Hybrid Binary-Ternary Number System for Elliptic Curve Cryptosystems

Single and double scalar multiplications are the most computational intensive operations in elliptic curve based cryptosystems. Improving the performance of these operations is generally achieved by means of integer recoding techniques, which aim at minimizing the scalars´ density of nonzero digits. The hybrid binary-ternary number system provides both short representations and small density. In this paper, we present three novel algorithms for both single and double scalar multiplication. We present a detailed theoretical analysis, together with timings and fair comparisons over both tripling-oriented Doche-Ichart-Kohel curves and generic Weierstrass curves. Our experiments show that our algorithms are almost always faster than their widely used counterparts.