Bob selects ElGamal Cryptosystem with $p=2539,e1=2$ as public. He keeps $d=42$ private. Alice wants to send him $2$ messages, so she splits it as P$1=1407$ with $r=100$ and P$2=1314$ with $r=300.$ Perform encryption for Alice and decryption for Bob.

In Elgamal Scheme, if Bob selects $p=7,e1=5$ as public. He keeps $d$ as private. Alice wants to send him message $P=6$ with $r=4.$ Perform encryption for Alice. Find $d$ and then perform decryption for Bob $.$

Users A and B use the Diffie$-$Hellman key exchange technique with common prime q $=11,$ a primitive root $=2$ and user $B$ has private key $xB=8.$ Show the calculation for questions below. i$.$If user A has private key $xA=6,$ what is A$\text{'}$s public key YA$?$ ii$.$What is the shared secret session key?

Assume two users, A and B$,$ have agreed to use Diffie Hellman Key Exchange with prime $p=23$ and generator $a=5.$ Assuming A randomly chose private $xA=7$ and $B$ randomly chose private $xB=8,$ find the shared secret key. if Man In The Middle attack can be performed by an attacker $Q$ with XQ$->$A $=13$ and XQ$->$B $=15,$ Whether $Q$ can decrypt any communications between A and B that use the secret shared between A and $B.$