erhant/moonmath

Solutions to exercises from MoonMath Manual to zkSNARKs.

🌑 Moon Math 🌕

Exercises & codes from the "MoonMath Manual to zkSNARKs" by Least Authority.

Chapters

1. Introduction
2. Software Used in This Book
3. Arithmetics
4. Algebra
5. Elliptic Curves
6. Statements
7. Circuit Compilers
8. Zero-Knowledge Protocols

moonmath's Issues

Does exercise #82 skipped deliberately?

Exc 6.

I'm looking for some unhinged solutions to this one, maybe using Huff or Uiua. Feel free to add your own!

exercise-66

Hi, @erhant ! Please tell me if such issues is welcome, since it's just a way of discussions for me. Also I'm not a Pythonist, so I can't suggest a nice commit in case...

So. I feel like https://github.com/erhant/moonmath/tree/master/elliptic-curves#exercise-66 isn't done in the spirit of the exercise. To me it looks like the idea was take all projective plane points and filter them getting the set of those which are in the curve.

It's still a question for me what's the best way not to double check projective points... Is there an iterator over them in Sage? Or just find out a fine traversing algorithm, which seems not a huge headache in a small field.

Exc. 82

$\mathbb{G}_1$ and $\mathbb{G}_2$ turn out to be equal because $k=1$ in this case? Is our solution correct?

Exc. 80

I couldn't find any way to compute an element, but is there a way?

Possible error in Exercise 1

Exercise: https://github.com/erhant/moonmath/blob/master/arithmetics/README.md#exercise-5

We have to find the Euclidean decomposition of (-1687, 11). The given solution is (-153, 7), but that doesn't solve the equation:

  -1687 = (-153) x 11 + 7

whereas (-154, 7) does solve the equation:

  -1687 = (-154) * 11 + 7

Small fix for exc. 5.4

In exc. 5.4 we should have m=-154, not -153.

Thanks @alptoksoz for notifying.

FIx `*` in math notation

GIthub likes to treat every * as a font styling instruction, but if we do \* within the math notation it seems to render correctly.

For example, below we would like to render multiplicative groups for Z5 and Z3 at the same time, but one of them bugs out.

• $\mathbb{Z}_5^$ and $\mathbb{Z}_3^$
• $\mathbb{Z}_5^{*}$ and $\mathbb{Z}_3^{*}$