$4.$a$)$ Consider the RSA cryptography algorithm from class. Answer the questions below to build an encryption key. You must start with the prime numbers: $p=7$ and $q=11.[3$ marks$]$

Compute $n=pq$ and $m=(p-1)(q-1)$

Pick any $e$ such that the $gcd(m,e)=1.$

Pick any $d$ such that $ed=Qm+1,$ where $Q$ is any whole number. In other words, find a $d$ such that $((d)(e))mod(m)=1.$ Hint: look up a table of multiples of $e$ and compare them to a table of multiples of $m.$

b$)$ Encrypt the number $12$ using the encryption key: $(a^e)mod(n).$ Call this encrypted number $A.$ Now decrypt A using the key: $(A^d)mod(n).[2$ marks$]$