1# sigmabus-poc
 2Proof 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).
 3
 4> Experimental code, do not use in production.
 5
 6
 7This 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)).
 8
 9Proving $X = x \cdot G$ 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.
10
11Let $\mathbb{G}$ be [BN254](https://hackmd.io/@jpw/bn254)'s $G1$, an example of usage would be:
12```rust
13// generate the trusted setup
14let params = Sigmabus::<Bn254>::setup(&mut rng, &poseidon_config);
15
16// compute X = x * G
17let x = Fr::rand(&mut rng);
18let X = G1Projective::generator().mul(x);
19
20// generate Sigmabus proof for X==x*G
21let mut transcript_p = PoseidonTranscript::<G1Projective>::new(&poseidon_config);
22let proof = Sigmabus::<Bn254>::prove(&mut rng, &params, &mut transcript_p, x);
23
24// verify Sigmabus proof for X==x*G
25let mut transcript_v = PoseidonTranscript::<G1Projective>::new(&poseidon_config);
26Sigmabus::<Bn254>::verify(&params, &mut transcript_v, proof, X).unwrap();
27```