1. yes you can get n-hole tori as quotients of hyperbolic plane, discussed in Thurston's book. You just use a regular hyperbolic N-gon with the correct N and the correct side-identifications. 2. that discrete log crypto development sounds important. It in fact was a highly discussed direction to use fields of order 2^k for k large, allegedly for efficiency reasons; the other main direction was p^1 for prime p large. Presumably we should now discard the first of these approaches.