New Composite Operations and Precomputation Scheme for Elliptic Curve Cryptosystems over Prime Fields

We present a new methodology to derive faster composite operations of the form dP + Q, where d is a small integer ≥ 2, for generic ECC scalar multiplications over prime fields. In particular, we present an efficient Doubling-Addition (DA) operation that can be exploited to accelerate most scalar multiplication methods, including multiscalar variants. We also present a new precomputation scheme useful for window-based scalar multiplication that is shown to achieve the lowest cost among all known methods using only one inversion. In comparison to theremaining approaches that use none or several inversions, our scheme offers higher performance for most common I/M ratios. By combining the benefits of our precomputation scheme and the new DA operation, we can save up to 6.2% on the scalar multiplication using fractional wNAF.