## zero-knowledge proofs

<br>

### tl; dr

<br>

* suppose that you have a (public) function `f`, a (private) input `x`, and a (public) output `y`. 
* you want to prove that you know an `x` such that  `f(x) = y`, without revealing what `x` is. 
* for the proof to be succinct, you want it to be verifiable much more quickly than computing itself.
* a **trusted setup ceremony** is a procedure that is done to generate a piece of data that must be used every time some cryptographic protocol is run.
* for some proofs to work, such as zk-snarks, it's necessary to create a **common reference string (CRS)**, which provides public parameters for proving and verifying validity proofs. 
* the security of the proving system depends on the csr setup and some zk-rollups attempt to solve this problem by using a **multi-party computation ceremony (mpc)** with trusted individuals.
* modern protocols use the **power-of-tau** setup, which has 1-of-N trust model, with N around hundreds.

<br>

<p align="center">
<img width="300" src="https://user-images.githubusercontent.com/1130416/234407214-ed3974fd-85cc-471b-a08b-e2edf0efd1a2.png">
</p>

<br>

#### comparison of proof systems

<p align="center">
<img width="300"  src="https://user-images.githubusercontent.com/1130416/234476377-f7c88f31-919f-4503-8b60-203ca9b0c06d.png">
<img width="300"  src="https://user-images.githubusercontent.com/1130416/234476566-df847c7f-b1ad-42cf-b5dd-85ba2cf7a997.png">
</p>

<br>

#### common reference strings, structured reference strings, trusted setup, multi-party computation ceremony

<br>

<p align="center">
<img width="250" src="https://user-images.githubusercontent.com/1130416/235269418-3cb7b4ca-83b7-4930-a367-586cb8be4fc7.png">
</p>

<br>

<br>

----

### chapters

<br>

* **[zk-snarks](zk-snarks)**
* **[zk-starks](zk-starks)**
* **[plonk](plonk)**
* **[halo2](halo2)**
* **[nova](nova)**
* **[bulletproofs](bulletproofs)**
* **[kate](kate)**
* **[circom](circom)**

<br>

---

### cool resources

<br>

* **[how do trusted setups work, by vub](https://vitalik.ca/general/2022/03/14/trustedsetup.html)**
* **[the original paper for sonic, by m. maller et al](https://eprint.iacr.org/2019/099)**
* **[a python script for trusted setup](https://github.com/ethereum/research/blob/master/trusted_setup/trusted_setup.py)**