Computational Algebra Seminar: Doche -- Double-Base Number System in Elliptic Curve Cryptography

Speaker: Christophe Doche (Macquarie)
Title: Double-Base Number System in Elliptic Curve Cryptography
Time & Place: 3:05-4pm, Thursday 9 August, Carslaw 535

Abstract:
We present the Double-Base Number system (DBNS) and its
applications to cryptography, mainly to speed-up scalar multiplications on
elliptic curves.

After a brief introduction, we focus on 2 practical contributions:
* The first scalar multiplication algorithm having sublinear complexity.
This method relies on a generalisation of the DBNS in the context of Koblitz
curves
* The fastest scalar multiplication algorithm for generic curves when some
precomputations are available. This work relies on the so-called extended
DBNS which is also a natural generalisation of the DBNS.