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In addition to CRT-based optimizations (as Derek Atkins noted),
consistency checks may (or should) look at the p,q, and u values,
to detect modifications in the secret key packet. In the wake of
an "attack" discovered by some Czech researchers recently,
I expect most implementations to have such checks in place now.
(No pun intended. :-)
Consequently, a key without these fields will not be usable by most other
implementations.
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