Are there any applications of checksums and/or cryptographic hash functions in pure mathematics?

I've tried Googling this and haven't found anything.

If you've got any other application of cryptography or coding theory in pure mathematics, please tell me in the comments.

Note: I'm not asking about applications of pure mathematics to cryptography, but the other way round.

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    $\begingroup$ This might be stretching it, but from what I understand the Leech lattice can be constructed from the binary Golay code, and the Leech lattice has been used to find a sphere packing in $\mathbb{R}^{24}$ that is very close to being as optimal as theoretically possible. $\endgroup$ – Kaj Hansen Jun 1 '15 at 21:25

Combinatorics uses a lot of codes in it -- codes are basically subsets (non-linear code)/subspaces(linear code) of $\mathbb{F}^n$ where $\mathbb{F}$ is some finite field.

By using the appropriate code, you can count or identify or other things of particular combinatorial objects. For example, codes are intimately related to block designs and other things (the Fano plane being one of the simplest examples).

You can also use codes to study things like RIP matrices:

Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka. Explicit constructions of RIP matrices and related problems. Duke Math. J. 159 (2011), no. 1, 145--185

(In fact, a lot of Bourgain's work would fit your requirements)

See also the book by Conway and Sloane: Sphere packing, lattices and groups.


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