Get the script instance associated with a collider

So I'm still not completely solid on how a GameObject is composed and how to access its various parts.

I have a reference to a Collider, and need to cast it to the type of a script on the same GameObject, but I'm not sure what this would look like.

My scenario looks like this (using C#):

• Two objects:
  • PlayerPrefab, which has a collider/rigid body, and the Player script.
  • EnemyPrefab, which has a collider/rigid body, and the Enemy script.

Scripts:

public class Player : MonoBehavior {
    public void Kill() { //... }
}

And:

public class Enemy : MonoBehavior {
    void OnTriggerEnter( Collider other ) {
        Player p = (Player)other;  // This does not work!
        p.Kill();
    }
}

So how exactly do I perform that cast in the Enemy script?

Thanks.