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//! This module implements various gadgets necessary for folding R1CS types.
use crate::{
gadgets::{
ecc::AllocatedPoint,
utils::{
alloc_bignat_constant, alloc_scalar_as_base, conditionally_select,
conditionally_select_bignat, le_bits_to_num,
},
},
poseidon::{NovaPoseidonConstants, PoseidonROGadget},
r1cs::{R1CSInstance, RelaxedR1CSInstance},
traits::Group,
};
use bellperson::{
gadgets::{boolean::Boolean, num::AllocatedNum, Assignment},
ConstraintSystem, SynthesisError,
};
use bellperson_nonnative::{
mp::bignat::BigNat,
util::{convert::f_to_nat, num::Num},
};
use ff::Field;
/// An Allocated R1CS Instance
#[derive(Clone)]
pub struct AllocatedR1CSInstance<G>
where
G: Group,
{
pub(crate) W: AllocatedPoint<G::Base>,
pub(crate) X0: AllocatedNum<G::Base>,
pub(crate) X1: AllocatedNum<G::Base>,
}
impl<G> AllocatedR1CSInstance<G>
where
G: Group,
{
/// Takes the r1cs instance and creates a new allocated r1cs instance
pub fn alloc<CS: ConstraintSystem<<G as Group>::Base>>(
mut cs: CS,
u: Option<R1CSInstance<G>>,
) -> Result<Self, SynthesisError> {
// Check that the incoming instance has exactly 2 io
let W = AllocatedPoint::alloc(
cs.namespace(|| "allocate W"),
u.get()
.map_or(None, |u| Some(u.comm_W.comm.to_coordinates())),
)?;
let X0 = alloc_scalar_as_base::<G, _>(
cs.namespace(|| "allocate X[0]"),
u.get().map_or(None, |u| Some(u.X[0])),
)?;
let X1 = alloc_scalar_as_base::<G, _>(
cs.namespace(|| "allocate X[1]"),
u.get().map_or(None, |u| Some(u.X[1])),
)?;
Ok(AllocatedR1CSInstance { W, X0, X1 })
}
/// Absorb the provided instance in the RO
pub fn absorb_in_ro(&self, ro: &mut PoseidonROGadget<G::Base>) {
ro.absorb(self.W.x.clone());
ro.absorb(self.W.y.clone());
ro.absorb(self.W.is_infinity.clone());
ro.absorb(self.X0.clone());
ro.absorb(self.X1.clone());
}
}
/// An Allocated Relaxed R1CS Instance
pub struct AllocatedRelaxedR1CSInstance<G>
where
G: Group,
{
pub(crate) W: AllocatedPoint<G::Base>,
pub(crate) E: AllocatedPoint<G::Base>,
pub(crate) u: AllocatedNum<G::Base>,
pub(crate) X0: BigNat<G::Base>,
pub(crate) X1: BigNat<G::Base>,
}
impl<G> AllocatedRelaxedR1CSInstance<G>
where
G: Group,
{
/// Allocates the given RelaxedR1CSInstance as a witness of the circuit
pub fn alloc<CS: ConstraintSystem<<G as Group>::Base>>(
mut cs: CS,
inst: Option<RelaxedR1CSInstance<G>>,
limb_width: usize,
n_limbs: usize,
) -> Result<Self, SynthesisError> {
let W = AllocatedPoint::alloc(
cs.namespace(|| "allocate W"),
inst
.get()
.map_or(None, |inst| Some(inst.comm_W.comm.to_coordinates())),
)?;
let E = AllocatedPoint::alloc(
cs.namespace(|| "allocate E"),
inst
.get()
.map_or(None, |inst| Some(inst.comm_E.comm.to_coordinates())),
)?;
// u << |G::Base| despite the fact that u is a scalar.
// So we parse all of its bytes as a G::Base element
let u = alloc_scalar_as_base::<G, _>(
cs.namespace(|| "allocate u"),
inst.get().map_or(None, |inst| Some(inst.u)),
)?;
let X0 = BigNat::alloc_from_nat(
cs.namespace(|| "allocate X[0]"),
|| Ok(f_to_nat(&inst.get()?.X[0])),
limb_width,
n_limbs,
)?;
let X1 = BigNat::alloc_from_nat(
cs.namespace(|| "allocate X[1]"),
|| Ok(f_to_nat(&inst.get()?.X[1])),
limb_width,
n_limbs,
)?;
Ok(AllocatedRelaxedR1CSInstance { W, E, u, X0, X1 })
}
/// Allocates the hardcoded default RelaxedR1CSInstance in the circuit.
/// W = E = 0, u = 1, X0 = X1 = 0
pub fn default<CS: ConstraintSystem<<G as Group>::Base>>(
mut cs: CS,
limb_width: usize,
n_limbs: usize,
) -> Result<Self, SynthesisError> {
let W = AllocatedPoint::default(cs.namespace(|| "allocate W"))?;
let E = W.clone();
let u = W.x.clone(); // In the default case, W.x = u = 0
let X0 = BigNat::alloc_from_nat(
cs.namespace(|| "allocate x_default[0]"),
|| Ok(f_to_nat(&G::Scalar::zero())),
limb_width,
n_limbs,
)?;
let X1 = BigNat::alloc_from_nat(
cs.namespace(|| "allocate x_default[1]"),
|| Ok(f_to_nat(&G::Scalar::zero())),
limb_width,
n_limbs,
)?;
Ok(AllocatedRelaxedR1CSInstance { W, E, u, X0, X1 })
}
/// Absorb the provided instance in the RO
pub fn absorb_in_ro<CS: ConstraintSystem<<G as Group>::Base>>(
&self,
mut cs: CS,
ro: &mut PoseidonROGadget<G::Base>,
) -> Result<(), SynthesisError> {
ro.absorb(self.W.x.clone());
ro.absorb(self.W.y.clone());
ro.absorb(self.W.is_infinity.clone());
ro.absorb(self.E.x.clone());
ro.absorb(self.E.y.clone());
ro.absorb(self.E.is_infinity.clone());
ro.absorb(self.u.clone());
// Analyze X0 as limbs
let X0_bn = self
.X0
.as_limbs::<CS>()
.iter()
.enumerate()
.map(|(i, limb)| {
limb
.as_sapling_allocated_num(cs.namespace(|| format!("convert limb {} of X_r[0] to num", i)))
})
.collect::<Result<Vec<AllocatedNum<G::Base>>, _>>()?;
// absorb each of the limbs of X[0]
for limb in X0_bn.into_iter() {
ro.absorb(limb);
}
// Analyze X1 as limbs
let X1_bn = self
.X1
.as_limbs::<CS>()
.iter()
.enumerate()
.map(|(i, limb)| {
limb
.as_sapling_allocated_num(cs.namespace(|| format!("convert limb {} of X_r[1] to num", i)))
})
.collect::<Result<Vec<AllocatedNum<G::Base>>, _>>()?;
// absorb each of the limbs of X[1]
for limb in X1_bn.into_iter() {
ro.absorb(limb);
}
Ok(())
}
/// Folds self with a relaxed r1cs instance and returns the result
pub fn fold_with_r1cs<CS: ConstraintSystem<<G as Group>::Base>>(
&self,
mut cs: CS,
u: AllocatedR1CSInstance<G>,
T: AllocatedPoint<G::Base>,
poseidon_constants: NovaPoseidonConstants<G::Base>,
limb_width: usize,
n_limbs: usize,
) -> Result<AllocatedRelaxedR1CSInstance<G>, SynthesisError> {
// Compute r:
let mut ro: PoseidonROGadget<G::Base> = PoseidonROGadget::new(poseidon_constants);
u.absorb_in_ro(&mut ro);
ro.absorb(T.x.clone());
ro.absorb(T.y.clone());
ro.absorb(T.is_infinity.clone());
let r_bits = ro.get_challenge(cs.namespace(|| "r bits"))?;
let r = le_bits_to_num(cs.namespace(|| "r"), r_bits.clone())?;
// W_fold = self.W + r * u.W
let rW = u.W.scalar_mul(cs.namespace(|| "r * u.W"), r_bits.clone())?;
let W_fold = self.W.add(cs.namespace(|| "self.W + r * u.W"), &rW)?;
// E_fold = self.E + r * T
let rT = T.scalar_mul(cs.namespace(|| "r * T"), r_bits)?;
let E_fold = self.E.add(cs.namespace(|| "self.E + r * T"), &rT)?;
// u_fold = u_r + r
let u_fold = AllocatedNum::alloc(cs.namespace(|| "u_fold"), || {
Ok(*self.u.get_value().get()? + r.get_value().get()?)
})?;
cs.enforce(
|| "Check u_fold",
|lc| lc,
|lc| lc,
|lc| lc + u_fold.get_variable() - self.u.get_variable() - r.get_variable(),
);
// Fold the IO:
// Analyze r into limbs
let r_bn = BigNat::from_num(
cs.namespace(|| "allocate r_bn"),
Num::from(r.clone()),
limb_width,
n_limbs,
)?;
// Allocate the order of the non-native field as a constant
let m_bn = alloc_bignat_constant(
cs.namespace(|| "alloc m"),
&G::get_order(),
limb_width,
n_limbs,
)?;
// Analyze X0 to bignat
let X0_bn = BigNat::from_num(
cs.namespace(|| "allocate X0_bn"),
Num::from(u.X0.clone()),
limb_width,
n_limbs,
)?;
// Fold self.X[0] + r * X[0]
let (_, r_0) = X0_bn.mult_mod(cs.namespace(|| "r*X[0]"), &r_bn, &m_bn)?;
// add X_r[0]
let r_new_0 = self.X0.add::<CS>(&r_0)?;
// Now reduce
let X0_fold = r_new_0.red_mod(cs.namespace(|| "reduce folded X[0]"), &m_bn)?;
// Analyze X1 to bignat
let X1_bn = BigNat::from_num(
cs.namespace(|| "allocate X1_bn"),
Num::from(u.X1.clone()),
limb_width,
n_limbs,
)?;
// Fold self.X[1] + r * X[1]
let (_, r_1) = X1_bn.mult_mod(cs.namespace(|| "r*X[1]"), &r_bn, &m_bn)?;
// add X_r[1]
let r_new_1 = self.X1.add::<CS>(&r_1)?;
// Now reduce
let X1_fold = r_new_1.red_mod(cs.namespace(|| "reduce folded X[1]"), &m_bn)?;
Ok(Self {
W: W_fold,
E: E_fold,
u: u_fold,
X0: X0_fold,
X1: X1_fold,
})
}
/// If the condition is true then returns this otherwise it returns the other
pub fn conditionally_select<CS: ConstraintSystem<<G as Group>::Base>>(
&self,
mut cs: CS,
other: AllocatedRelaxedR1CSInstance<G>,
condition: &Boolean,
) -> Result<AllocatedRelaxedR1CSInstance<G>, SynthesisError> {
let W = AllocatedPoint::conditionally_select(
cs.namespace(|| "W = cond ? self.W : other.W"),
&self.W,
&other.W,
condition,
)?;
let E = AllocatedPoint::conditionally_select(
cs.namespace(|| "E = cond ? self.E : other.E"),
&self.E,
&other.E,
condition,
)?;
let u = conditionally_select(
cs.namespace(|| "u = cond ? self.u : other.u"),
&self.u,
&other.u,
condition,
)?;
let X0 = conditionally_select_bignat(
cs.namespace(|| "X[0] = cond ? self.X[0] : other.X[0]"),
&self.X0,
&other.X0,
condition,
)?;
let X1 = conditionally_select_bignat(
cs.namespace(|| "X[1] = cond ? self.X[1] : other.X[1]"),
&self.X1,
&other.X1,
condition,
)?;
Ok(AllocatedRelaxedR1CSInstance { W, E, u, X0, X1 })
}
}
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