Differential Power Analysis, first introduced by Kocher et al. in , is a powerful technique allowing to recover secret smart card information by monitoring power signals. In  a specific DPA attack against smart-cards running the DES algorithm was described. As few as 1000 encryptions were sufficient to recover the secret key. In this paper we generalize DPA attack to elliptic curve (EC) cryptosystems and describe a DPA on EC Diffie-Hellman key exchange and EC EI-Gamal type encryption. Those attacks enable to recover the private key stored inside the smart-card. Moreover, we suggest countermeasures that thwart our attack.