intro to Cryptography. If you know of any tutorials regarding this topic in Cryptography please post it as well.

1. Consider the elliptic curve E given by the equation 3/2 = 51:3 1:. (a) First, suppose E is dened over the real numbers. Let E(R) denote its set of points. Draw a graph of E (R) (b) Let P be the point (0,0) in E(R). What is P + P (also denoted 2P)? (c) For the remainder of this question, consider the elliptic curve E : y2 = a: :6 dened over Zp, Where p is an odd prime. The set of points of E in this setting is denoted E(Zp). If P is the point (0,0), what is 2P? (d) Find 3P. (e) Let p = 5. Find all points on the elliptic curve (including its point at innity) (f) Give the addition table for E (Z5). (g) The point Q in E(Z5) satises 3Q : (2,4). What point is Q? 3