Satoh Point Counting in Characteristic 2 (Extended Abstract) (gzipped version)
Note that this is purely mathematical and have not been implemented yet. An implementation of something similar has been done by Mireille Fouquet, Pierrick Gaudry and Robert Harley, with amazing result. For more on this please visit their page.
Here are the slides which I used for my talk at the summerschool in Nordfjordeid.