On the Attacks over the Elliptic Curve-Based Cryptosystems

The aim of this paper is to a present survey of attacks on the elliptic curve cryptosystems. We propose a taxonomy for these attacks and a brief presentation for each type of attack and its complexity. The attacks´ complexity demonstrates the high security level of the elliptic curve-based cryptosystems. Also, there are presented the most known elliptic curves-based cryptographic protocols: the Elliptic Curves-based Diffie-Hellman Key Exchange, ElGamal Public Key Cryptosystem and Elliptic Curve Digital Signature Algorithm.