Alice likes to use the Tiger hash algorithm, which produces a 192-bit hash value. However, for a particular application, Alice only requires a 64-bit hash. Answer the following questions, assuming that the Tiger hash is secure.

a. Is it safe for Alice to simply truncate the Tiger hash, that is, can she use the first 64 bits of the 192-bit output? Why or why not?

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b. Is it acceptable for Alice to take every third bit of the Tiger hash? Why or why not?

c. Is it secure for Alice to take the three 64-bit words of the Tiger hash and XOR them together? Why or why not?

Suppose we modify the hashing scheme as follows: Given a message M that Alice wants to sign, she randomly selects R, then she computes the signature as S = [h(M, R)]A\ice, and sends (M, R, S) to Bob. Does this prevent the attack? Why or why not?

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