https://github.com/arnaucube/sigmabus-poc

Proof of concept implementation of Sigmabus https://eprint.iacr.org/2023/1406
https://github.com/arnaucube/sigmabus-poc

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Proof of concept implementation of Sigmabus https://eprint.iacr.org/2023/1406

• Host: GitHub
• URL: https://github.com/arnaucube/sigmabus-poc
• Owner: arnaucube
• License: gpl-3.0
• Created: 2023-09-29T13:16:48.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2023-12-20T17:23:57.000Z (11 months ago)
• Last Synced: 2024-04-16T22:33:56.813Z (7 months ago)
• Language: Rust
• Size: 18.6 KB
• Stars: 9
• Watchers: 3
• Forks: 2
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# sigmabus-poc

Proof of concept implementation of Sigmabus https://eprint.iacr.org/2023/1406, a cool idea by [George Kadianakis](https://twitter.com/asn_d6) and [Mary Maller](https://www.marymaller.com/) and [Andrija Novakovic](https://twitter.com/AndrijaNovakov6).

> Experimental code, do not use in production.

This PoC implements [Sigmabus](https://eprint.iacr.org/2023/1406) to prove & verify that $X = x \cdot G \in \mathbb{G}$ for a public input $X \in \mathbb{G}$ and a private input $x \in \mathbb{F}_r$ ($\mathbb{G}$'s ScalarField), while the circuit is defined on $\mathbb{F}_r$ (note that $\mathbb{G}$ coordinates are on $\mathbb{F}_q$ ($\mathbb{G}$'s BaseField)).

Proving $X = x \cdot G$ with a 'traditional' approach in a zkSNARK circuit, would require non-native arithmetic for computing the scalar multiplication $x \cdot G \in \mathbb{G}$ over $\mathbb{F}_r$, which would take lot of constraints. The number of constraints in the circuit for this Sigmabus instantiation mainly depends on the constraints needed for 2 Poseidon hashes.

Let $\mathbb{G}$ be [BN254](https://hackmd.io/@jpw/bn254)'s $G1$, an example of usage would be:

```rust

// generate the trusted setup

let params = Sigmabus::::setup(&mut rng, &poseidon_config);

// compute X = x * G

let x = Fr::rand(&mut rng);

let X = G1Projective::generator().mul(x);

// generate Sigmabus proof for X==x*G

let mut transcript_p = PoseidonTranscript::::new(&poseidon_config);

let proof = Sigmabus::::prove(&mut rng, &params, &mut transcript_p, x);

// verify Sigmabus proof for X==x*G

let mut transcript_v = PoseidonTranscript::::new(&poseidon_config);

Sigmabus::::verify(&params, &mut transcript_v, proof, X).unwrap();

```