In this exercise we will go through and perform the Diffie$-$Hellman key exchange as a collaborative effort.

$1.$ I will begin by choosing a prime number $\backslash ($ p $\backslash )$ that will serve as our modulus. The number I choose will be equal to $571.$ Henceforth, $\backslash ($ p$=571\backslash ).$ What other information must we agree upon to begin the DiffieHellman key exchange?

$2.$ Henceforth, the other piece of public information we are missing will now be equal to $27.$

$3.$ Choose your secret integer a$.$ Based on your secret integer, what information would you send me publicly?.

$4.$ The information I send you is the number $429.$ Is this number my secret number? If yes, why is this information fair to share? If no$,$ how did I actually calculate this number?

$5.$ What would our agreed upon key be based on the information in $\backslash$#$1\backslash$#$4?$