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Add Sigmabus PoC implementation

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/target
/Cargo.lock

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[package]
name = "sigmabus-poc"
version = "0.1.0"
edition = "2021"
# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
[dependencies]
ark-std = "0.4.0"
ark-ff = "0.4.0"
ark-ec = "0.4.2"
ark-poly = "0.4.0"
ark-serialize = { version = "0.4.0", default-features = false, features = [ "derive" ] }
rand = { version = "0.8", features = [ "std", "std_rng" ] }
ark-crypto-primitives = { version = "^0.4.0", default-features = false, features = [ "r1cs", "snark", "sponge", "crh" ] }
ark-r1cs-std = { version = "^0.4.0", default-features = false }
ark-relations = { version = "^0.4.0", default-features = false }
ark-snark = { version = "^0.4.0", default-features = false }
ark-groth16 = { version = "^0.4.0" }
thiserror = "1.0"
[dev-dependencies]
ark-bn254 = "0.4.0"

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This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail.
If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:
<program> Copyright (C) <year> <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<https://www.gnu.org/licenses/>.
The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<https://www.gnu.org/licenses/why-not-lgpl.html>.

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# 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::<Bn254>::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::<G1Projective>::new(&poseidon_config);
let proof = Sigmabus::<Bn254>::prove(&mut rng, &params, &mut transcript_p, x);
// verify Sigmabus proof for X==x*G
let mut transcript_v = PoseidonTranscript::<G1Projective>::new(&poseidon_config);
Sigmabus::<Bn254>::verify(&params, &mut transcript_v, proof, X).unwrap();
```

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use ark_crypto_primitives::crh::{
poseidon::constraints::{CRHGadget, CRHParametersVar},
CRHSchemeGadget,
};
use ark_crypto_primitives::sponge::{poseidon::PoseidonConfig, Absorb};
use ark_ec::{AffineRepr, CurveGroup};
use ark_r1cs_std::{alloc::AllocVar, eq::EqGadget, fields::fp::FpVar};
use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystemRef, SynthesisError};
use core::marker::PhantomData;
// CF (ConstraintField)
pub type CF<C> = <<C as CurveGroup>::Affine as AffineRepr>::ScalarField;
#[derive(Debug, Clone)]
pub struct GenZKCircuit<C: CurveGroup> {
pub _c: PhantomData<C>,
pub poseidon_config: PoseidonConfig<C::ScalarField>,
// public
pub cm: C::ScalarField,
pub s: C::ScalarField,
pub r_h: C::ScalarField,
pub c: C::ScalarField,
// private
pub x: C::ScalarField,
pub r: C::ScalarField,
pub o_h: C::ScalarField,
}
impl<C: CurveGroup> ConstraintSynthesizer<CF<C>> for GenZKCircuit<C>
where
C::ScalarField: Absorb,
{
fn generate_constraints(self, cs: ConstraintSystemRef<CF<C>>) -> Result<(), SynthesisError> {
// public inputs
let cmVar = FpVar::<C::ScalarField>::new_input(cs.clone(), || Ok(self.cm))?;
let sVar = FpVar::<C::ScalarField>::new_input(cs.clone(), || Ok(self.s))?;
let r_hVar = FpVar::<C::ScalarField>::new_input(cs.clone(), || Ok(self.r_h))?;
let cVar = FpVar::<C::ScalarField>::new_input(cs.clone(), || Ok(self.c))?;
// private inputs
let xVar = FpVar::<C::ScalarField>::new_witness(cs.clone(), || Ok(self.x))?;
let rVar = FpVar::<C::ScalarField>::new_witness(cs.clone(), || Ok(self.r))?;
let o_hVar = FpVar::<C::ScalarField>::new_witness(cs.clone(), || Ok(self.o_h))?;
let crh_params =
CRHParametersVar::<C::ScalarField>::new_witness(
cs.clone(),
|| Ok(self.poseidon_config),
)
.unwrap();
Self::check(&crh_params, cmVar, sVar, r_hVar, cVar, xVar, rVar, o_hVar)?;
Ok(())
}
}
impl<C: CurveGroup> GenZKCircuit<C>
where
C::ScalarField: Absorb,
{
#[allow(clippy::too_many_arguments)]
pub fn check(
crh_params: &CRHParametersVar<C::ScalarField>,
// public inputs:
cm: FpVar<C::ScalarField>,
s: FpVar<C::ScalarField>,
r_h: FpVar<C::ScalarField>,
c: FpVar<C::ScalarField>,
// private inputs:
x: FpVar<C::ScalarField>,
r: FpVar<C::ScalarField>,
o_h: FpVar<C::ScalarField>,
) -> Result<(), SynthesisError> {
// cm == Commit(x) (Poseidon)
let computed_cm = CRHGadget::<C::ScalarField>::evaluate(crh_params, &[x.clone()]).unwrap();
computed_cm.enforce_equal(&cm)?;
// r_h == HCommit(r, o_h) (Poseidon)
let computed_r_h =
CRHGadget::<C::ScalarField>::evaluate(crh_params, &[r.clone(), o_h.clone()]).unwrap();
computed_r_h.enforce_equal(&r_h)?;
// s == r + c * x
s.enforce_equal(&(r + (c * x)))?;
Ok(())
}
}
#[cfg(test)]
pub mod tests {
use super::*;
use ark_bn254::{Fr, G1Projective};
use ark_crypto_primitives::sponge::{poseidon::PoseidonSponge, CryptographicSponge};
use ark_ec::Group;
use ark_r1cs_std::{alloc::AllocVar, fields::fp::FpVar};
use ark_relations::r1cs::ConstraintSystem;
use ark_std::UniformRand;
use std::ops::Mul;
use crate::sigmabus::SigmaProof;
use crate::transcript::{tests::poseidon_test_config, PoseidonTranscript};
#[test]
fn test_gen_zk() {
let mut rng = ark_std::test_rng();
let poseidon_config = poseidon_test_config::<Fr>();
let mut transcript = PoseidonTranscript::<G1Projective>::new(&poseidon_config);
let x = Fr::rand(&mut rng);
// the next lines do the same that is done in Sigmabus::prove but here in the test to have
// access to the internal values:
let mut sponge = PoseidonSponge::<Fr>::new(&poseidon_config);
sponge.absorb(&x);
let cm: Fr = sponge.squeeze_field_elements(1)[0];
transcript.absorb(&cm);
let r = Fr::rand(&mut rng);
let o_h = Fr::rand(&mut rng);
let R = G1Projective::generator().mul(r);
let mut sponge = PoseidonSponge::<Fr>::new(&poseidon_config);
sponge.absorb(&vec![r, o_h]);
let r_h: Fr = sponge.squeeze_field_elements(1)[0];
transcript.absorb_point(&R);
transcript.absorb(&r_h);
let c = transcript.get_challenge();
let s = r + c * x;
let sigma_proof = SigmaProof { s, R, r_h };
// end of Sigmabus::prove
let cs = ConstraintSystem::<Fr>::new_ref();
// public inputs
let cmVar = FpVar::<Fr>::new_witness(cs.clone(), || Ok(cm)).unwrap();
let sVar = FpVar::<Fr>::new_witness(cs.clone(), || Ok(sigma_proof.s)).unwrap();
let r_hVar = FpVar::<Fr>::new_witness(cs.clone(), || Ok(sigma_proof.r_h)).unwrap();
let cVar = FpVar::<Fr>::new_witness(cs.clone(), || Ok(c)).unwrap();
// private inputs
let xVar = FpVar::<Fr>::new_witness(cs.clone(), || Ok(x)).unwrap();
let rVar = FpVar::<Fr>::new_witness(cs.clone(), || Ok(r)).unwrap();
let o_hVar = FpVar::<Fr>::new_witness(cs.clone(), || Ok(o_h)).unwrap();
let crh_params =
CRHParametersVar::<Fr>::new_witness(cs.clone(), || Ok(poseidon_config)).unwrap();
// GenZK
GenZKCircuit::<G1Projective>::check(
&crh_params,
cmVar,
sVar,
r_hVar,
cVar,
xVar,
rVar,
o_hVar,
)
.unwrap();
assert!(cs.is_satisfied().unwrap());
dbg!("num_constraints={:?}", cs.num_constraints());
}
}

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#![allow(non_snake_case)]
#![allow(non_upper_case_globals)]
/// Proof of concept implementation of [Sigmabus](https://eprint.iacr.org/2023/1406) as described in section 3 of the paper, using Groth16's zkSNARK scheme.
pub mod circuits;
pub mod sigmabus;
pub mod transcript;
use thiserror::Error;
#[derive(Debug, Error)]
pub enum Error {
#[error("SigmaProof verification failed")]
SigmaFail,
#[error("GenZK verification failed")]
GenZKFail,
}

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use ark_crypto_primitives::{
crh::{poseidon::CRH, CRHScheme},
snark::SNARK,
sponge::{poseidon::PoseidonConfig, Absorb},
};
use ark_ec::{pairing::Pairing, CurveGroup, Group};
use ark_groth16::{Groth16, Proof as Groth16Proof};
use ark_std::{
rand::{CryptoRng, Rng},
UniformRand, Zero,
};
use std::marker::PhantomData;
use std::ops::Mul;
use crate::circuits::GenZKCircuit;
use crate::transcript::PoseidonTranscript;
use crate::Error;
/// Proof represents the Sigmabus proof
pub struct Proof<E: Pairing> {
cm: E::ScalarField,
sigma_proof: SigmaProof<E::G1>,
zkproof: Groth16Proof<E>,
}
/// SigmaProof represents the Sigma protocol proof (not Sigmabus proof)
pub struct SigmaProof<C: CurveGroup> {
pub s: C::ScalarField,
pub R: C,
pub r_h: C::ScalarField,
}
pub struct Params<E: Pairing> {
_e: PhantomData<E>,
poseidon_config: PoseidonConfig<E::ScalarField>,
pk: <Groth16<E> as SNARK<E::ScalarField>>::ProvingKey,
vk: <Groth16<E> as SNARK<E::ScalarField>>::VerifyingKey,
}
/// Sigmabus implements [Sigmabus](https://eprint.iacr.org/2023/1406) prover & verifier for proving
/// X=x*G as described in section 3 of the paper, using Groth16's zkSNARK scheme.
pub struct Sigmabus<E: Pairing> {
_e: PhantomData<E>,
}
impl<E: Pairing> Sigmabus<E>
where
E::ScalarField: Absorb,
{
pub fn setup<R: Rng + CryptoRng>(
rng: &mut R,
poseidon_config: &PoseidonConfig<E::ScalarField>,
) -> Params<E> {
let circuit = GenZKCircuit::<E::G1> {
_c: PhantomData,
poseidon_config: poseidon_config.clone(),
// public
cm: E::ScalarField::zero(),
s: E::ScalarField::zero(),
r_h: E::ScalarField::zero(),
c: E::ScalarField::zero(),
// private
x: E::ScalarField::zero(),
r: E::ScalarField::zero(),
o_h: E::ScalarField::zero(),
};
// generate the snark proof
let (pk, vk) = Groth16::<E>::circuit_specific_setup(circuit.clone(), rng).unwrap();
Params::<E> {
_e: PhantomData,
poseidon_config: poseidon_config.clone(),
pk,
vk,
}
}
pub fn prove<R: Rng + CryptoRng>(
rng: &mut R,
params: &Params<E>,
transcript: &mut PoseidonTranscript<E::G1>,
x: E::ScalarField,
) -> Result<Proof<E>, Error> {
// cm
let cm: E::ScalarField =
CRH::<E::ScalarField>::evaluate(&params.poseidon_config, [x]).unwrap();
transcript.absorb(&cm);
let r = E::ScalarField::rand(rng);
let o_h = E::ScalarField::rand(rng);
let R = E::G1::generator().mul(r);
let r_h: E::ScalarField =
CRH::<E::ScalarField>::evaluate(&params.poseidon_config, [r, o_h]).unwrap();
transcript.absorb_point(&R);
transcript.absorb(&r_h);
let c = transcript.get_challenge();
let s = r + c * x;
let circuit = GenZKCircuit::<E::G1> {
_c: PhantomData,
poseidon_config: params.poseidon_config.clone(),
// public
cm,
s,
r_h,
c,
// private
x,
r,
o_h,
};
// generate the snark proof
let zkproof = Groth16::<E>::prove(&params.pk, circuit.clone(), rng).unwrap();
Ok(Proof {
cm,
sigma_proof: SigmaProof { s, R, r_h },
zkproof,
})
}
pub fn verify(
params: &Params<E>,
transcript: &mut PoseidonTranscript<E::G1>,
proof: Proof<E>,
X: E::G1,
) -> Result<(), Error> {
let lhs = E::G1::generator().mul(proof.sigma_proof.s);
transcript.absorb(&proof.cm);
transcript.absorb_point(&proof.sigma_proof.R);
transcript.absorb(&proof.sigma_proof.r_h);
let c = transcript.get_challenge();
let rhs = proof.sigma_proof.R + X.mul(c);
if lhs != rhs {
return Err(Error::SigmaFail);
}
// verify zkSNARK proof
let public_input = [proof.cm, proof.sigma_proof.s, proof.sigma_proof.r_h, c];
let valid_proof = Groth16::<E>::verify(&params.vk, &public_input, &proof.zkproof).unwrap();
if !valid_proof {
return Err(Error::GenZKFail);
}
Ok(())
}
}
#[cfg(test)]
mod tests {
use super::*;
use ark_bn254::{Bn254, Fr, G1Projective};
use ark_std::rand::{RngCore, SeedableRng};
use ark_std::test_rng;
use crate::transcript::tests::poseidon_test_config;
#[test]
fn test_sigmabus_prove_verify() {
let mut rng = ark_std::rand::rngs::StdRng::seed_from_u64(test_rng().next_u64());
let poseidon_config = poseidon_test_config::<Fr>();
// generate the trusted setup
let params = Sigmabus::<Bn254>::setup(&mut rng, &poseidon_config);
// compute X = x * G
let x = Fr::rand(&mut rng);
let X = G1Projective::generator().mul(x);
let mut transcript_p = PoseidonTranscript::<G1Projective>::new(&poseidon_config);
// generate Sigmabus proof for X==x*G
let proof = Sigmabus::<Bn254>::prove(&mut rng, &params, &mut transcript_p, x).unwrap();
// verify Sigmabus proof for X==x*G
let mut transcript_v = PoseidonTranscript::<G1Projective>::new(&poseidon_config);
Sigmabus::<Bn254>::verify(&params, &mut transcript_v, proof, X).unwrap();
}
}

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use ark_crypto_primitives::sponge::{
poseidon::{PoseidonConfig, PoseidonSponge},
Absorb, CryptographicSponge,
};
use ark_ec::{AffineRepr, CurveGroup, Group};
use ark_ff::{BigInteger, Field, PrimeField};
pub struct PoseidonTranscript<C: CurveGroup>
where
<C as Group>::ScalarField: Absorb,
{
sponge: PoseidonSponge<C::ScalarField>,
}
impl<C: CurveGroup> PoseidonTranscript<C>
where
<C as Group>::ScalarField: Absorb,
{
pub fn new(poseidon_config: &PoseidonConfig<C::ScalarField>) -> Self {
let sponge = PoseidonSponge::<C::ScalarField>::new(poseidon_config);
Self { sponge }
}
pub fn absorb(&mut self, v: &C::ScalarField) {
self.sponge.absorb(&v);
}
pub fn absorb_point(&mut self, p: &C) {
self.sponge.absorb(&prepare_point(p));
}
pub fn get_challenge(&mut self) -> C::ScalarField {
let c = self.sponge.squeeze_field_elements(1);
self.sponge.absorb(&c[0]);
c[0]
}
}
// Returns the point coordinates in Fr, so it can be absrobed by the transcript. It does not work
// over bytes in order to have a logic that can be reproduced in-circuit.
fn prepare_point<C: CurveGroup>(p: &C) -> Vec<C::ScalarField> {
let binding = p.into_affine();
let p_coords = &binding.xy().unwrap();
let x_bi = p_coords
.0
.to_base_prime_field_elements()
.next()
.expect("a")
.into_bigint();
let y_bi = p_coords
.1
.to_base_prime_field_elements()
.next()
.expect("a")
.into_bigint();
vec![
C::ScalarField::from_le_bytes_mod_order(x_bi.to_bytes_le().as_ref()),
C::ScalarField::from_le_bytes_mod_order(y_bi.to_bytes_le().as_ref()),
]
}
#[cfg(test)]
pub mod tests {
use super::*;
use ark_crypto_primitives::sponge::poseidon::find_poseidon_ark_and_mds;
/// WARNING the method poseidon_test_config is for tests only
#[cfg(test)]
pub fn poseidon_test_config<F: PrimeField>() -> PoseidonConfig<F> {
let full_rounds = 8;
let partial_rounds = 31;
let alpha = 5;
let rate = 2;
let (ark, mds) = find_poseidon_ark_and_mds::<F>(
F::MODULUS_BIT_SIZE as u64,
rate,
full_rounds,
partial_rounds,
0,
);
PoseidonConfig::new(
full_rounds as usize,
partial_rounds as usize,
alpha,
mds,
ark,
rate,
1,
)
}
}