The Mathematics behind zkSNARKS

In this workshop, we review the mathematical principles of verified computing as described in the Pinocchio protocol. The session includes the concepts of circuits, quadratic arithmetic programs and verified computation.
Be prepared for some math! We will do a simple Zero Knowledge Snark from the beginning to the end to understand the fundamentals of Zero Knowledge proofs.
Slides: leastauthority.com/static/sli...
Prerequisites: Participants should have some understanding of zero knowledge proofs, as this workshop will not get into the general theory. Simplified cryptography will be used that requires only basic addition, subtraction and multiplication in finite fields.
About the Presenter: Mirco Richter is a mathematician with an academic background. He has been working and conducting research in the Blockchain space since 2011 with a focus on Cryptography and Consensus Algorithms. He is involved in the cCoin movement and has authored the accompanying paper: A (somewhat) easy pen & paper example of the Pinocchio protocol (Part 1).
Many thanks to Electric Coin Co. for supporting this workshop!
Electric Coin Company launched and supports the development of Zcash - a privacy-protecting, digital currency built on strong science. Since its launch in 2016, Zcash has quickly grown to be one of the most valued and admired cryptocurrencies in the world.
Although we discovered the underlying scientific principles and designed the Zcash protocol, we do not control the currency, its mining or its distribution. Every user of Zcash contributes to its decentralization, helping to protect it against failure and corruption. Our team is one among many participants in the network.
The MoonMath Manual to zkSNARKs, by Least Authority, is a resource for anyone interested in understanding and unlocking the potential of zk-SNARKs, from beginners to experts. Visit our website to learn more and a free download of the manual - leastauthority.com/community-...

[@AChainofBlocks]

This guy is next level...

[@dellusionald1794]

The slide at 36:00 finally made it clear to me what the idea behind QAPs is (together with the so often repeated comment "addition comes for free"). But you must know about Lagrange basis polynomials beforehand. It is explained briefly at 41:45, but wouldn't it be easier to say that if the assignment is valid, p is zero at all m_j, and this is why t divides p?

[@stephenparker7997]

great information.

[@JohnAlanWoods]

Great video, I think the slide on DAGs confuses sources and leafs. A source is a root. - best explanation of SNARKS on KZbin that I've found thus far.

[@mircorichter1375]

I would call the leafs the sources, because sources, as leafs, have only outgoing edges and I would call the root a sink... It depends on the arrow convention, though.

[@ddolgov]

Unfortunately the zk-part was only 5 minutes long and felt a little rushed. Otherwise, great talk! Why are there 6 pairing functions conditions, I thought we needed to check polynomial equality at one point only?

[@lherfel]

Thanks

[@eyenosenothing]

Link at 4:53 -- drive.google.com/file/d/0B-WxC9ydKhlRZG92dnJ0RmdWRkZKUXR5Q3FTd0pZMl9Tdnln/view

[@user-nx8dc5vs9o]

this link is not openable.

[@kelleclark4521]

We’re the slides ever published?

[@leastauthority8545]

Yes, a link to the slides was included in the video description. You can find them here: leastauthority.com/static/slides/ZKsnarks_workshop_slides.pdf

[@DimitrisSfounis]

Was it really that hard for that audience to understand modulo division and finite fields? Jesus Christ.

[@mattlm64]

Surely that's the easy part.

[@joshhoover1202]

Ikr. I imagine most of the attendees already understand this anyways.

[@mircorichter1375]

.. Modulo Errors ... Of Course

[@bulut3731]

i get 9+\frac{5x+9}{x^2+10x+2} on slide 31. am i going crazy?

[@mircorichter1375]

@@bulut3731 did you do the computation in modular 11 arithmetics?

[@bulut3731]

​@@mircorichter1375 i did. let me do a sanity check here: the claim is that: (x^2 + 10x + 2) * (9+\frac(5x+4)(x^2+10x+2)) = 9x^2+7x+5 (all operations in mod11) LHS = 9x^2 + 90x + 18 + 5x + 4 = 9x^2 + 95x + 22 = 9x^2 + 7x + 22 (since 95 \equiv 7 \mod 11) = 9x^2 + 7x + 0 (since 22 \equiv 0 \mod 11) we seem to be missing a 5 somewhere, no?

[@user-nx8dc5vs9o]

@@mircorichter1375 i need help in ZK-SNARK.

[@mircorichter1375]

@@bulut3731 i think you Mix Up Mod 11 and non Mod Terms in the computation

[@water3745]

Can I just point out how impatient the audiences are?

[@islamic-videos-together]

how is 2^5=9 if the exponents are converted into a finite field than its 10, and also 2^4 != 16 if we were following finite field, Can anyone explain? 18:45

[@leastauthority8545]

The exponents are integers. This is because x^a essentially means: multiply x with itself a-times. Of course you can multiply as many times as you want.