Let E : Y2 = X + aX +b be an elliptic curve defined over Zp. Let n = #E(Z,), and suppose that n is prime. Design and analyze a polynomial-time algorithm (repeated double-and-add) which, on input p, a, b, n, PE E(Zp) and l E [1,n 1], outputs (P. Explain why your algorithm takes polynomial-time.