Suppose we have a computer with a $4\mathrm{.}2$ GHz $16-$core processor that executes $4\mathrm{.}2\backslash$times $109$ cycles per second per core. Considering that it can test $20$ keys per CPU cycle, calculate:

a$)$ The average time $($in years$)$ to find a key by the brute$-$force attack if the key size is $56$ bits.

b$)$ The average time $($in years$)$ to find a key by the brute$-$force attack if the key size is $128$ bits