Mid-Square Hash Quality From "mid-square random number generation", let me simply define the "128-hash" as
the middle bits of the square of a 128-bit number.

Does this hash have any known collisions?

Are there any known impossible hashes?  In other words, is there a known "128-hash"
which would never occur even if all starting 128-bit numbers were tried?
Does this hash have any known collisions?


Of course; any value with 96 leading zeros (that is, between $0$ and $2^{32}-1$) will middle square to 0, hence that gives a $2^{32}$-wide collision right there.