Tutorial for STARKs with supporting code in python

Overview

stark-anatomy

STARK tutorial with supporting code in python

Outline:

  • introduction
  • overview of STARKs
  • basic tools -- algebra and polynomials
  • FRI low degree test
  • STARK information theoretical protocol
  • speeding things up with NTT and preprocessing

Visit the Github Pages website here: https://aszepieniec.github.io/stark-anatomy/

Running locally (the website, not the tutorial)

  1. Install ruby
  2. Install bundler
  3. Change directory to docs/ and install Jekyll: $> sudo bundle install
  4. Run Jekyll: $> bundle exec jekyll serve
  5. Surf to http://127.0.0.1:4000/

LaTeX and Github Pages

Github-Pages uses Kramdown as the markdown processor. Kramdown does not support LaTeX. Instead, there is a javascript header that loads MathJax, parses the page, and replaces LaTeX maths instructions with their proper formulae. Here is how to do it:

  1. Open _includes/head-custom.html and paste the following code:
MathJax.Hub.Config({ TeX: { equationNumbers: { autoNumber: "AMS" } }, tex2jax: { inlineMath: [ ['$', '$'], ['\\(', '\\)'] ], displayMath: [ ['$$', '$$'], ['\\[', '\\]'] ], processEscapes: true, } }); MathJax.Hub.Register.MessageHook("Math Processing Error",function (message) { alert("Math Processing Error: "+message[1]); }); MathJax.Hub.Register.MessageHook("TeX Jax - parse error",function (message) { alert("Math Processing Error: "+message[1]); }); ">
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
    TeX: {
      equationNumbers: {
        autoNumber: "AMS"
      }
    },
    tex2jax: {
    inlineMath: [ ['$', '$'], ['\\(', '\\)'] ],
    displayMath: [ ['$$', '$$'], ['\\[', '\\]'] ],
    processEscapes: true,
  }
});
MathJax.Hub.Register.MessageHook("Math Processing Error",function (message) {
	  alert("Math Processing Error: "+message[1]);
	});
MathJax.Hub.Register.MessageHook("TeX Jax - parse error",function (message) {
	  alert("Math Processing Error: "+message[1]);
	});
</script>
<script type="text/javascript" async
  src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
</script>

Jekyll, the site engine used by Github Pages, will load this header automatically. There is no need to change the _config.yml file.

Note that Kramdown interprets every underscore (_) that is followed by a non-whitespace character, as starting an emphasised piece of text. This interpretation interfereces with subscript in LaTeX formulae, which also uses underscores. The workaround is to re-write the LaTeX formulas by introducing a space after every underscore. Also, consider replacing:

  • \{ by \lbrace and \} by \rbrace,
  • | by \vert.
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