[throw0101a]

> If I took an AES library and changed the order of some inner loop wouldn't it require extensive statistical analysis to notice the difference?

Unless you knew why it was organized the way it is in the original spec, altering it may weaken it. The DES S-boxes were altered by the NSA and everyone was suspicious, but it turns out they had made things stronger:

* https://en.wikipedia.org/wiki/Differential_cryptanalysis

Turns out the NSA was (at the time) over a decade ahead in crypto knowledge than the public.

As it stands, AES is approved for even TOP SECRET labelled information:

* https://en.wikipedia.org/wiki/NSA_Suite_B_Cryptography#Comme...

As are the various ECDH NIST curves that so many people are anxious about.