## plonk
### tl; dr
* **[introduced in 2019](https://eprint.iacr.org/2019/953.pdf)**, plonk stands for **"permutations over lagrange-bases for ecumenical noninteractive arguments of knowledge"**, brining enhancements to the usability of zkps by giving a **universal fully-succinct zk-SNARK with significantly improved prover run time compared to fully-succinct sonic**. * while plonk still requires a trusted setup procedure similar to snarks, but it's **universal and updateable trusted setup**, meaning: - instead of there being one separate trusted setup for every program to be proved, there is one single trusted setup for the whole scheme. - there is a way for multiple parties to participate in the trsuted setup such that it's secure as long as any one of them is honest, and this multi-party procedure is fully sequential (polynomial commitment, in this case, kate). * there are two types of constraints: - gate constraints (equations between wires attached to the same gate, e.g., `a1 * b1 = c1`). - copy constraints (claims about equality of different wires anywhere in the circuit, e.g., `ao = a1`) * **polynomial commitments** is a short object that represents a polynomial, allowing evaluations verification without needing all the data in the polynomial. * if someone gives you a commitment representing `c` they can give you a proof that can convince you, for some specific `z`, what the value of `P(z)`. * a commitment to a degree-d polynomial is made by multiplying each of the first d+1 points in the proving key by the corresponding coefficient in the polynomial, and adding the results together, providing an evaluation of that polynomial at `s` without knowing `s`.


--- ### cool resources
* **[understanding plonk, by vub](https://vitalik.ca/general/2019/09/22/plonk.html)** * **[plonk original paper, by a. gabizon et al.](https://eprint.iacr.org/2019/953.pdf)** * **[plookup original paper, by a. gabizon et al.](https://eprint.iacr.org/2020/315)**