If you want to keep the information secret, you need a way to store it. Assuming number generation must be coordinated centrally (to prevent collisions), that does not seem like an impossible task. A system that involves a cryptographic hash could divide the id space up into different segments without being dectpherable from the outside world unless the cryptography is broken. A periodic key rotation system could reduce the impact of a compromise.

To me, the real question is why embed that information in the passport number at all? Even if driven by cryptography, it seems to represent a risk for which i don't understand the benefit.