Question 4

Recall from Lecture 10 that a 51% attacker is an attacker who holds at least 51% of the total hash power. Let α represent the proportion of hash power held by this attacker. Then, α ≥ 0.51. Suppose this attacker wants to suppress Carol’s transactions by not including any of her transactions. To do so, whenever the attacker (or the attacker’s nodes) solves the hash puzzle, it proposes a block without Carol’s transactions. Show that the attacker will be successful in the sense that the longest valid consensus chain will eventually be the one proposed by the attacker. Why this will not be the case if α < 0.5?