A program implementing your crafty author’s Bobcat hash algorithm can be found on the textbook website. This hash is essentially a scaleddown version of Tiger—whereas the Tiger hash produces a 192-bit output (three 64-bit words), the Bobcat hash produces a 48-bit value (three 16-bit words).

a. Find a collision for the 12-bit version of Bobcat, where you truncate the 48-bit hash value to obtain a 12-bit hash. How many hashes did you compute before you found your first 12-bit collision?

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b. Find a collision for the full 48-bit Bobcat hash.

Suppose that h is a secure hash that generates an n-bit hash value.

a. What is the expected number of hashes that must be computed to find one collision?

b. What is the expected number of hashes that must be computed to find 10 collisions? That is, what is the expected number of hashes that must be computed to find pairs (XÌ,ZÌ) with h(x_{i}) = h(z_{i}), fori = 0,1,2,…, 9?

c. What is the expected number of hashes that must be computed to find m collisions?

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