[Cryptography] LUKS on ATA versus on SSD

[Jon Callas]

> On Jan 3, 2026, at 12:59, Ron Garret <ron at flownet.com> wrote:
> 
> 
> That's true, but the *definition* of a hash function is a function that maps data of arbitrary size to FIXED-SIZE VALUES, so a perfect hash must have a finite domain.  A Godel numbering scheme has to be able to handle an infinite number of strings.

Ron, you're right that in the abstract, Godel numbering handles infinite sets (or iteration). However, does your statement mean that one cannot Godel-number a finite set? I still think that it's obviously informal to think about that way, and it's not a bad way to think about it, even if it doesn't really align.

The point of Godel numbering is that you take a set of symbols and properties and you can perform operations with them to assemble them, and that iterates. Godel's proof lets you iterate an infinite number of times, but if you have finite symbols and finite iteration, then you can construct some mapping that looks like a hash function if you squint at it the right way. If the numbering is in a finite field, like mod some prime, it starts looking a lot like a hash function. 

If Douglas finds it useful as an analogy to help understand the other problem, it seems like a quibble to say that well, it's only Godel numbering if the disk has infinite storage. Consider some suitable finite subset of the general problem, like strings that are less than 2^1,000,000 bits long. We (probably) can't represent strings longer than that in our material world anyway.

	Jon