## 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?