Calculate your personal key as

$a-=(I{D}_1+I{D}_2+I{D}_4+I{D}_6)*(mod26),$

where $I{D}_m$ is the $m-$th digit in your NJT ID $($the index starts with $"1").$ Example: NJIT id $"31234567",a-=(3+1+3+5)(mod26)-=12(mod26).$ If $a=0,$ set $a$:$=13.$ If $a=1,$ set $a$:$=17.$

Demonstrate the Diffie$-$Hellman key exchange using an elliptic curve $y^2-=x^3+ax+9(modp),$ where $p=8011.$ Use $x_A=119,x_B=121.$ Find a perfect generator point or a generator point with the highest order if a perfect generator cannot be found for the first $30$ points. List the values of the order of both the elliptic curve and generator point.

$(35$ pts$)$