The NSA has a bad historical reputation for this sort of thing - intentionally weakening crypto standards to make things easier for themselves to break, while keeping them "strong enough" that other agencies outside of NSA/GCHQ/GRU can't. The Crypto AG scandal [0] was pretty bad, with Clipper/Skipjack & Dual_EC_DRBG [1] being more recent ones. The NSA could do what you are asking to do, but they probably won't let us know what the really bad holes are because they want to keep using them.

Notes:

0 - https://www.washingtonpost.com/graphics/2020/world/national-...

1 - https://www.scientificamerican.com/article/nsa-nist-encrypti..., https://en.wikipedia.org/wiki/Dual_EC_DRBG