c$)$ Using AES $128-$CTR to encrypt a $1-$block message m of $128$ bit long, given a $128$ bit IV and a random key k$,$ after encryption we get two blocks of ciphertext $($total $256$ bits$)$ as IV $||$ m $$ AES $128($k$,$ IV$+1).$ Why this scheme is CPA secure$,$ but not CCA secure$?$ d$)$ What are differences between PRF and PRP$?$ Say F: $40,13$n x $40,13$n $->\{0,13$n is defined by F$($k$,$ x$)=$ k $*$x$,$ explain why F is not a secure PRF$?$ e$)$ We want a hash function H to have collision$-$resistant property. Say, if we want finding collisions for H to be as difficult as an exhaustive search over $256-$bit key, then at least what should the output length of the hash function $($in bits$)$ be$?$ And why?