> We could not measure all possible angular momentums but it was possible to measure one or two that would not be known to the attacker.

You only need to measure three angular momentums, all other can be calculated. See https://en.wikipedia.org/wiki/Moment_of_inertia#Motion_in_sp...

"This shows that the inertia matrix can be used to calculate the moment of inertia of a body around any specified rotation axis in the body."

On the attacker side, they only need to make sure three angular momentums match.