librustzcash/bellman/src/groth16/mod.rs

use group::{CurveAffine, EncodedPoint};
use pairing::{
    Engine,
    PairingCurveAffine,
};

use ::{
    SynthesisError
};

use multiexp::SourceBuilder;
use std::io::{self, Read, Write};
use std::sync::Arc;
use byteorder::{BigEndian, WriteBytesExt, ReadBytesExt};

#[cfg(test)]
mod tests;

mod generator;
mod prover;
mod verifier;

pub use self::generator::*;
pub use self::prover::*;
pub use self::verifier::*;

#[derive(Clone)]
pub struct Proof<E: Engine> {
    pub a: E::G1Affine,
    pub b: E::G2Affine,
    pub c: E::G1Affine
}

impl<E: Engine> PartialEq for Proof<E> {
    fn eq(&self, other: &Self) -> bool {
        self.a == other.a &&
        self.b == other.b &&
        self.c == other.c
    }
}

impl<E: Engine> Proof<E> {
    pub fn write<W: Write>(
        &self,
        mut writer: W
    ) -> io::Result<()>
    {
        writer.write_all(self.a.into_compressed().as_ref())?;
        writer.write_all(self.b.into_compressed().as_ref())?;
        writer.write_all(self.c.into_compressed().as_ref())?;

        Ok(())
    }

    pub fn read<R: Read>(
        mut reader: R
    ) -> io::Result<Self>
    {
        let mut g1_repr = <E::G1Affine as CurveAffine>::Compressed::empty();
        let mut g2_repr = <E::G2Affine as CurveAffine>::Compressed::empty();

        reader.read_exact(g1_repr.as_mut())?;
        let a = g1_repr
                .into_affine()
                .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
                .and_then(|e| if e.is_zero() {
                    Err(io::Error::new(io::ErrorKind::InvalidData, "point at infinity"))
                } else {
                    Ok(e)
                })?;

        reader.read_exact(g2_repr.as_mut())?;
        let b = g2_repr
                .into_affine()
                .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
                .and_then(|e| if e.is_zero() {
                    Err(io::Error::new(io::ErrorKind::InvalidData, "point at infinity"))
                } else {
                    Ok(e)
                })?;

        reader.read_exact(g1_repr.as_mut())?;
        let c = g1_repr
                .into_affine()
                .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
                .and_then(|e| if e.is_zero() {
                    Err(io::Error::new(io::ErrorKind::InvalidData, "point at infinity"))
                } else {
                    Ok(e)
                })?;

        Ok(Proof {
            a: a,
            b: b,
            c: c
        })
    }
}

#[derive(Clone)]
pub struct VerifyingKey<E: Engine> {
    // alpha in g1 for verifying and for creating A/C elements of
    // proof. Never the point at infinity.
    pub alpha_g1: E::G1Affine,

    // beta in g1 and g2 for verifying and for creating B/C elements
    // of proof. Never the point at infinity.
    pub beta_g1: E::G1Affine,
    pub beta_g2: E::G2Affine,

    // gamma in g2 for verifying. Never the point at infinity.
    pub gamma_g2: E::G2Affine,

    // delta in g1/g2 for verifying and proving, essentially the magic
    // trapdoor that forces the prover to evaluate the C element of the
    // proof with only components from the CRS. Never the point at
    // infinity.
    pub delta_g1: E::G1Affine,
    pub delta_g2: E::G2Affine,

    // Elements of the form (beta * u_i(tau) + alpha v_i(tau) + w_i(tau)) / gamma
    // for all public inputs. Because all public inputs have a dummy constraint,
    // this is the same size as the number of inputs, and never contains points
    // at infinity.
    pub ic: Vec<E::G1Affine>
}

impl<E: Engine> PartialEq for VerifyingKey<E> {
    fn eq(&self, other: &Self) -> bool {
        self.alpha_g1 == other.alpha_g1 &&
        self.beta_g1 == other.beta_g1 &&
        self.beta_g2 == other.beta_g2 &&
        self.gamma_g2 == other.gamma_g2 &&
        self.delta_g1 == other.delta_g1 &&
        self.delta_g2 == other.delta_g2 &&
        self.ic == other.ic
    }
}

impl<E: Engine> VerifyingKey<E> {
    pub fn write<W: Write>(
        &self,
        mut writer: W
    ) -> io::Result<()>
    {
        writer.write_all(self.alpha_g1.into_uncompressed().as_ref())?;
        writer.write_all(self.beta_g1.into_uncompressed().as_ref())?;
        writer.write_all(self.beta_g2.into_uncompressed().as_ref())?;
        writer.write_all(self.gamma_g2.into_uncompressed().as_ref())?;
        writer.write_all(self.delta_g1.into_uncompressed().as_ref())?;
        writer.write_all(self.delta_g2.into_uncompressed().as_ref())?;
        writer.write_u32::<BigEndian>(self.ic.len() as u32)?;
        for ic in &self.ic {
            writer.write_all(ic.into_uncompressed().as_ref())?;
        }

        Ok(())
    }

    pub fn read<R: Read>(
        mut reader: R
    ) -> io::Result<Self>
    {
        let mut g1_repr = <E::G1Affine as CurveAffine>::Uncompressed::empty();
        let mut g2_repr = <E::G2Affine as CurveAffine>::Uncompressed::empty();

        reader.read_exact(g1_repr.as_mut())?;
        let alpha_g1 = g1_repr.into_affine().map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))?;

        reader.read_exact(g1_repr.as_mut())?;
        let beta_g1 = g1_repr.into_affine().map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))?;

        reader.read_exact(g2_repr.as_mut())?;
        let beta_g2 = g2_repr.into_affine().map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))?;

        reader.read_exact(g2_repr.as_mut())?;
        let gamma_g2 = g2_repr.into_affine().map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))?;

        reader.read_exact(g1_repr.as_mut())?;
        let delta_g1 = g1_repr.into_affine().map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))?;

        reader.read_exact(g2_repr.as_mut())?;
        let delta_g2 = g2_repr.into_affine().map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))?;

        let ic_len = reader.read_u32::<BigEndian>()? as usize;

        let mut ic = vec![];

        for _ in 0..ic_len {
            reader.read_exact(g1_repr.as_mut())?;
            let g1 = g1_repr
                     .into_affine()
                     .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
                     .and_then(|e| if e.is_zero() {
                         Err(io::Error::new(io::ErrorKind::InvalidData, "point at infinity"))
                     } else {
                         Ok(e)
                     })?;

            ic.push(g1);
        }

        Ok(VerifyingKey {
            alpha_g1: alpha_g1,
            beta_g1: beta_g1,
            beta_g2: beta_g2,
            gamma_g2: gamma_g2,
            delta_g1: delta_g1,
            delta_g2: delta_g2,
            ic: ic
        })
    }
}

#[derive(Clone)]
pub struct Parameters<E: Engine> {
    pub vk: VerifyingKey<E>,

    // Elements of the form ((tau^i * t(tau)) / delta) for i between 0 and 
    // m-2 inclusive. Never contains points at infinity.
    pub h: Arc<Vec<E::G1Affine>>,

    // Elements of the form (beta * u_i(tau) + alpha v_i(tau) + w_i(tau)) / delta
    // for all auxiliary inputs. Variables can never be unconstrained, so this
    // never contains points at infinity.
    pub l: Arc<Vec<E::G1Affine>>,

    // QAP "A" polynomials evaluated at tau in the Lagrange basis. Never contains
    // points at infinity: polynomials that evaluate to zero are omitted from
    // the CRS and the prover can deterministically skip their evaluation.
    pub a: Arc<Vec<E::G1Affine>>,

    // QAP "B" polynomials evaluated at tau in the Lagrange basis. Needed in
    // G1 and G2 for C/B queries, respectively. Never contains points at
    // infinity for the same reason as the "A" polynomials.
    pub b_g1: Arc<Vec<E::G1Affine>>,
    pub b_g2: Arc<Vec<E::G2Affine>>
}

impl<E: Engine> PartialEq for Parameters<E> {
    fn eq(&self, other: &Self) -> bool {
        self.vk == other.vk &&
        self.h == other.h &&
        self.l == other.l &&
        self.a == other.a &&
        self.b_g1 == other.b_g1 &&
        self.b_g2 == other.b_g2
    }
}

impl<E: Engine> Parameters<E> {
    pub fn write<W: Write>(
        &self,
        mut writer: W
    ) -> io::Result<()>
    {
        self.vk.write(&mut writer)?;

        writer.write_u32::<BigEndian>(self.h.len() as u32)?;
        for g in &self.h[..] {
            writer.write_all(g.into_uncompressed().as_ref())?;
        }

        writer.write_u32::<BigEndian>(self.l.len() as u32)?;
        for g in &self.l[..] {
            writer.write_all(g.into_uncompressed().as_ref())?;
        }

        writer.write_u32::<BigEndian>(self.a.len() as u32)?;
        for g in &self.a[..] {
            writer.write_all(g.into_uncompressed().as_ref())?;
        }

        writer.write_u32::<BigEndian>(self.b_g1.len() as u32)?;
        for g in &self.b_g1[..] {
            writer.write_all(g.into_uncompressed().as_ref())?;
        }

        writer.write_u32::<BigEndian>(self.b_g2.len() as u32)?;
        for g in &self.b_g2[..] {
            writer.write_all(g.into_uncompressed().as_ref())?;
        }

        Ok(())
    }

    pub fn read<R: Read>(
        mut reader: R,
        checked: bool
    ) -> io::Result<Self>
    {
        let read_g1 = |reader: &mut R| -> io::Result<E::G1Affine> {
            let mut repr = <E::G1Affine as CurveAffine>::Uncompressed::empty();
            reader.read_exact(repr.as_mut())?;

            if checked {
                repr
                .into_affine()
            } else {
                repr
                .into_affine_unchecked()
            }
            .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
            .and_then(|e| if e.is_zero() {
                Err(io::Error::new(io::ErrorKind::InvalidData, "point at infinity"))
            } else {
                Ok(e)
            })
        };

        let read_g2 = |reader: &mut R| -> io::Result<E::G2Affine> {
            let mut repr = <E::G2Affine as CurveAffine>::Uncompressed::empty();
            reader.read_exact(repr.as_mut())?;

            if checked {
                repr
                .into_affine()
            } else {
                repr
                .into_affine_unchecked()
            }
            .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
            .and_then(|e| if e.is_zero() {
                Err(io::Error::new(io::ErrorKind::InvalidData, "point at infinity"))
            } else {
                Ok(e)
            })
        };

        let vk = VerifyingKey::<E>::read(&mut reader)?;

        let mut h = vec![];
        let mut l = vec![];
        let mut a = vec![];
        let mut b_g1 = vec![];
        let mut b_g2 = vec![];

        {
            let len = reader.read_u32::<BigEndian>()? as usize;
            for _ in 0..len {
                h.push(read_g1(&mut reader)?);
            }
        }

        {
            let len = reader.read_u32::<BigEndian>()? as usize;
            for _ in 0..len {
                l.push(read_g1(&mut reader)?);
            }
        }

        {
            let len = reader.read_u32::<BigEndian>()? as usize;
            for _ in 0..len {
                a.push(read_g1(&mut reader)?);
            }
        }

        {
            let len = reader.read_u32::<BigEndian>()? as usize;
            for _ in 0..len {
                b_g1.push(read_g1(&mut reader)?);
            }
        }

        {
            let len = reader.read_u32::<BigEndian>()? as usize;
            for _ in 0..len {
                b_g2.push(read_g2(&mut reader)?);
            }
        }

        Ok(Parameters {
            vk: vk,
            h: Arc::new(h),
            l: Arc::new(l),
            a: Arc::new(a),
            b_g1: Arc::new(b_g1),
            b_g2: Arc::new(b_g2)
        })
    }
}

pub struct PreparedVerifyingKey<E: Engine> {
    /// Pairing result of alpha*beta
    alpha_g1_beta_g2: E::Fqk,
    /// -gamma in G2
    neg_gamma_g2: <E::G2Affine as PairingCurveAffine>::Prepared,
    /// -delta in G2
    neg_delta_g2: <E::G2Affine as PairingCurveAffine>::Prepared,
    /// Copy of IC from `VerifiyingKey`.
    ic: Vec<E::G1Affine>
}

pub trait ParameterSource<E: Engine> {
    type G1Builder: SourceBuilder<E::G1Affine>;
    type G2Builder: SourceBuilder<E::G2Affine>;

    fn get_vk(
        &mut self,
        num_ic: usize
    ) -> Result<VerifyingKey<E>, SynthesisError>;
    fn get_h(
        &mut self,
        num_h: usize
    ) -> Result<Self::G1Builder, SynthesisError>;
    fn get_l(
        &mut self,
        num_l: usize
    ) -> Result<Self::G1Builder, SynthesisError>;
    fn get_a(
        &mut self,
        num_inputs: usize,
        num_aux: usize
    ) -> Result<(Self::G1Builder, Self::G1Builder), SynthesisError>;
    fn get_b_g1(
        &mut self,
        num_inputs: usize,
        num_aux: usize
    ) -> Result<(Self::G1Builder, Self::G1Builder), SynthesisError>;
    fn get_b_g2(
        &mut self,
        num_inputs: usize,
        num_aux: usize
    ) -> Result<(Self::G2Builder, Self::G2Builder), SynthesisError>;
}

impl<'a, E: Engine> ParameterSource<E> for &'a Parameters<E> {
    type G1Builder = (Arc<Vec<E::G1Affine>>, usize);
    type G2Builder = (Arc<Vec<E::G2Affine>>, usize);

    fn get_vk(
        &mut self,
        _: usize
    ) -> Result<VerifyingKey<E>, SynthesisError>
    {
        Ok(self.vk.clone())
    }

    fn get_h(
        &mut self,
        _: usize
    ) -> Result<Self::G1Builder, SynthesisError>
    {
        Ok((self.h.clone(), 0))
    }

    fn get_l(
        &mut self,
        _: usize
    ) -> Result<Self::G1Builder, SynthesisError>
    {
        Ok((self.l.clone(), 0))
    }

    fn get_a(
        &mut self,
        num_inputs: usize,
        _: usize
    ) -> Result<(Self::G1Builder, Self::G1Builder), SynthesisError>
    {
        Ok(((self.a.clone(), 0), (self.a.clone(), num_inputs)))
    }

    fn get_b_g1(
        &mut self,
        num_inputs: usize,
        _: usize
    ) -> Result<(Self::G1Builder, Self::G1Builder), SynthesisError>
    {
        Ok(((self.b_g1.clone(), 0), (self.b_g1.clone(), num_inputs)))
    }

    fn get_b_g2(
        &mut self,
        num_inputs: usize,
        _: usize
    ) -> Result<(Self::G2Builder, Self::G2Builder), SynthesisError>
    {
        Ok(((self.b_g2.clone(), 0), (self.b_g2.clone(), num_inputs)))
    }
}

#[cfg(test)]
mod test_with_bls12_381 {
    use super::*;
    use {Circuit, SynthesisError, ConstraintSystem};

    use ff::Field;
    use rand::{Rand, thread_rng};
    use pairing::bls12_381::{Bls12, Fr};

    #[test]
    fn serialization() {
        struct MySillyCircuit<E: Engine> {
            a: Option<E::Fr>,
            b: Option<E::Fr>
        }

        impl<E: Engine> Circuit<E> for MySillyCircuit<E> {
            fn synthesize<CS: ConstraintSystem<E>>(
                self,
                cs: &mut CS
            ) -> Result<(), SynthesisError>
            {
                let a = cs.alloc(|| "a", || self.a.ok_or(SynthesisError::AssignmentMissing))?;
                let b = cs.alloc(|| "b", || self.b.ok_or(SynthesisError::AssignmentMissing))?;
                let c = cs.alloc_input(|| "c", || {
                    let mut a = self.a.ok_or(SynthesisError::AssignmentMissing)?;
                    let b = self.b.ok_or(SynthesisError::AssignmentMissing)?;

                    a.mul_assign(&b);
                    Ok(a)
                })?;

                cs.enforce(
                    || "a*b=c",
                    |lc| lc + a,
                    |lc| lc + b,
                    |lc| lc + c
                );

                Ok(())
            }
        }

        let rng = &mut thread_rng();

        let params = generate_random_parameters::<Bls12, _, _>(
            MySillyCircuit { a: None, b: None },
            rng
        ).unwrap();

        {
            let mut v = vec![];

            params.write(&mut v).unwrap();
            assert_eq!(v.len(), 2136);

            let de_params = Parameters::read(&v[..], true).unwrap();
            assert!(params == de_params);

            let de_params = Parameters::read(&v[..], false).unwrap();
            assert!(params == de_params);
        }

        let pvk = prepare_verifying_key::<Bls12>(&params.vk);

        for _ in 0..100 {
            let a = Fr::rand(rng);
            let b = Fr::rand(rng);
            let mut c = a;
            c.mul_assign(&b);

            let proof = create_random_proof(
                MySillyCircuit {
                    a: Some(a),
                    b: Some(b)
                },
                &params,
                rng
            ).unwrap();

            let mut v = vec![];
            proof.write(&mut v).unwrap();

            assert_eq!(v.len(), 192);

            let de_proof = Proof::read(&v[..]).unwrap();
            assert!(proof == de_proof);

            assert!(verify_proof(&pvk, &proof, &[c]).unwrap());
            assert!(!verify_proof(&pvk, &proof, &[a]).unwrap());
        }
    }
}