More discussions, more questions

From the discussion at Math Dept. today:

  1. Why and when Koblitz curve?
  2. Why cyclic group/subgroup? Does it have to be cyclic? Or does it have to be non-cyclic?
  3. When I have F_p with the order of the group \left|G \right| = p where p is a prime number then the group will be cyclic. What if the \left|G \right| is q which is also a prime number not equal to p . Will the group be cyclic?