Your security needs are not going to be lowered because a device happens to be in the IoT. (Ever hear of the "Fine Dining Attack"?) In other words, you need to apply your security profile across the entire aggregated attack surface. And the other thing we need to keep in mind is that IoT devices tend to be leaky and have few, if any, updates.
As Mr. Schneier has said, cryptographic hashes are the workhorses of cryptography. We have to use them correctly without cutting corners on salts, etc. Hashing is probably too resource intensive for most IoT devices, especially when done right.
One thing that makes sense for use in the IoT is obviously elliptic curve cryptography because the key sizes are much smaller. Curve 25519 is recommended over the NIST curves, for sure.
In fact, if we really get into the nitty-gritty for tiny devices, it may start to make sense to use a one-time pad, especially when there is a bit of storage available. If we go with a proper OTP for confidentiality, then Poly1305 makes sense for authentication. Or shared secrets might start being used in authentication. es.
I see the IoT as a big threat. Instead of lowering security to meet device capabilities, we need to assure security every step of the way and that may very well mean shared secrets and storage of strongly generated (made elsewhere) keys. Otherwise the IoT will be the attacker's dream come true.