Hash Function $(30$ points$)).$ Let F : $\{0,1\}$n $\{0,1\}$n $\{0,1\}$n be a strong

pseudorandom permutation, for each of the following constructions of a compression

function h : $\{0,1\}2$n $\{0,1\}$n$,$ state whether it is collision resistant or not. If yes, prove

it; if not, show an attack:

$1.(15$ points$)$ h$($a$,$ b$)=$ Fa$($b$).$ That is$,$ the public input of h is $($a$,$ b$).$ a is used as the

key of the pseudorandom permutation F $,$ and b is used as its input.

$2.(15$ points$)$ h$($a$,$ b$)=$ Fa$($b$)$ a