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If user A and user B decide to use a hash function where the hash output is a 512-bits-long binary string, given a message M

If user A and user B decide to use a hash function where the hash output is a 512-bits-long binary string, given a message M and its corresponding hash output H(M), how many attempts an attacker have to make to find another message m=? m that has the same hash output?

If user A and user B decide to use a hash function where the hash output is a 512-bits-long binary string, given a message M and its corresponding hash output H(M), how many attempts would an attacker have to make to find two messages m and m that are not the same, but have the same hash output?

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