Two efficient algorithms against power attacks for elliptic curve cryptosystems

Novel power attacks including Refined Power Attack (RPA), Zero-value Point Attack (ZPA), and doubling attack have been new threats to elliptic curve cryptosystems. In this paper, we first propose an improved Hitchcock's SPA-resistant algorithm using the random initial points, which can protect against novel power attacks including RPA, ZPA, and doubling attack. With one additional stored point, it can save 16.7% of the point additions and doublings compared with Mamiya's BRIP algorithm. Secondly, we propose a window based countermeasure algorithm using the 2
^w
-torsion points in the subgroup E[2
^w
], which can save 50% of the stored points and w point doublings compared with Mamiya's WBRIP algorithm.