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This article dances around the problem of encrypting small values a bunch. Here's a Rogaway paper on how to do it:

https://www.cs.ucdavis.edu/~rogaway/papers/thorp.pdf

(You do not need to limit yourself to inputs that are multiples of the AES block size).

There's another one like this, I forget the name.

SHA-2 is just fine, and is usually a saner choice than SHA-3 (if you want to be a crypto-hipster, use Blake2, not SHA-3; it's usually an easier dep to pull in, and more things use it).



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