Consider the EC example given in the lecture slides $15-18.$ For the values used in this example,

$-$Write a Python program that will continue computing the point additions up until a value of $(19\backslash$alpha $)$ in order to verify that $(5,1)$ is truly a generator.

$-$Make sure to compare the list you generate with values in the table given in the notes. If you compute a point addition that does not appear on the table, then something is wrong with your program.

$-$Apply the extended Euclidean algorithm to compute inverses modulo p in the point addition formula.

$-$Use the generator $(5,1)$ to simulate ECDH and verify the key exchange.