Your math is bogus. 7-8 bits? If there's one entry, that would give false positives of 1/256, or 0.3%. Even given 1k entries would likely hit the vast majority

Your math is bogus. 7-8 bits? If there's one entry, that would give false positives of 1/256, or 0.3%. Even given 1k entries would likely hit the vast majority of entries. Or, flipping this: every time you add a password, you check that it hasn't been used before. You can only set 256 passwords, total, before the space of truncated hashes is filled.