$1.$ Suppose there are $1000$ users, and an attacker has a dictionary of $5000$ common passwords. An attacker has stolen the database of hashed passwords.

a$.$ If the users$$ password in the database were hashed without salt, how many Hash computation does the attacker need to find all users that have the passwords in the dictionary?

b$.$ Calculate the number of Hash computations again, now assuming salt is used for the hash.

Show you computation steps and give necessary explanations to get full credit.

$2.$In class $$authentication$,$ we explained storing Hash$10000($password$)$ as one way to $$make the guessing work expensive$.$ While doing this indeed slows down the attacker$$s offline password guessing attempt, it also significantly increases the server$$s effort. Suppose the server still stores Hash$10000($password$),$ but when Alice logs in$,$ her client machine first computes Hash$9999($password$)$ and sends that to the server.

a$.$ Will there still be the advantage gained by storing Hash$10000($password$)?$

b$.$ Will this save the server computation?

To answer both questions, first clearly give a Yes$/$No$,$ and then use a few sentences to explain why you make this conclusion.