Is SHA-3 normally used with a LUT or hash table?
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Outside of use in microchips and FPGAs does SHA-3 have a lookup table?
(I'm answering the title and the question; the question might be interpreted as 'do you use SHA-3 to implement a LUT or hash table?')
Well, some implementations have the per-round constant in the Iota transform stored as a look up table (however, those are not hard to compute, so some implementations do compute them on the fly).
Other than that, the transforms that SHA-3 does internally are regular enough that we generally don't find a look up table useful.

poncho
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markdown operator. I know you're reading a lot about these things, but we all learn these the different ways, so some context are often needed. – DannyNiu Apr 14 '23 at 01:08