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//! Gadgets for elliptic curve operations.
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use std::fmt;
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use halo2::{
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arithmetic::CurveAffine,
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circuit::{Chip, Layouter},
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plonk::Error,
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};
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/// Trait allowing circuit's fixed points to be enumerated.
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pub trait FixedPoints<C: CurveAffine>: Clone + fmt::Debug {}
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/// The set of circuit instructions required to use the ECC gadgets.
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pub trait EccInstructions<C: CurveAffine>: Chip<C::Base> {
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/// Variable representing a full-width element of the elliptic curve's scalar field, to be used for fixed-base scalar mul.
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type ScalarFixed: Clone + fmt::Debug;
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/// Variable representing a signed short element of the elliptic curve's scalar field, to be used for fixed-base scalar mul.
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type ScalarFixedShort: Clone + fmt::Debug;
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/// Variable representing an elliptic curve point.
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type Point: Clone + fmt::Debug;
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/// Variable representing the x-coordinate of an elliptic curve point.
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type X: Clone + fmt::Debug;
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/// Variable representing the set of fixed bases in the circuit.
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type FixedPoints: FixedPoints<C>;
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/// Variable representing a fixed elliptic curve point (constant in the circuit).
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type FixedPoint: Clone + fmt::Debug;
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/// Witnesses the given full-width scalar as a private input to the circuit for fixed-based scalar mul.
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fn witness_scalar_fixed(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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value: Option<C::Scalar>,
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) -> Result<Self::ScalarFixed, Error>;
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/// Witnesses the given signed short scalar as a private input to the circuit for fixed-based scalar mul.
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fn witness_scalar_fixed_short(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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value: Option<C::Scalar>,
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) -> Result<Self::ScalarFixedShort, Error>;
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/// Witnesses the given point as a private input to the circuit.
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fn witness_point(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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value: Option<C>,
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) -> Result<Self::Point, Error>;
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/// Extracts the x-coordinate of a point.
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fn extract_p(point: &Self::Point) -> &Self::X;
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/// Gets a fixed point into the circuit.
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fn get_fixed(&self, fixed_points: Self::FixedPoints) -> Result<Self::FixedPoint, Error>;
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/// Performs point addition, returning `a + b`.
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fn add(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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a: &Self::Point,
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b: &Self::Point,
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) -> Result<Self::Point, Error>;
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/// Performs complete point addition, returning `a + b`.
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fn add_complete(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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a: &Self::Point,
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b: &Self::Point,
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) -> Result<Self::Point, Error>;
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/// Performs variable-base scalar multiplication, returning `[scalar] base`.
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fn mul(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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scalar: C::Scalar,
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base: &Self::Point,
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) -> Result<Self::Point, Error>;
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/// Performs fixed-base scalar multiplication using a full-width scalar, returning `[scalar] base`.
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fn mul_fixed(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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scalar: &Self::ScalarFixed,
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base: &Self::FixedPoint,
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) -> Result<Self::Point, Error>;
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/// Performs fixed-base scalar multiplication using a short signed scalar, returning `[scalar] base`.
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fn mul_fixed_short(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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scalar: &Self::ScalarFixedShort,
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base: &Self::FixedPoint,
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) -> Result<Self::Point, Error>;
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}
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/// A full-width element of the given elliptic curve's scalar field, to be used for fixed-base scalar mul.
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#[derive(Debug)]
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pub struct ScalarFixed<C: CurveAffine, EccChip: EccInstructions<C> + Clone> {
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chip: EccChip,
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inner: EccChip::ScalarFixed,
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}
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impl<C: CurveAffine, EccChip: EccInstructions<C> + Clone> ScalarFixed<C, EccChip> {
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/// Constructs a new ScalarFixed with the given value.
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pub fn new(
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chip: EccChip,
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mut layouter: impl Layouter<C::Base>,
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value: Option<C::Scalar>,
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) -> Result<Self, Error> {
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chip.witness_scalar_fixed(&mut layouter, value)
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.map(|inner| ScalarFixed {
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chip: chip.clone(),
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inner,
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})
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}
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}
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/// A signed short element of the given elliptic curve's scalar field, to be used for fixed-base scalar mul.
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#[derive(Debug)]
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pub struct ScalarFixedShort<C: CurveAffine, EccChip: EccInstructions<C> + Clone> {
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chip: EccChip,
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inner: EccChip::ScalarFixedShort,
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}
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impl<C: CurveAffine, EccChip: EccInstructions<C> + Clone> ScalarFixedShort<C, EccChip> {
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/// Constructs a new ScalarFixedShort with the given value.
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pub fn new(
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chip: EccChip,
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mut layouter: impl Layouter<C::Base>,
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value: Option<C::Scalar>,
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) -> Result<Self, Error> {
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chip.witness_scalar_fixed_short(&mut layouter, value)
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.map(|inner| ScalarFixedShort {
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chip: chip.clone(),
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inner,
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})
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}
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}
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/// An elliptic curve point over the given curve.
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#[derive(Debug)]
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pub struct Point<C: CurveAffine, EccChip: EccInstructions<C> + Clone> {
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chip: EccChip,
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inner: EccChip::Point,
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}
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impl<C: CurveAffine, EccChip: EccInstructions<C> + Clone> Point<C, EccChip> {
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/// Constructs a new point with the given value.
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pub fn new(
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&self,
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mut layouter: impl Layouter<C::Base>,
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value: Option<C>,
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) -> Result<Self, Error> {
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self.chip
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.witness_point(&mut layouter, value)
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.map(|inner| Point {
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chip: self.chip.clone(),
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inner,
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})
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}
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/// Extracts the x-coordinate of a point.
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pub fn extract_p(&self) -> X<C, EccChip> {
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X::from_inner(self.chip.clone(), EccChip::extract_p(&self.inner).clone())
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}
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/// Wraps the given point (obtained directly from an instruction) in a gadget.
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pub fn from_inner(chip: EccChip, inner: EccChip::Point) -> Self {
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Point { chip, inner }
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}
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/// Returns `self + other`.
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pub fn add(&self, mut layouter: impl Layouter<C::Base>, other: &Self) -> Result<Self, Error> {
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self.chip
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.add(&mut layouter, &self.inner, &other.inner)
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.map(|inner| Point {
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chip: self.chip.clone(),
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inner,
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})
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}
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/// Returns `[by] self`.
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pub fn mul(&self, mut layouter: impl Layouter<C::Base>, by: C::Scalar) -> Result<Self, Error> {
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self.chip
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.mul(&mut layouter, by, &self.inner)
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.map(|inner| Point {
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chip: self.chip.clone(),
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inner,
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})
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}
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}
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/// The x-coordinate of an elliptic curve point over the given curve.
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#[derive(Debug)]
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pub struct X<C: CurveAffine, EccChip: EccInstructions<C> + Clone> {
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chip: EccChip,
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inner: EccChip::X,
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}
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impl<C: CurveAffine, EccChip: EccInstructions<C> + Clone> X<C, EccChip> {
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/// Wraps the given x-coordinate (obtained directly from an instruction) in a gadget.
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pub fn from_inner(chip: EccChip, inner: EccChip::X) -> Self {
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X { chip, inner }
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}
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}
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/// A constant elliptic curve point over the given curve, for which scalar multiplication
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/// is more efficient.
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#[derive(Clone, Debug)]
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pub struct FixedPoint<C: CurveAffine, EccChip: EccInstructions<C> + Clone> {
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chip: EccChip,
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inner: EccChip::FixedPoint,
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}
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impl<C: CurveAffine, EccChip: EccInstructions<C> + Clone> FixedPoint<C, EccChip> {
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/// Gets a reference to the specified fixed point in the circuit.
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pub fn get(chip: EccChip, point: EccChip::FixedPoints) -> Result<Self, Error> {
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chip.get_fixed(point).map(|inner| FixedPoint {
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chip: chip.clone(),
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inner,
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})
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}
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/// Returns `[by] self`.
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pub fn mul(
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&self,
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mut layouter: impl Layouter<C::Base>,
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by: &ScalarFixed<C, EccChip>,
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) -> Result<Point<C, EccChip>, Error> {
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self.chip
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.mul_fixed(&mut layouter, &by.inner, &self.inner)
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.map(|inner| Point {
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chip: self.chip.clone(),
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inner,
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})
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}
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}
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