Explain what it means for a hash function to be strongly collision resistant and

Question

Explain what it means for a hash function to be strongly collision resistant and what is means to be weakly collision resistant. Consider a Hash function that takes a binary message of any size m more than 160-bits and produces a 160-bits hash. The hash is constructing by keeping the last 160-bits of the message and XOR ing them with a with a sequence of 160 ones. Is this hash function weakly and strongly collision resistant? If yes explain why if not by showing a why to attack strong and weak collision resistance.

Explanation / Answer

a) let h(a) represent the hash function. h(a) is strongly collision resistant if for a given a, there does not exist any b such that h(a) = h(b). In other words, for any 2 given keys which are not same, the hash function will give different result.

b) The hash function is weakly collision resistance. The XOR of last 160 bits with 160 ones will give the complement of the last 160 bits. Since the message is more than 160 bit long, the hash function will give same output for all messages with same last 160 bits. This will result in collisions and thus the scheme is weakly collision resistant.

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