https://github.com/erhant/arithmetic-circuits
Moda Palas Blackboard Cryptography II - Arithmetic Circuits & R1CS
https://github.com/erhant/arithmetic-circuits
circuits cryptography qap r1cs rust
Last synced: 7 months ago
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Moda Palas Blackboard Cryptography II - Arithmetic Circuits & R1CS
- Host: GitHub
- URL: https://github.com/erhant/arithmetic-circuits
- Owner: erhant
- License: mit
- Created: 2024-12-27T19:00:26.000Z (9 months ago)
- Default Branch: main
- Last Pushed: 2025-01-03T22:39:11.000Z (9 months ago)
- Last Synced: 2025-01-22T06:37:41.477Z (9 months ago)
- Topics: circuits, cryptography, qap, r1cs, rust
- Language: Rust
- Homepage: https://lu.ma/c6wrtj5b
- Size: 366 KB
- Stars: 3
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# ModaPalas Blackboard | Cryptography II: Arithmetic Circuits
This repository contains the material for the event [ModaPalas Blackboard | Cryptography II](https://lu.ma/c6wrtj5b?tk=dJKwGa) lecture "Arithmetic Circuits" by [erhant](https://github.com/erhant).
## Lecture Notes
We have lecture notes as follows:
1. [Introduction](./docs/1-intro.md)
2. [Groups](./docs/2-groups.md)
3. [Usage in Zero Knowledge Cryptography](./docs/3-usage.md)
4. [Rank-1 Constraint Systems](./docs/4-r1cs.md)
5. [Quadratic Arithmetic Programs](./docs/5-qap.md)
6. [Designing Circuits](./docs/6-circuits.md)
If you have `mdbook` installed with Mermaid preprocessor, you can also open this in a book via:
```sh
mdbook serve --open
```
## Implementations
We also have some pieces of code:
- [R1CS](./src/r1cs.rs): a simple implementation of Rank-1 Constraint System.
- [QAP](./src/qap.rs): a simple implementation of Quadratic Arithmetic Program, connected to the R1CS implementation.
- [Circuits](./src/circuits/mod.rs): a "wire" implementation and some circuit examples over it.
You can run some tests and see the results by running:
```sh
cargo test -- --show-output
```
We have an example R1CS & QAP implementation that you can run, which shows you all the results:
```rs
// A interpolations:
A_0(x) = 51*x^2 + 41*x + 5
A_1(x) = x^2 + 93*x + 4
A_2(x) = 96*x^2 + 4*x + 94
A_3(x) = 49*x^2 + 47*x + 1
// A evaluations:
A_0(1) = 0 A_0(2) = 0 A_0(3) = 5
A_1(1) = 1 A_1(2) = 0 A_1(3) = 1
A_2(1) = 0 A_2(2) = 1 A_2(3) = 0
A_3(1) = 0 A_3(2) = 0 A_3(3) = 1
// B interpolations:
B_0(x) = 0
B_1(x) = 48*x^2 + 50*x
B_2(x) = 0
B_3(x) = 0
// B evaluations:
B_0(1) = 0 B_0(2) = 0 B_0(3) = 0
B_1(1) = 1 B_1(2) = 1 B_1(3) = 0
B_2(1) = 0 B_2(2) = 0 B_2(3) = 0
B_3(1) = 0 B_3(2) = 0 B_3(3) = 0
// C interpolations:
C_0(x) = 0
C_1(x) = 0
C_2(x) = 49*x^2 + 46*x + 3
C_3(x) = 96*x^2 + 4*x + 94
// C evaluations:
C_0(1) = 0 C_0(2) = 0 C_0(3) = 0
C_1(1) = 0 C_1(2) = 0 C_1(3) = 0
C_2(1) = 1 C_2(2) = 0 C_2(3) = 0
C_3(1) = 0 C_3(2) = 1 C_3(3) = 0
// P(x) built from QAP for a valid instance
P(x) = 82*x^4 + 81*x^3 + 83*x^2 + 88*x + 54
P(x) / T(x) = 82*x + 88
```
We can also design circuits with the existing gates (see [this example](./tests/circuits_test.rs)) and then print a wire's lavel to see its gates, everything is composed of `+` and `*` only!
```py
# for equal wires a, b in a field of order 97
a == b is given by (1+(96*((a+(96*b))*0))): 1
```
## See Also
- [Ying Tong Lai - Modern ZK Cryptography: Lecture 7 (MIT IAP 2023)](https://assets.super.so/9c1ce0ba-bad4-4680-8c65-3a46532bf44a/files/e11309fb-7356-42ad-9c78-565341abd80d.pdf)
- [0xPARC - R1CS Explainer](https://learn.0xparc.org/materials/circom/additional-learning-resources/r1cs%20explainer/)
- [Vitalik Buterin - QAP: Zero-to-Hero](https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649)
- [RareSkills - R1CS](https://www.rareskills.io/post/rank-1-constraint-system)
- [erhant - notes from ZKP MOOC Lecture 3: Programming ZKPs](https://crypto.erhant.me/zklearning/programming-zkps.html)
- [Risen Crypto - R1CS and QAP](https://risencrypto.github.io/R1CSQAP/)