An analysis of Goubin's refined power analysis attack

Power analysis attacks on elliptic curve based systems work by analysing the point multiplication algorithm. Recently Goubin observed that if an attacker can choose the point P to enter into the point multiplication algorithm then none of the standard three randomizations can fully defend against a DPA attack. In this paper we examine Goubin's attack in more detail and completely discount its effectiveness when the attacker chooses a point of finite order, for the remaining cases we propose a defence based on using isogenies of small degree.