use crate::traits::{
algorithms::snark::SNARKVerifierGadget,
curves::{GroupGadget, PairingGadget},
utilities::{
alloc::{AllocBytesGadget, AllocGadget},
eq::EqGadget,
uint::UInt8,
ToBitsBEGadget,
ToBytesGadget,
},
};
use snarkvm_algorithms::snark::groth16::{Groth16, Proof, VerifyingKey};
use snarkvm_curves::traits::{AffineCurve, PairingEngine};
use snarkvm_fields::{Field, ToConstraintField};
use snarkvm_r1cs::{errors::SynthesisError, ConstraintSynthesizer, ConstraintSystem};
use snarkvm_utilities::bytes::FromBytes;
use std::{borrow::Borrow, marker::PhantomData};
#[derive(Derivative)]
#[derivative(Clone(bound = "P::G1Gadget: Clone, P::G2Gadget: Clone"))]
pub struct ProofGadget<PairingE: PairingEngine, ConstraintF: Field, P: PairingGadget<PairingE, ConstraintF>> {
pub a: P::G1Gadget,
pub b: P::G2Gadget,
pub c: P::G1Gadget,
}
#[derive(Derivative)]
#[derivative(Clone(bound = "P::G1Gadget: Clone, P::GTGadget: Clone, P::G1PreparedGadget: Clone, \
P::G2PreparedGadget: Clone, "))]
pub struct VerifyingKeyGadget<PairingE: PairingEngine, ConstraintF: Field, P: PairingGadget<PairingE, ConstraintF>> {
pub alpha_g1: P::G1Gadget,
pub beta_g2: P::G2Gadget,
pub gamma_g2: P::G2Gadget,
pub delta_g2: P::G2Gadget,
pub gamma_abc_g1: Vec<P::G1Gadget>,
}
impl<PairingE: PairingEngine, ConstraintF: Field, P: PairingGadget<PairingE, ConstraintF>>
VerifyingKeyGadget<PairingE, ConstraintF, P>
{
pub fn prepare<CS: ConstraintSystem<ConstraintF>>(
&self,
mut cs: CS,
) -> Result<PreparedVerifyingKeyGadget<PairingE, ConstraintF, P>, SynthesisError> {
let mut cs = cs.ns(|| "Preparing verifying key");
let alpha_g1_pc = P::prepare_g1(&mut cs.ns(|| "Prepare alpha_g1"), self.alpha_g1.clone())?;
let beta_g2_pc = P::prepare_g2(&mut cs.ns(|| "Prepare beta_g2"), self.beta_g2.clone())?;
let alpha_g1_beta_g2 = P::pairing(
&mut cs.ns(|| "Precompute e(alpha_g1, beta_g2)"),
alpha_g1_pc,
beta_g2_pc,
)?;
let gamma_g2_neg = self.gamma_g2.negate(&mut cs.ns(|| "Negate gamma_g2"))?;
let gamma_g2_neg_pc = P::prepare_g2(&mut cs.ns(|| "Prepare gamma_g2_neg"), gamma_g2_neg)?;
let delta_g2_neg = self.delta_g2.negate(&mut cs.ns(|| "Negate delta_g2"))?;
let delta_g2_neg_pc = P::prepare_g2(&mut cs.ns(|| "Prepare delta_g2_neg"), delta_g2_neg)?;
Ok(PreparedVerifyingKeyGadget {
alpha_g1_beta_g2,
gamma_g2_neg_pc,
delta_g2_neg_pc,
gamma_abc_g1: self.gamma_abc_g1.clone(),
})
}
}
#[derive(Derivative)]
#[derivative(Clone(
bound = "P::G1Gadget: Clone, P::GTGadget: Clone, P::G1PreparedGadget: Clone, P::G2PreparedGadget: Clone"
))]
pub struct PreparedVerifyingKeyGadget<
PairingE: PairingEngine,
ConstraintF: Field,
P: PairingGadget<PairingE, ConstraintF>,
> {
pub alpha_g1_beta_g2: P::GTGadget,
pub gamma_g2_neg_pc: P::G2PreparedGadget,
pub delta_g2_neg_pc: P::G2PreparedGadget,
pub gamma_abc_g1: Vec<P::G1Gadget>,
}
pub struct Groth16VerifierGadget<PairingE, ConstraintF, P>
where
PairingE: PairingEngine,
ConstraintF: Field,
P: PairingGadget<PairingE, ConstraintF>,
{
_pairing_engine: PhantomData<PairingE>,
_engine: PhantomData<ConstraintF>,
_pairing_gadget: PhantomData<P>,
}
impl<PairingE, ConstraintF, P, C, V> SNARKVerifierGadget<Groth16<PairingE, C, V>, ConstraintF>
for Groth16VerifierGadget<PairingE, ConstraintF, P>
where
PairingE: PairingEngine,
ConstraintF: Field,
C: ConstraintSynthesizer<PairingE::Fr>,
V: ToConstraintField<PairingE::Fr>,
P: PairingGadget<PairingE, ConstraintF>,
{
type ProofGadget = ProofGadget<PairingE, ConstraintF, P>;
type VerificationKeyGadget = VerifyingKeyGadget<PairingE, ConstraintF, P>;
fn check_verify<'a, CS, I, T>(
mut cs: CS,
vk: &Self::VerificationKeyGadget,
mut public_inputs: I,
proof: &Self::ProofGadget,
) -> Result<(), SynthesisError>
where
CS: ConstraintSystem<ConstraintF>,
I: Iterator<Item = &'a T>,
T: 'a + ToBitsBEGadget<ConstraintF> + ?Sized,
{
let pvk = vk.prepare(&mut cs.ns(|| "Prepare vk"))?;
let PreparedVerifyingKeyGadget {
alpha_g1_beta_g2,
gamma_g2_neg_pc,
delta_g2_neg_pc,
mut gamma_abc_g1,
} = pvk;
let mut gamma_abc_g1_iter = gamma_abc_g1.iter_mut();
let g_ic = {
let mut cs = cs.ns(|| "Process input");
let mut g_ic = gamma_abc_g1_iter.next().cloned().unwrap();
let mut input_len = 1;
for (i, (input, b)) in public_inputs.by_ref().zip(gamma_abc_g1_iter).enumerate() {
let input_bits = input.to_bits_be(cs.ns(|| format!("Input {}", i)))?;
g_ic = b.mul_bits(cs.ns(|| format!("Mul {}", i)), &g_ic, input_bits.into_iter())?;
input_len += 1;
}
assert!(input_len == gamma_abc_g1.len() && public_inputs.next().is_none());
g_ic
};
let test_exp = {
let proof_a_prep = P::prepare_g1(cs.ns(|| "Prepare proof a"), proof.a.clone())?;
let proof_b_prep = P::prepare_g2(cs.ns(|| "Prepare proof b"), proof.b.clone())?;
let proof_c_prep = P::prepare_g1(cs.ns(|| "Prepare proof c"), proof.c.clone())?;
let g_ic_prep = P::prepare_g1(cs.ns(|| "Prepare g_ic"), g_ic)?;
P::miller_loop(cs.ns(|| "Miller loop 1"), &[proof_a_prep, g_ic_prep, proof_c_prep], &[
proof_b_prep,
gamma_g2_neg_pc,
delta_g2_neg_pc,
])?
};
let test = P::final_exponentiation(cs.ns(|| "Final Exp"), &test_exp).unwrap();
test.enforce_equal(cs.ns(|| "Test 1"), &alpha_g1_beta_g2)?;
Ok(())
}
}
impl<PairingE, ConstraintF, P> AllocGadget<VerifyingKey<PairingE>, ConstraintF>
for VerifyingKeyGadget<PairingE, ConstraintF, P>
where
PairingE: PairingEngine,
ConstraintF: Field,
P: PairingGadget<PairingE, ConstraintF>,
{
#[inline]
fn alloc<FN, T, CS: ConstraintSystem<ConstraintF>>(mut cs: CS, value_gen: FN) -> Result<Self, SynthesisError>
where
FN: FnOnce() -> Result<T, SynthesisError>,
T: Borrow<VerifyingKey<PairingE>>,
{
value_gen().and_then(|vk| {
let VerifyingKey {
alpha_g1,
beta_g2,
gamma_g2,
delta_g2,
gamma_abc_g1,
} = vk.borrow();
let alpha_g1 = P::G1Gadget::alloc(cs.ns(|| "alpha_g1"), || Ok(alpha_g1.into_projective()))?;
let beta_g2 = P::G2Gadget::alloc(cs.ns(|| "beta_g2"), || Ok(beta_g2.into_projective()))?;
let gamma_g2 = P::G2Gadget::alloc(cs.ns(|| "gamma_g2"), || Ok(gamma_g2.into_projective()))?;
let delta_g2 = P::G2Gadget::alloc(cs.ns(|| "delta_g2"), || Ok(delta_g2.into_projective()))?;
let gamma_abc_g1 = gamma_abc_g1
.iter()
.enumerate()
.map(|(i, gamma_abc_i)| {
P::G1Gadget::alloc(cs.ns(|| format!("gamma_abc_{}", i)), || {
Ok(gamma_abc_i.into_projective())
})
})
.collect::<Result<Vec<_>, _>>()?;
Ok(Self {
alpha_g1,
beta_g2,
gamma_g2,
delta_g2,
gamma_abc_g1,
})
})
}
#[inline]
fn alloc_input<FN, T, CS: ConstraintSystem<ConstraintF>>(mut cs: CS, value_gen: FN) -> Result<Self, SynthesisError>
where
FN: FnOnce() -> Result<T, SynthesisError>,
T: Borrow<VerifyingKey<PairingE>>,
{
value_gen().and_then(|vk| {
let VerifyingKey {
alpha_g1,
beta_g2,
gamma_g2,
delta_g2,
gamma_abc_g1,
} = vk.borrow();
let alpha_g1 = P::G1Gadget::alloc_input(cs.ns(|| "alpha_g1"), || Ok(alpha_g1.into_projective()))?;
let beta_g2 = P::G2Gadget::alloc_input(cs.ns(|| "beta_g2"), || Ok(beta_g2.into_projective()))?;
let gamma_g2 = P::G2Gadget::alloc_input(cs.ns(|| "gamma_g2"), || Ok(gamma_g2.into_projective()))?;
let delta_g2 = P::G2Gadget::alloc_input(cs.ns(|| "delta_g2"), || Ok(delta_g2.into_projective()))?;
let gamma_abc_g1 = gamma_abc_g1
.iter()
.enumerate()
.map(|(i, gamma_abc_i)| {
P::G1Gadget::alloc_input(cs.ns(|| format!("gamma_abc_{}", i)), || {
Ok(gamma_abc_i.into_projective())
})
})
.collect::<Result<Vec<_>, _>>()?;
Ok(Self {
alpha_g1,
beta_g2,
gamma_g2,
delta_g2,
gamma_abc_g1,
})
})
}
}
impl<PairingE, ConstraintF, P> AllocBytesGadget<Vec<u8>, ConstraintF> for VerifyingKeyGadget<PairingE, ConstraintF, P>
where
PairingE: PairingEngine,
ConstraintF: Field,
P: PairingGadget<PairingE, ConstraintF>,
{
#[inline]
fn alloc_bytes<FN, T, CS: ConstraintSystem<ConstraintF>>(mut cs: CS, value_gen: FN) -> Result<Self, SynthesisError>
where
FN: FnOnce() -> Result<T, SynthesisError>,
T: Borrow<Vec<u8>>,
{
value_gen().and_then(|vk_bytes| {
let vk: VerifyingKey<PairingE> = FromBytes::read(&vk_bytes.borrow()[..])?;
Self::alloc(cs.ns(|| "alloc_bytes"), || Ok(vk))
})
}
#[inline]
fn alloc_input_bytes<FN, T, CS: ConstraintSystem<ConstraintF>>(
mut cs: CS,
value_gen: FN,
) -> Result<Self, SynthesisError>
where
FN: FnOnce() -> Result<T, SynthesisError>,
T: Borrow<Vec<u8>>,
{
value_gen().and_then(|vk_bytes| {
let vk: VerifyingKey<PairingE> = FromBytes::read(&vk_bytes.borrow()[..])?;
Self::alloc_input(cs.ns(|| "alloc_input_bytes"), || Ok(vk))
})
}
}
impl<PairingE, ConstraintF, P> AllocGadget<Proof<PairingE>, ConstraintF> for ProofGadget<PairingE, ConstraintF, P>
where
PairingE: PairingEngine,
ConstraintF: Field,
P: PairingGadget<PairingE, ConstraintF>,
{
#[inline]
fn alloc<FN, T, CS: ConstraintSystem<ConstraintF>>(mut cs: CS, value_gen: FN) -> Result<Self, SynthesisError>
where
FN: FnOnce() -> Result<T, SynthesisError>,
T: Borrow<Proof<PairingE>>,
{
value_gen().and_then(|proof| {
let Proof { a, b, c, .. } = proof.borrow();
let a = P::G1Gadget::alloc_checked(cs.ns(|| "a"), || Ok(a.into_projective()))?;
let b = P::G2Gadget::alloc_checked(cs.ns(|| "b"), || Ok(b.into_projective()))?;
let c = P::G1Gadget::alloc_checked(cs.ns(|| "c"), || Ok(c.into_projective()))?;
Ok(Self { a, b, c })
})
}
#[inline]
fn alloc_input<FN, T, CS: ConstraintSystem<ConstraintF>>(mut cs: CS, value_gen: FN) -> Result<Self, SynthesisError>
where
FN: FnOnce() -> Result<T, SynthesisError>,
T: Borrow<Proof<PairingE>>,
{
value_gen().and_then(|proof| {
let Proof { a, b, c, .. } = proof.borrow();
let a = P::G1Gadget::alloc_input(cs.ns(|| "a"), || Ok(a.into_projective()))?;
let b = P::G2Gadget::alloc_input(cs.ns(|| "b"), || Ok(b.into_projective()))?;
let c = P::G1Gadget::alloc_input(cs.ns(|| "c"), || Ok(c.into_projective()))?;
Ok(Self { a, b, c })
})
}
}
impl<PairingE, ConstraintF, P> AllocBytesGadget<Vec<u8>, ConstraintF> for ProofGadget<PairingE, ConstraintF, P>
where
PairingE: PairingEngine,
ConstraintF: Field,
P: PairingGadget<PairingE, ConstraintF>,
{
#[inline]
fn alloc_bytes<FN, T, CS: ConstraintSystem<ConstraintF>>(mut cs: CS, value_gen: FN) -> Result<Self, SynthesisError>
where
FN: FnOnce() -> Result<T, SynthesisError>,
T: Borrow<Vec<u8>>,
{
value_gen().and_then(|proof_bytes| {
let proof: Proof<PairingE> = FromBytes::read(&proof_bytes.borrow()[..])?;
Self::alloc(cs.ns(|| "alloc_bytes"), || Ok(proof))
})
}
#[inline]
fn alloc_input_bytes<FN, T, CS: ConstraintSystem<ConstraintF>>(
mut cs: CS,
value_gen: FN,
) -> Result<Self, SynthesisError>
where
FN: FnOnce() -> Result<T, SynthesisError>,
T: Borrow<Vec<u8>>,
{
value_gen().and_then(|proof_bytes| {
let proof: Proof<PairingE> = FromBytes::read(&proof_bytes.borrow()[..])?;
Self::alloc_input(cs.ns(|| "alloc_input_bytes"), || Ok(proof))
})
}
}
impl<PairingE, ConstraintF, P> ToBytesGadget<ConstraintF> for VerifyingKeyGadget<PairingE, ConstraintF, P>
where
PairingE: PairingEngine,
ConstraintF: Field,
P: PairingGadget<PairingE, ConstraintF>,
{
#[inline]
fn to_bytes<CS: ConstraintSystem<ConstraintF>>(&self, mut cs: CS) -> Result<Vec<UInt8>, SynthesisError> {
let mut bytes = Vec::new();
bytes.extend_from_slice(&self.alpha_g1.to_bytes(&mut cs.ns(|| "alpha_g1 to bytes"))?);
bytes.extend_from_slice(&self.beta_g2.to_bytes(&mut cs.ns(|| "beta_g2 to bytes"))?);
bytes.extend_from_slice(&self.gamma_g2.to_bytes(&mut cs.ns(|| "gamma_g2 to bytes"))?);
bytes.extend_from_slice(&self.delta_g2.to_bytes(&mut cs.ns(|| "delta_g2 to bytes"))?);
bytes.extend_from_slice(&UInt8::alloc_vec(
&mut cs.ns(|| "gamma_abc_g1_length"),
&(self.gamma_abc_g1.len() as u32).to_le_bytes()[..],
)?);
for (i, g) in self.gamma_abc_g1.iter().enumerate() {
let mut cs = cs.ns(|| format!("Iteration {}", i));
bytes.extend_from_slice(&g.to_bytes(&mut cs.ns(|| "g"))?);
}
Ok(bytes)
}
#[inline]
fn to_bytes_strict<CS: ConstraintSystem<ConstraintF>>(&self, mut cs: CS) -> Result<Vec<UInt8>, SynthesisError> {
let mut bytes = Vec::new();
bytes.extend_from_slice(&self.alpha_g1.to_bytes_strict(&mut cs.ns(|| "alpha_g1 to bytes"))?);
bytes.extend_from_slice(&self.beta_g2.to_bytes_strict(&mut cs.ns(|| "beta_g2 to bytes"))?);
bytes.extend_from_slice(&self.gamma_g2.to_bytes_strict(&mut cs.ns(|| "gamma_g2 to bytes"))?);
bytes.extend_from_slice(&self.delta_g2.to_bytes_strict(&mut cs.ns(|| "delta_g2 to bytes"))?);
bytes.extend_from_slice(&UInt8::alloc_vec(
&mut cs.ns(|| "gamma_abc_g1_length"),
&(self.gamma_abc_g1.len() as u32).to_le_bytes()[..],
)?);
for (i, g) in self.gamma_abc_g1.iter().enumerate() {
let mut cs = cs.ns(|| format!("Iteration {}", i));
bytes.extend_from_slice(&g.to_bytes_strict(&mut cs.ns(|| "g"))?);
}
Ok(bytes)
}
}
#[cfg(test)]
mod test {
use super::*;
use crate::{curves::bls12_377::PairingGadget as Bls12_377PairingGadget, traits::utilities::boolean::Boolean};
use snarkvm_algorithms::snark::groth16::*;
use snarkvm_curves::bls12_377::{Bls12_377, Fq, Fr};
use snarkvm_fields::PrimeField;
use snarkvm_r1cs::{ConstraintSynthesizer, ConstraintSystem, TestConstraintSystem};
use snarkvm_utilities::{test_rng, to_bytes, BitIteratorBE, ToBytes};
use rand::Rng;
type TestProofSystem = Groth16<Bls12_377, Bench<Fr>, Fr>;
type TestVerifierGadget = Groth16VerifierGadget<Bls12_377, Fq, Bls12_377PairingGadget>;
type TestProofGadget = ProofGadget<Bls12_377, Fq, Bls12_377PairingGadget>;
type TestVkGadget = VerifyingKeyGadget<Bls12_377, Fq, Bls12_377PairingGadget>;
struct Bench<F: Field> {
inputs: Vec<Option<F>>,
num_constraints: usize,
}
impl<F: Field> ConstraintSynthesizer<F> for Bench<F> {
fn generate_constraints<CS: ConstraintSystem<F>>(&self, cs: &mut CS) -> Result<(), SynthesisError> {
assert!(self.inputs.len() >= 2);
assert!(self.num_constraints >= self.inputs.len());
let mut variables: Vec<_> = Vec::with_capacity(self.inputs.len());
for (i, input) in self.inputs.iter().cloned().enumerate() {
let input_var = cs.alloc_input(
|| format!("Input {}", i),
|| input.ok_or(SynthesisError::AssignmentMissing),
)?;
variables.push((input, input_var));
}
for i in 0..self.num_constraints {
let new_entry = {
let (input_1_val, input_1_var) = variables[i];
let (input_2_val, input_2_var) = variables[i + 1];
let result_val = input_1_val.and_then(|input_1| input_2_val.map(|input_2| input_1 * &input_2));
let result_var = cs.alloc(
|| format!("Result {}", i),
|| result_val.ok_or(SynthesisError::AssignmentMissing),
)?;
cs.enforce(
|| format!("Enforce constraint {}", i),
|lc| lc + input_1_var,
|lc| lc + input_2_var,
|lc| lc + result_var,
);
(result_val, result_var)
};
variables.push(new_entry);
}
Ok(())
}
}
#[test]
fn groth16_verifier_test() {
let num_inputs = 100;
let num_constraints = num_inputs;
let rng = &mut test_rng();
let mut inputs: Vec<Option<Fr>> = Vec::with_capacity(num_inputs);
for _ in 0..num_inputs {
inputs.push(Some(rng.gen()));
}
let params = {
let c = Bench::<Fr> {
inputs: vec![None; num_inputs],
num_constraints,
};
generate_random_parameters(&c, rng).unwrap()
};
{
let proof = {
let c = Bench {
inputs: inputs.clone(),
num_constraints,
};
create_random_proof(&c, ¶ms, rng).unwrap()
};
let mut cs = TestConstraintSystem::<Fq>::new();
let inputs = inputs.into_iter().map(|input| input.unwrap());
let mut input_gadgets = Vec::new();
{
let mut cs = cs.ns(|| "Allocate Input");
for (i, input) in inputs.enumerate() {
let mut input_bits = BitIteratorBE::new(input.into_repr()).collect::<Vec<_>>();
input_bits.reverse();
let input_bits =
Vec::<Boolean>::alloc_input(cs.ns(|| format!("Input {}", i)), || Ok(input_bits)).unwrap();
input_gadgets.push(input_bits);
}
}
let vk_gadget = TestVkGadget::alloc_input(cs.ns(|| "Vk"), || Ok(¶ms.vk)).unwrap();
let proof_gadget = TestProofGadget::alloc(cs.ns(|| "Proof"), || Ok(proof.clone())).unwrap();
println!("Time to verify!\n\n\n\n");
<TestVerifierGadget as SNARKVerifierGadget<TestProofSystem, Fq>>::check_verify(
cs.ns(|| "Verify"),
&vk_gadget,
input_gadgets.iter(),
&proof_gadget,
)
.unwrap();
if !cs.is_satisfied() {
println!("=========================================================");
println!("Unsatisfied constraints:");
println!("{:?}", cs.which_is_unsatisfied().unwrap());
println!("=========================================================");
}
assert!(cs.is_satisfied());
}
}
#[test]
fn groth16_verifier_bytes_test() {
let num_inputs = 100;
let num_constraints = num_inputs;
let rng = &mut test_rng();
let mut inputs: Vec<Option<Fr>> = Vec::with_capacity(num_inputs);
for _ in 0..num_inputs {
inputs.push(Some(rng.gen()));
}
let params = {
let c = Bench::<Fr> {
inputs: vec![None; num_inputs],
num_constraints,
};
generate_random_parameters::<Bls12_377, _, _>(&c, rng).unwrap()
};
{
let proof = {
let c = Bench {
inputs: inputs.clone(),
num_constraints,
};
create_random_proof(&c, ¶ms, rng).unwrap()
};
let mut cs = TestConstraintSystem::<Fq>::new();
let inputs: Vec<_> = inputs.into_iter().map(|input| input.unwrap()).collect();
let mut input_gadgets = Vec::new();
{
let mut cs = cs.ns(|| "Allocate Input");
for (i, input) in inputs.into_iter().enumerate() {
let mut input_bits = BitIteratorBE::new(input.into_repr()).collect::<Vec<_>>();
input_bits.reverse();
let input_bits =
Vec::<Boolean>::alloc_input(cs.ns(|| format!("Input {}", i)), || Ok(input_bits)).unwrap();
input_gadgets.push(input_bits);
}
}
let vk_bytes = to_bytes![params.vk].unwrap();
let proof_bytes = to_bytes![proof].unwrap();
let vk_gadget = TestVkGadget::alloc_input_bytes(cs.ns(|| "Vk"), || Ok(vk_bytes)).unwrap();
let proof_gadget = TestProofGadget::alloc_bytes(cs.ns(|| "Proof"), || Ok(proof_bytes)).unwrap();
println!("Time to verify!\n\n\n\n");
<TestVerifierGadget as SNARKVerifierGadget<TestProofSystem, Fq>>::check_verify(
cs.ns(|| "Verify"),
&vk_gadget,
input_gadgets.iter(),
&proof_gadget,
)
.unwrap();
if !cs.is_satisfied() {
println!("=========================================================");
println!("Unsatisfied constraints:");
println!("{:?}", cs.which_is_unsatisfied().unwrap());
println!("=========================================================");
}
assert!(cs.is_satisfied());
}
}
}