$1.$ Elliptic Curves: Let E$\_17(0,7)$ be an elliptic curve defined over Z$\_17.$

a$.$ Please write down the cubic equation of the given elliptic curve. $(5$ points$)$

b$.$ Assume two people A and B want to exchange a secret key using Elliptic Curve Diffie$-$Hellman Key Exchange $($ECDH$)$ method. Given the primitive element $($generator$)$ G $=(15,13),$ the two private key n$\_$A$=2$ and n$\_$B$=3,$ please calculate the public keys P$\_$A and P$\_$B and the secret key K$.(45$ points$)$

Please give complete procedure.