I am looking for a good, meaty cryptography algorithm that involves a good amount of number theory in which I can explore. I'm researching, and AES (Advanced Encryption System) seems interesting, but does not really seem to involve number theory all that much.


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  • $\begingroup$ Elliptic Curves are also based on number (or rather group-) theory. $\endgroup$ – Maarten Bodewes Nov 16 '20 at 17:10

The Falcon digital signature algorithm is as "meaty" as one can be.

  • It has an NTRU-like key generation procedure and public key lattice structure;

  • its security is based on conjectured difficulty of lattice reduction in classical and quantum computers;

  • its efficiency is based on number-theoretic transformation and fast discrete normal distribution sampling;

  • its compactness is based on entropy coding.

Some more to be listed.

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    $\begingroup$ "Some more to be listed."? Those are quite a few good reasons though. And note that Falcon is a 3rd level candidate for the PQC competition by NIST. It might not make it, but studying Post Quantum lattice based cryptosystems is certainly a good idea. $\endgroup$ – Maarten Bodewes Nov 16 '20 at 16:49

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