Earlier quoted context omitted.
My first guess would be conditionals, but I'd guess there is no real branching in the execution of operations on data. Another would be evaluating comparisons, but those aren't very easy to do in bitwise terms, and you can't read the output either.
But the thing about this setting is that you don't possess the secrets, so you can't reveal the secrets by noticing how long things take. An analogy to think about might be blind signatures. In blind signatures you sign a blinded token and then the other party can unblind it to get a valid signature from you over a message whose content you don't know. This is classical public-key cryptography. In that case there is…
the "side channel" i am referring to is in however this impliments this mixing you refer to.
if you can observe how the internal state is changing given a cloud keyset you should be able to infer the secret key. in the same way you can infer the iv used in a mesernine twister from like 27 cycles (or whatever).
downvotes and promises definately wont reduce my skeptacism.