1. Digital cash system. (a.) (6 points) Suppose that a hacker discovers the Bank's secret identity r. Explairn how coins can be produced and spent without having an account with the bank (b.) (6 points) Show that a valid coin (A, B, z, a, b, r) satisfies the verification equations: gr ahH(A,B,2,a,b) Ar-:"(A,B,:,a,b)b (mod p) (mod p) mod p Here, all parameters and functions are dehned in Lecture 18 Hint: Recall that q = (p-1)/2 and g is the square of a primitive root mod p. So r 1c + a2 (mod q) if an only if gr-gaiq+02 (mod p). This in turn leads to Ataa (mod p)