This question focuses on the

shattered.io attack.

$($a$)$ What is the expected complexity of the attack?

$($b$)$ What is a "disturbance vector" with respect to this attack?

$($c$)$ With the results of Stevens et al$.,$ and exhausting the differentials calculating the

optimal probabilities, what is the theoretical limit for the complexity of this attack?

$($d$)$ What is a "neutral$-$bit" and how is it used in attacks on SHA$-0?$

$($e$)$ How many neutral bits were used in the second block of the attack?