In most algorithms involving elliptic and hyperelliptic curves, the costliest part consists in computing multiples of ideal classes. This paper investigates how to compute faster doubling over fields of characteristic two.
We derive explicit doubling formulae making strong use of the defining equation of the curve. We analyze how many field operations are needed depending on the curve making clear how much generality one loses by the respective choices. Note, that none of the proposed types is known to be weak – one only could be suspicious because of the more special types. Our results allow to choose curves from a large enough variety which have extremely fast doubling needing only half the time of an addition. Combined with a sliding window method this leads to fast computation of scalar multiples. We also speed up the general case.
|Title of host publication||Selected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers|
|Editors||H. Handschuh, M.A. Hasan, R.L. Wainwright, L.M. Liebrock|
|Place of Publication||Berlin|
|Number of pages||12|
|Publication status||Published - 1 Dec 2004|
|Name||Lecture Notes in Computer Science|
- Binary fields
- Explicit group operations
- Fast arithmetic
- Hyperelliptic curves