Consider the elliptic curve E : y 2 =x 3 + 7x + b (mod 11). a. Determine ò so that the point P = (4,5) is on the curve E. b. Using the b found in part a, list all points on E. c. Using the b found in...

Consider the elliptic curve

E : y
²
=x
³
+ 7x + b (mod 11).

a. Determine ò so that the point P = (4,5) is on the curve E.

b. Using the b found in part a, list all points on E.

c. Using the b found in part a, find the sum (4,5) + (5,4) on E.

d. Using the 6 found in part a, find the point 3(4,5).