mahnaz mohammadi - Department of Electrical and Electronic Eng., Science and Research Branch, Islamic Azad University, Tehran, Iran
alireza zolghadr - Faculty of Computer and Electrical Eng., Department of Communication and Electronics, Shiraz University, Shiraz, Iran
mohammad pourmina - Department of Electrical and Electronic Eng., Science and Research Branch, Islamic Azad University, Tehran, Iran

Since the time public-key cryptography was introduced by Diffie andHellman in ۱۹۷۶, numerous public-key algorithms have been proposed. Some of thesealgorithms are insecure and the others that seem secure, many are impractical, eitherthey have too large keys or the cipher text they produce is much longer than theplaintext. This paper focuses on efficient implementation and analysis of two mostpopular of these algorithms, RSA and ElGamal for key generation and the encryptionscheme (encryption/decryption operation). RSA relies on the difficulty of primefactorization of a very large number, and the hardness of ElGamal algorithm isessentially equivalent to the hardness of finding discrete logarithm modulo a largeprime. These two systems are compared to each other from different parameters pointsof view such as performance, security, speed and applications. To have a goodcomparison and also to have a good level of security correspond to users need thesystems implemented are designed flexibly in terms of the key size.

Cryptography, Public Key Cryptosystems, RSA, ElGamal