Encode the letters A to Z as the numbers $10$ to $35$ respectively. Take the first letter of your family name and

convert it into one of these numbers. Call this number m$.$ Take p $=11$ and q $=19.$

$($a$)$ Fix b $=5.$ Using a variant of the Rabin Cryptosystem, what is the value that we transmit? That is$,$ what

is the value c such that

c $$ m$($m $+$ b$)$ mod pq$?$

$($b$)$ With the value that you have transmitted, decrypt the message. You must show full working, including all

of your calculations.