Suppose that a $10$

$-$bit hash function behaves randomly. The probability p

of successfully solving a puzzle is given by p$=$target space$210=$target space$1024$

$.$ The average number of attempts before success is given by $\backslash$mu $=1/$p

$.$ We choose $\backslash$mu

such that it takes about $10$ minutes to solve the puzzle. Suppose that current evidence suggests that it takes $10$ minutes to do $24=16$

hash computations.

a$)(2$ marks$)$ Calculate the target space, i$.$e$.,$ its size, such that it takes about $10$ minutes to solve the hash puzzle?

Answer $1$ Question $18$

b$)(1$ mark$)$ Based on part $($a$),$ what will you choose the value of target in H$()$