I just want to point out that the P-curves need not have unique features that allow for more efficient computations during code breaking in order to be "weak" o

I just want to point out that the P-curves need not have unique features that allow for more efficient computations during code breaking in order to be "weak" or "backdoored". Simply the fact that the curves are standardized may allow expedited code breaking. We saw this with POISON NUT/CORAL REEF (where specialized hardware (PIQ Blade), pre-computation work, and an otherwise fine small standardized set of primitives allowed for rapidly broken encryption).