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.