AUTHENTICATED AND SECURE El-GAMAL CRYPTOSYSTEM OVER ELLIPTIC CURVES

Information technologies plays a major role in our information society, thus it is important to protect it against many kinds of threats or attacks which may lead to lose of money, or lose of reputation and thus destroy businesses. The El-Gamal public key cryptosystem over elliptic curves is often used in modern computer and communication technologies; it enables secure communication over public unsecure channels. This paper introduce the security of the El-Gamal cryptosystem based on elliptic curves, it suggests a modification that can make the cryptosystem more immune against some attacks. This modification solves a weakness in the basic El-Gamal scheme by including the identity parameter of the sender in the encryption process, thus making the cryptosystem immune against man-in-the-middle attack and known k parameter attack. The modification described in this paper can in analogy be implemented on the El-Gamal cryptosystem over finite fields. Other important benefit is that the El-Gamal cryptosystem described here can easily be implemented and is very suitable on small and limited devices (e.g. smart cards) due the use of elliptic curves. This paper also briefly describe some attacks on the El-Gamal cryptosystem and the suitable choice of El-Gamal cryptosystem parameter settings to avoid such attacks.