comparison of two public key cryptosystems

Since the time public-key cryptography was introduced by diffie and hellman in 1976, numerous public-key algorithms have been proposed. some of these algorithms are insecure and the others that seem secure, many are impractical, either they have too large keys or the cipher text they produce is much longer than the plaintext. this paper focuses on efficient implementation and analysis of two most popular of these algorithms, rsa and elgamal for key generation and the encryption scheme (encryption/decryption operation). rsa relies on the difficulty of prime factorization of a very large number, and the hardness of elgamal algorithm is essentially equivalent to the hardness of finding discrete logarithm modulo a large prime. these two systems are compared to each other from different parameters points of view such as performance, security, speed and applications. to have a good comparison and also to have a good level of security correspond to users need the systems implemented are designed flexibly in terms of the key size.