Consider a secure hash function H that produces a 60-bit hash.

A) Suppose that H(1) happens to hash to 0 (i.e., 60 zero bits). If you don't know anything further about H other than the fact that it's a secure hash function, what is the probability that H(2) also hashes to 0?

B) What is the probability that H has at least one collision?

C) Suppose that commodity hardware can compute a single computation of H in 10 nanoseconds (= 10^-8 sec). Within an order of magnitude, how many years will it take for an attacker using a single system to find an x such that H(x) = y for a specific y? You can approximate one year as 3.10⁷ sec.

D) Suppose now that a sustained form of Moore's Law means that after every year, H can be computed twice as quickly as for the previous year. (For this problem, assume that this acceleration happens discretely year-by-year, rather than being spread across a given year, as is actually more realistic.) Given this change, now about how many years will it take the attacker to find such an x?