This paper by Jean-Sébastien Coron discusses the vulnerability of elliptic curve cryptosystems to Differential Power Analysis (DPA) attacks. DPA, first introduced by Kocher et al., is a technique that recovers secret information by monitoring power signals during cryptographic operations. The paper generalizes DPA to elliptic curve (EC) cryptosystems, specifically focusing on EC Diffie-Hellman key exchange and EC El-Gamal encryption. It demonstrates how DPA can be used to recover the private key stored in smart cards. The author also proposes three countermeasures to thwart these attacks: randomizing the private exponent, blinding the point, and randomizing projective coordinates. These countermeasures are designed to make the attack infeasible by introducing randomness and making it difficult to predict the specific bits of the binary representation of the points involved in the computations. The paper concludes by emphasizing the importance of these countermeasures in protecting elliptic curve crypto-systems from DPA attacks.This paper by Jean-Sébastien Coron discusses the vulnerability of elliptic curve cryptosystems to Differential Power Analysis (DPA) attacks. DPA, first introduced by Kocher et al., is a technique that recovers secret information by monitoring power signals during cryptographic operations. The paper generalizes DPA to elliptic curve (EC) cryptosystems, specifically focusing on EC Diffie-Hellman key exchange and EC El-Gamal encryption. It demonstrates how DPA can be used to recover the private key stored in smart cards. The author also proposes three countermeasures to thwart these attacks: randomizing the private exponent, blinding the point, and randomizing projective coordinates. These countermeasures are designed to make the attack infeasible by introducing randomness and making it difficult to predict the specific bits of the binary representation of the points involved in the computations. The paper concludes by emphasizing the importance of these countermeasures in protecting elliptic curve crypto-systems from DPA attacks.