Suppose Alice and Bob are using a cryptosystem with a $128-$bit key, so there are

$2$

$128$

possible keys. Eve is trying a brute$-$force attack on the system.

Suppose it takes $1$ day for Eve to try

$2$

$64$

possible keys. At this rate, how long will it take for Eve to try all

$2$

$128$

keys? $($HINT: The answer is not $2$ days.$)$

Suppose Alice waits $10$ years and then buys a computer that is $100$ times faster than the one she now owns $($so it takes only $1/100$ of a day, which is $864$ seconds, to try

$2$

$64$

keys$).$ Will she finish trying all

$2$

$128$

keys before or after what she does in part $($a$)?$ be thourough