Good key update algorithms for key evolving schemes In schemes like SAKE(Symmetric-key Authenticated Key Exchange) , the master keys (used to authenticate parties and generate session keys) are evolving, ie undergo transition $K=update(K)$.

What is a good candidate for $update(.)$ function?

Would $K=\operatorname{AES}(K, S)$ have &quot;good properties&quot;, with $S$ being arbitrary block-length constant?Author of the algorithm state that $update(.)$ should be irreversible function.
AES is not irreversible, at least not when the key is known. I'd rather look at a PRF (Pseudo Random Function) rather than a PRP (Pseudo Random Permutation) such as AES.
A good PRF is HMAC. HMAC also has the nice properties of having no limit to the input message and a rather large, although statically sized output.

Even more specifically you might want to use a Key Based Key Derivation Function (KBKDF) such as HKDF - which is based on HMAC. A HKDF specifically takes input keying material to create output keying material.
It might be that KDF functions are e.g. present in hardware devices. This means that they keying material could stay into the hardware device, while ciphertext or HMAC values are commonly exported.