Decade of Lattice Cryptography

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1. bliblibloFeb 2023
   I could not find on which algorithm this compiler is based at first sight.

   I know of an other library for homomorphic encryption Lattigo (https://github.com/tuneinsight/lattigo) which is based on Ring Learning with Errors.

   The security of RLWE is "believed" to be strong (meaning there has not been a proof of the opposite yet). It is based on the Lattice problem which is likely to be resistant even to quantum computers.

   For a more formal and complete explanation, the paper "A Decade of Lattice Cryptography" was very instructive. https://eprint.iacr.org/2015/939.pdf

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2. throwawaymathApr 2019
   There are many such books! It's hard to suggest something in particular because almost everything about computers comes from some area of theory. I'll try giving you a few specific suggestions while also touring some broad areas.

   One really active area of research is type theory. Another easy one is differential geometry and linear algebra, which are fundamental to machine learning. Try searching for resources about manifolds and dimensionality reduction. While we're at it, any kind of vectorized computation can also be modeled through linear algebra. There's probably material somewhere that formalizes a lot of Intel CPU architecture algebraically.

   Actually, we can basically just take linear algebra and talk about its applications to nearly any area of computing, since it's one of the most ubiquitous areas of mathematical theory. What are you interested in? Graphics? Algorithm design? Data analysis? Parallelism? Statistics?

   Combinatorics is also a big one. Knuth's The Art of Computer Programming has a wealth of material on combinatorics and its applications to computing (and in particular, algorithms thereof). You also might like learning about the way complex numbers and quaternions are used to computing spatial rotations.

   I'm not personally a fan of category theory, but if abstractions are your thing you might enjoy Bartosz Milewski's Category Theory for Programmers. Along similar lines (and circling back to type theory), there's CMU's Software Foundations series of books[1].

   If you are interested in cryptography, you might really enjoy reading Chris Peikert's A Decade of Lattice Cryptography[2]. The author is a prominent researcher in post-quantum cryptography, and walks through the last decade or so of research in cryptography based on a type of structure in abstract algebra called a lattice. This is very technical material, since it's more like a survey than a book.

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   1. https://softwarefoundations.cis.upenn.edu/

   2. https://web.eecs.umich.edu/~cpeikert/pubs/lattice-survey.pdf

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