$8.$ Let h be a secure cryptographic hash function. For this problem, a password consists of a maximum of $14-$characters and there are $32$ possible choices for each character. If a password is less than $14$ characters, it$$s padded with nulls until it is exactly $14$ characters. Let P be the resulting $14$ character password. Consider the following two distinct password hashing schemes:

i$)$ The password P is split into two parts, with X equal to the first $7$ characters and Y equal to the last $7$ characters. The password is stored as $($h$($X$),$h$($Y $)).$ No salt is used.

ii$)$ The password is stored as h$($P $).$ Again, no salt is used.

Note that the method in scheme i$)$ was used in Windows to store the so$-$called LANMAN password.

$8$a$)$ Assuming a brute force attack, how much easier is it to crack the password if scheme i$)$ is used as compared with scheme ii$)?$

$8$b$)$ If scheme i$)$ is used, why might a $10-$character password be less secure than a $7-$character password?$13$