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I'm interested in some sort of "compendium" on lattice based crypto. There are a bunch of maths behind FALCON and other stuff. A lot of articles are devoted to lattice crypto, but not of them are of paramount importance. The other problem is that there are papers which are obviously influential, but they are hard to understand "from scratch".

To start with something I may notice some of them:

GPV framework:

  1. "How to Use a Short Basis: Trapdoors for Hard Lattices and New Cryptographic Constructions".

Cryptanalysis:

  1. "Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures"

Basic courses :

  1. winter school on lattice based crypto (https://cyber.biu.ac.il/event/the-2nd-biu-winter-school)
  2. Regev course on lattices in CS (https://cims.nyu.edu/~regev/teaching/lattices_fall_2004/)
  3. Vinod's course (http://people.csail.mit.edu/vinodv/6876-Fall2015/index.html)

Surveys :

  1. "Lattice-based Cryptography" part from the book "Post-Quantum Cryptography".
  2. "A Decade of Lattice Cryptography", Peikert.

Unfortunately i didn't find anything on discrete gaussian distributions and properties of continious gaussians (why is it "not far from" uniform over any "small" parallelopiped), how to generate them; on smoothing parameter and its "intuitive" meaning. Also reductions from average to worst case are somewhat tricky and uneasy to understand form Ajtai papers. And there is a direction of research on ideal lattices, which somehow related to integer rings of number fields ($\mathbb{Z}_K$), this is completely obscure..

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    $\begingroup$ Did you check "a decade of lattice based crypto" by Chris Peikert? $\endgroup$ – Geoffroy Couteau Sep 16 at 7:42
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    $\begingroup$ @GeoffroyCouteau nice, i will definitely check this source and will add to the list of "basics". However, a first glimpse gave me the feeling that this is just too terse to understand from scratch. $\endgroup$ – Kirill Tsar. Sep 16 at 10:08

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