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A second-preimage attack is where you want to find m' where h(m) == h(m')... and you know m already. This is not very useful for password hashing; it would give you a second password that would also work to log into the account, but what's the point of that if you already know the first password? The relevant attack for password hashing is a regular preimage attack, where you don't know m (and it would be acceptable to find either m itself or any other string that hashes to the same value).





You don't need to know m, just h(m) which is commonly found in database breaches

That's just a "pre-image attack". A "second pre-image attack" is a different scenario, not relevant to password-hashing for the reasons grandparent described, where you already know a pre-image, and must find a different one.



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