New Composite Operations and Precomputation Scheme for Elliptic Curve Cryptosystems over Prime Fields (full version)

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 DoublingAddition (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 multiplications that is shown to achieve the lowest cost among all known methods using only one inversion. In comparison to the remaining 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% in the scalar multiplication using fractional wNAF.