A single AES encryption block is the same size as a UUID and cheap to compute.
And I guess if the user references specific resources by ID you'd have to translate back? Assuming the session has been maintained correctly,which I guess is a plus for stateful sessions. And it doesn't really matter if you get a collision on the encrypted output.
I spent enough time in the nibling comment talking about my doubts about that advice not to publicly share the identifying key. But I'll add one more point; it feels like a bunch of added complexity for marginal benefit.
It is literally encrypting whatever type you are using as a handle for records that you send the user, typically an integer, a UUID, or some slightly more complex composite key. The only restriction is that the key should not be longer than 128-bits so that you can encrypt it to a UUID-like value; in practice you can almost always guarantee this [0]. The encryption only happens at the trust boundary i.e. when sending it to a random user. That encrypted key is not stored or used at all internally, it just changes the value of the key the user sees.
Most obvious ways of generating handles in a database leak private state. This is routinely exploited almost to the point of being a meme. Encrypting the handles you show the user prevents that.
An advantage of this is that if you are systematically encrypting exported keys then you can attach sensitive metadata to those keys at runtime if you wish, which can be very convenient. You have 128 bits to work with and a unique serial only needs 64 at most. If you are paranoid, there are schemes that enable some degree of key authentication. And while well beyond the scope here, similar constructions work nicely for compact keys in federate data models.
At scale, the cost (storage, compute, etc) of all of this matters. Encryption of keys, if done intelligently, is atypically efficient on all accounts while providing explicit inspectable security guarantees.
[0] There are reasons you might want to expand the exported key to a 256-bit value, particularly in high-assurance type environments, but the advantage of 128-bits is that it is literally drop-in compatible with UUIDs almost everywhere.
I didn’t realise this! The UUID spec mandates some values for specific digits, so I assume this would not be strictly valid UUIDs?
To be honest many companies are not using strictly standard conforming UUIDs everywhere, and UUID has become a synonym for opaque 128-bit identifier. Consumers of the value just need them to be unique. All standard UUID versions are sometimes prohibited in environments, except maybe UUIDv8, so this semantic ambiguity is helpful.
Technically, you could make it present as a standard UUIDv4 or UUIDv8 by setting a few bits, as long as you remember to add them back if you ever need to decrypt it. The entropy might be a bit off for a UUIDv4 if someone actually checks but you can guarantee the uniqueness.
Using AES to produce a UUID-like key is an old but useful trick. Both ARM and x86 do that encryption in hardware — it is cheaper to generate than the standardized UUID versions in most cases.