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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.

EDIT: Not RSA.

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    $\begingroup$ You may want to check out our help center on how open-ended and opinion-based questions should be avoided. Then, you can edit your question to be more focused, because we want to make sure a large majority of questions can be useful to at least multiple people. $\endgroup$ – DannyNiu Nov 16 '20 at 3:45
  • $\begingroup$ Elliptic Curves are also based on number (or rather group-) theory. $\endgroup$ – Maarten Bodewes♦ Nov 16 '20 at 17:10
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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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