2×2 matrix containing four primitive roots of the selected prime number. The Plaintext is considered in uppercase letters and then converted into uppercase and lowercase letters alternatively. ASCII alphabet is used to obtain the corresponding numerical values for each letter and decomposed into blocks of 2×2 matrices. The security of this system rests on the intrinsic complexity of the discrete logarithm problem, a computational challenge well-documented for its arduousness. Additionally, our proposed system maintains resilience against Chosen Plaintext Attacks (CPA), further bolstering its security posture.