COPMUTER SCIENCE - CRYPTOGRAPHY ASAP. PLEASE ANSWER ALL 3 CLEARLY Suppose that h

Question

COPMUTER SCIENCE - CRYPTOGRAPHY ASAP.

PLEASE ANSWER ALL 3 CLEARLY

Suppose that h is a secure hash that generates an n-bit hash value. What is the expected number of hashes that must be computed to find one collision? 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 (x_i, z_i) with h(x_i) = h(z_i), for i = 0, 1, 2, ..., 9? What is the expected number of hashes that must be computed to find m collisions?

Explanation / Answer

a) Given x and h (x), it's infeasible to find any y, with y ö x, such that h (y) = h (x) then the number of hashes that can be computed to find a collision is 2 n / 2.

b) 2 n / 2 * 10 , for 10 expected collisions.

c) 2 n / 2 * (m) , for m expected collisions

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