Issue No. 02 - February (2011 vol. 60)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2010.138
Jithra Adikari , University of Calgary, Calgary
Vassil S. Dimitrov , University of Calgary, Calgary
Laurent Imbert , University of Calgary, Calgary and Université Montpellier, Montpellier
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.
Elliptic curve cryptography, single/double scalar multiplication, hybrid binary-ternary number system, DIK-3 curves.
J. Adikari, V. S. Dimitrov and L. Imbert, "Hybrid Binary-Ternary Number System for Elliptic Curve Cryptosystems," in IEEE Transactions on Computers, vol. 60, no. , pp. 254-265, 2010.