In this eighth video, I explain how the prover and the verifier can perform a "polynomial dance" in order to construct the circuit polynomial $f$. The principle is simple: the prover doesn't want to leak information about the private inputs and the intermediary values in the circuit, and the verifier doesn't want to give the prover too much freedom in the way they construct the circuit polynomial $f$.
In this sixth video, I explain the compilation, or even compression, of a set of equations into a single polynomial. That polynomial represents all of our constraints, as long as it vanishes in an agreed set of points. With a polynomial in hand, we will be able to create a protocol with our polynomial-based proof system.
In this fifth video, I explain how we can "compile" an arithmetic circuit into something PLONK can understand: a constraint system. Specifically, a PLONK-flavored constraint system, which is a series of equations that must if equal to zero correctly describe our program (or circuit).
In this third video, I start by explaining what the protocol will use at the end: polynomials. It'll give you a glimpse as to what direction we'll be taking when we transform our program into something we can prove.
In this second video, I give some intuition on how to think about zero-knowledge proof systems, with the example of proving the solution of a sudoku, then I give an overview of what I'll explain in this series of video.
I recently got into general-purpose zero-knowledge proof systems (cryptographic primitives that allow you to prove the execution of a program without revealing some of the inputs), specifically the state-of-the-art PLONK proof system. This is a series of video I made to explain what I understood and learned in the past few months. There might be some inaccuracies, so I apologize in advance for that. You can check all the videos via the playlist here: https://www.youtube.com/watch?v=RUZcam_jrz0&list=PLBJMt6zV1c7Gh9Utg-Vng2V6EYVidTFCC
In this first video, I simply explain what general-purpose zero-knowledge proofs are, specifically zk-SNARKs, and what PLONK is.