Final answer:
The El Gamal cryptosystem is based on the Diffie-Hellman cryptographic algorithm, utilizing the discrete logarithm problem for secure key exchange.
Step-by-step explanation:
The cryptographic algorithm that forms the basis of the El Gamal cryptosystem is Diffie-Hellman. El Gamal is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie-Hellman key exchange. It was designed by Taher Elgamal in 1985 and is used in various applications for secure data transmission. The core idea behind El Gamal is the difficulty of calculating discrete logarithms in a finite field which is the same mathematical principle that protects the security of the Diffie-Hellman method.