Given is the same curve as in 9.7. The order of this curve is known to be #E = 37. Furthermore, an additional point Q = 15 · P = (14,23) on this curve is given. Determine the result of the following point multiplications by using as few group operations as possible, i.e., make smart use of the known point Q. Specify how you simplified the calculation each time.
You should be able to perform the scalar multiplications with considerably fewer steps than a straightforward application of the double-and-add algorithm would allow.