[Cryptography] Exotic Operations in Primitive Construction

[Sid Spry]

Hello,

I noticed the other day that bit shifts and rotates are very popular in
primitive construction. Why is this the case? Intuitively it seems to me like
these operations are some of the most irregular that a computer has to offer.
Bit shifting is related to division, but bit rotation does not seem closely
related to any other easy to analyze operation. But I have no explanation for
why it feels this way.

Perhaps the only more irregular operation I can think of is a lookup.

Are any operations particularly hard to analyze? I realize some of this is
irrelevant, lots of attacks operate on the statistical properties of the output
and the input. But it is still important.

Cheers.