$(1$ point$)$ Consider the elliptic curve group based on the equation

$y^2-=x^3+ax+b,$modp

where $a=2440,b=295,$ and $p=3391.$

We will use these values as the parameters for a session of Elliptic Curve Diffie$-$Hellman Key Exchange. We

will use $P=(2,808)$ as a subgroup generator.

You may want to use mathematical software to help with the computations, such as the Sage Cell Server

$($SCS$).$

On the SCS you can construct this group as:

$G=$Elliptic Curve$($GF$(3391),[2440,295]$

Here is a working example.

$($Note that the output on SCS is in the form of homogeneous coordinates. If you do not care about the details

simply ignore the $3$ rd coordinate of output.$)$

Alice selects the private key $18$ and Bob selects the private key $15.$

What is $A,$ the public key of Alice?

What is $B,$ the public key of Bob?

After exchanging public keys, Alice and Bob both derive the same secret elliptic curve point $T_{AB}.$ The shared

secret will be the $x-$coordinate of $T_{AB}.$ What is it$?$