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?

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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?

A fc-way collision is a set of values xo, x\,…, X_{k-i} that all hash to the same value, that is,

h(x0) = h(xi) = · · · = h(x_{k-i}).

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 fc-way collision?

b. What is the expected number of hashes that must be computed to find two fc-way collision?

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

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