Faster side-channel resistant elliptic curve scalar multiplication
Alexandre Venelli, François Dassance · Contemporary mathematics - American Mathematical Society · 2010
We present a new point scalar multiplication algorithm on classical Weierstrass elliptic curves over fields of characteristic greater than 3. Using Meloni's formula that efficiently adds two points with the same Z-coordinates, we develop an algorithm computing [k]P only with these point additions. We combine Meloni's addition with a modified version of a Montgomery ladder, a well-established side-channel resistant method for scalar multiplication. Our aim is to construct an algorithm that is resistant, by construction, against Simple Power Analysis (SPA) and Fault Analysis (FA) while still being efficient. We present four versions of our algorithm with various speed-ups depending on the available memory of the device. Finally, we compare our method with state-of-the-art algorithms at the same level of side-channel resistance.