[orlp]

The input space is 32 + 32 = 64 bits. The output space is 64 bits. So the best you can do is an 1-to-1 mapping.

However, since a * b = b * a, our input space has a lot of duplicate outputs. So from this alone you can conclude roughly half of the output space must be uncovered by any input pair, simply because there aren't enough input pairs.

[HarHarVeryFunny]

OK - thanks. I must have misunderstood what the other poster was saying, since I thought they were objecting to the "most" characterization.

[Dylan16807]

I wasn't saying it's wrong, I was saying that "most" is so easy to reach that it's a trivial and rather boring threshold.