1) Let S to be the result when Alice digitally signs the message M = 25. What is S? If Bob receives M and S, explain the process Bob will use to verify the signature. Show that in this case the signature verification will succeed.

2) Consider a two-dimensional function f(x, y) whose values are known at the distinct (xi, yj ), i = 1, 2, 3, j = 1, 2. Find the Lagrangian interpolation polynomial approximation P(x, y) of f(x, y).