Calculation example in a small Galois field

I have had a closer look at the snark-explain blog posts, which are indeed much better than what I usually get to read on the subject, but in my impression, they are still very geared at explaining the rationale behind the math. The better starting point for applied math, is in my impression one or more calculation examples, obviously, in a small Galois field.

Since math rests entirely on provability, it is perfectly understandable that a math paper moves the formal proofs to the forefront, if only, because that is what the peers are going to judge the paper on. Unfortunately, that is what they do to the exclusion of everything else, while they forget that they may still desire to see people to actually applying their work. So, we would really benefit from an appendix to their paper, in which they would show annotated calculation examples. “These inputs, calculation after calculation, end up the following outputs.” That will allow applied math people to make their own exercises and better see what the numbers look like in the real world.

Of course, nobody denies the central place of provability in a math theory. It is the fact that we know that it is in the first place the fact that peer-reviewed proof exists, that attracts the interest of applied math people to the paper. Still, it is never the first thing that we also want to read. Annotated manual calculation examples are much more what will get us going.

So, I would want to do these zkSNARK calculation examples, but without the ability to pick a core mathematician’s brain, it may not pan out, and the results are actually even likely to be wrong.

So, the goal would be annotated calculation examples in a small Galois field, and the resources required, the time of someone on the core theoretical team to guide me through the task and if need be intervene with corrections. The reason why I would want to do this, is not entirely selfless, but indeed rather my morbid fascination with how you guys managed to pull this off. Still, it could also have wider community value to publish these annotated calculation examples? So, yes, it is about someone of you guys wasting his time on this. I can imagine that you are busy doing other things already, but maybe someone could unexpectedly still be interested?

Hey, I’m not completely sure what you mean. Perhaps you would be interested in writing such an example? If it comes out well we could link to it from the Zcash website.
On a similar note, Vitalik’s post has a concrete example of how to construct a QAP.

Also, when you say ‘their paper’ not sure what paper you are referring to.

Thanks! I am still working through the blog posts. Vitalik even wrote example programs in Python. Quite a smart guy! I am certainly not yet as far as Vitalik in the realm of calculating output from input. Unfortunately, even Vitalik does not always clarify required inputs and desired outputs. I am still reading now, but I suspect that it may turn out to be still not enough to finish the complete calculation example. But then again, if I manage to make progress towards the goal, things should be ok already. :wink:

I’m not sure what your refer to by complete example - Just the transition into QAP? Or also the actual SNARK verification? If it’s the latter, it might be hard to give a small example, as the computation of the pairing function used by the verifier is quite complex.