Consider the elliptic curve E: y 2 = x 3 + Ilx; + 19 (mod 167) a. Verify that the point P = (2,7) is on E. b. Suppose this E and P = (2,7) are used in an ECC Diffie-Hellman key exchange, where Alice...

Consider the elliptic curve

E: y
²
= x
³
+ Ilx; + 19 (mod 167)

a. Verify that the point P = (2,7) is on E.

b. Suppose this E and P = (2,7) are used in an ECC Diffie-Hellman key exchange, where Alice chooses the secret value A = 12 and Bob chooses the secret value B = 31. What value does Alice send to Bob? What does Bob send to Alice? What is the shared secret?