mirror of https://github.com/zcash/orchard.git
708 lines
23 KiB
Rust
708 lines
23 KiB
Rust
//! Gadgets for elliptic curve operations.
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use std::convert::{TryFrom, TryInto};
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use std::fmt::Debug;
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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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use crate::circuit::gadget::utilities::UtilitiesInstructions;
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pub mod chip;
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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> + UtilitiesInstructions<C::Base> {
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/// Variable representing an element of the elliptic curve's base field, that
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/// is used as a scalar in variable-base scalar mul.
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///
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/// It is not true in general that a scalar field element fits in a curve's
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/// base field, and in particular it is untrue for the Pallas curve, whose
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/// scalar field `Fq` is larger than its base field `Fp`.
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///
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/// However, the only use of variable-base scalar mul in the Orchard protocol
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/// is in deriving diversified addresses `[ivk] g_d`, and `ivk` is guaranteed
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/// to be in the base field of the curve. (See non-normative notes in
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/// https://zips.z.cash/protocol/nu5.pdf#orchardkeycomponents.)
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type ScalarVar: Clone + Debug;
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/// Variable representing a full-width element of the elliptic curve's
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/// scalar field, to be used for fixed-base scalar mul.
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type ScalarFixed: Clone + Debug;
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/// Variable representing a signed short element of the elliptic curve's
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/// scalar field, to be used for fixed-base scalar mul.
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///
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/// A `ScalarFixedShort` must be in the range [-(2^64 - 1), 2^64 - 1].
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type ScalarFixedShort: Clone + Debug;
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/// Variable representing an elliptic curve point.
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type Point: From<Self::NonIdentityPoint> + Clone + Debug;
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/// Variable representing a non-identity elliptic curve point.
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type NonIdentityPoint: TryFrom<Self::Point> + Clone + Debug;
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/// Variable representing the affine short Weierstrass x-coordinate of an
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/// elliptic curve point.
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type X: Clone + Debug;
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/// Enumeration of the set of fixed bases to be used in scalar mul with a full-width scalar.
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type FixedPoints: Clone + Debug;
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/// Enumeration of the set of fixed bases to be used in scalar mul with a base field element.
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type FixedPointsBaseField: Clone + Debug;
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/// Enumeration of the set of fixed bases to be used in short signed scalar mul.
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type FixedPointsShort: Clone + Debug;
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/// Constrains point `a` to be equal in value to point `b`.
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fn constrain_equal(
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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<(), Error>;
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/// Witnesses the given point as a private input to the circuit.
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/// This maps the identity to (0, 0) in affine coordinates.
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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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/// Witnesses the given point as a private input to the circuit.
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/// This returns an error if the point is the identity.
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fn witness_point_non_id(
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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::NonIdentityPoint, Error>;
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/// Extracts the x-coordinate of a point.
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fn extract_p<Point: Into<Self::Point> + Clone>(point: &Point) -> Self::X;
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/// Performs incomplete point addition, returning `a + b`.
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///
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/// This returns an error in exceptional cases.
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fn add_incomplete(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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a: &Self::NonIdentityPoint,
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b: &Self::NonIdentityPoint,
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) -> Result<Self::NonIdentityPoint, Error>;
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/// Performs complete point addition, returning `a + b`.
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fn add<A: Into<Self::Point> + Clone, B: Into<Self::Point> + Clone>(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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a: &A,
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b: &B,
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) -> Result<Self::Point, Error>;
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/// Performs variable-base scalar multiplication, returning `[scalar] base`.
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/// Multiplication of the identity `[scalar] 𝒪 ` returns an error.
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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: &Self::Var,
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base: &Self::NonIdentityPoint,
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) -> Result<(Self::Point, Self::ScalarVar), 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: Option<C::Scalar>,
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base: &Self::FixedPoints,
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) -> Result<(Self::Point, Self::ScalarFixed), Error>;
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/// Performs fixed-base scalar multiplication using a short signed scalar, returning
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/// `[magnitude * sign] 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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magnitude_sign: (Self::Var, Self::Var),
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base: &Self::FixedPointsShort,
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) -> Result<(Self::Point, Self::ScalarFixedShort), Error>;
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/// Performs fixed-base scalar multiplication using a base field element as the scalar.
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/// In the current implementation, this base field element must be output from another
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/// instruction.
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fn mul_fixed_base_field_elem(
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&self,
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layouter: &mut impl Layouter<C::Base>,
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base_field_elem: Self::Var,
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base: &Self::FixedPointsBaseField,
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) -> Result<Self::Point, Error>;
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}
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/// An element of the given elliptic curve's base field, that is used as a scalar
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/// in variable-base scalar mul.
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///
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/// It is not true in general that a scalar field element fits in a curve's
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/// base field, and in particular it is untrue for the Pallas curve, whose
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/// scalar field `Fq` is larger than its base field `Fp`.
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///
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/// However, the only use of variable-base scalar mul in the Orchard protocol
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/// is in deriving diversified addresses `[ivk] g_d`, and `ivk` is guaranteed
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/// to be in the base field of the curve. (See non-normative notes in
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/// https://zips.z.cash/protocol/nu5.pdf#orchardkeycomponents.)
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#[derive(Debug)]
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pub struct ScalarVar<C: CurveAffine, EccChip: EccInstructions<C> + Clone + Debug + Eq> {
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chip: EccChip,
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inner: EccChip::ScalarVar,
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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>
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where
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EccChip: EccInstructions<C> + Clone + Debug + Eq,
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{
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chip: EccChip,
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inner: EccChip::ScalarFixed,
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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>
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where
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EccChip: EccInstructions<C> + Clone + Debug + Eq,
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{
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chip: EccChip,
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inner: EccChip::ScalarFixedShort,
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}
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/// A non-identity elliptic curve point over the given curve.
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#[derive(Copy, Clone, Debug)]
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pub struct NonIdentityPoint<C: CurveAffine, EccChip: EccInstructions<C> + Clone + Debug + Eq> {
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chip: EccChip,
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inner: EccChip::NonIdentityPoint,
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}
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impl<C: CurveAffine, EccChip: EccInstructions<C> + Clone + Debug + Eq>
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NonIdentityPoint<C, EccChip>
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{
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/// Constructs a new point 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>,
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) -> Result<Self, Error> {
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let point = chip.witness_point_non_id(&mut layouter, value);
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point.map(|inner| NonIdentityPoint { chip, inner })
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}
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/// Constrains this point to be equal in value to another point.
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pub fn constrain_equal<Other: Into<Point<C, EccChip>> + Clone>(
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&self,
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mut layouter: impl Layouter<C::Base>,
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other: &Other,
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) -> Result<(), Error> {
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let other: Point<C, EccChip> = (other.clone()).into();
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self.chip.constrain_equal(
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&mut layouter,
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&Point::<C, EccChip>::from(self.clone()).inner,
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&other.inner,
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)
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}
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/// Returns the inner point.
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pub fn inner(&self) -> &EccChip::NonIdentityPoint {
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&self.inner
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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::NonIdentityPoint) -> Self {
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NonIdentityPoint { chip, inner }
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}
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/// Returns `self + other` using complete addition.
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pub fn add<Other: Into<Point<C, EccChip>> + Clone>(
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&self,
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mut layouter: impl Layouter<C::Base>,
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other: &Other,
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) -> Result<Point<C, EccChip>, Error> {
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let other: Point<C, EccChip> = (other.clone()).into();
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assert_eq!(self.chip, other.chip);
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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 `self + other` using incomplete addition.
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pub fn add_incomplete(
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&self,
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mut layouter: impl Layouter<C::Base>,
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other: &Self,
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) -> Result<Self, Error> {
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assert_eq!(self.chip, other.chip);
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self.chip
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.add_incomplete(&mut layouter, &self.inner, &other.inner)
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.map(|inner| NonIdentityPoint {
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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(
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&self,
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mut layouter: impl Layouter<C::Base>,
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by: &EccChip::Var,
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) -> Result<(Point<C, EccChip>, ScalarVar<C, EccChip>), Error> {
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self.chip
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.mul(&mut layouter, by, &self.inner.clone().into())
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.map(|(point, scalar)| {
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(
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Point {
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chip: self.chip.clone(),
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inner: point,
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},
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ScalarVar {
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chip: self.chip.clone(),
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inner: scalar,
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},
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)
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})
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}
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}
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impl<C: CurveAffine, EccChip: EccInstructions<C> + Clone + Debug + Eq>
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From<NonIdentityPoint<C, EccChip>> for Point<C, EccChip>
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{
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fn from(non_id_point: NonIdentityPoint<C, EccChip>) -> Self {
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Self {
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chip: non_id_point.chip,
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inner: non_id_point.inner.into(),
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}
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}
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}
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impl<C: CurveAffine, EccChip: EccInstructions<C> + Clone + Debug + Eq> TryFrom<Point<C, EccChip>>
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for NonIdentityPoint<C, EccChip>
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{
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type Error = Error;
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fn try_from(point: Point<C, EccChip>) -> Result<Self, Self::Error> {
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point
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.inner
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.clone()
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.try_into()
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.map(|inner| Self {
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chip: point.chip,
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inner,
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})
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.map_err(|_| Error::SynthesisError)
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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(Copy, Clone, Debug)]
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pub struct Point<C: CurveAffine, EccChip: EccInstructions<C> + Clone + Debug + Eq> {
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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 + Debug + Eq> Point<C, EccChip> {
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/// Constructs a new point with the given value.
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#[cfg(test)]
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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>,
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) -> Result<Self, Error> {
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let point = chip.witness_point(&mut layouter, value);
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point.map(|inner| Point { chip, inner })
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}
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/// Constrains this point to be equal in value to another point.
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pub fn constrain_equal<Other: Into<Point<C, EccChip>> + Clone>(
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&self,
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mut layouter: impl Layouter<C::Base>,
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other: &Other,
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) -> Result<(), Error> {
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let other: Point<C, EccChip> = (other.clone()).into();
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self.chip.constrain_equal(
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&mut layouter,
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&Point::<C, EccChip>::from(self.clone()).inner,
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&other.inner,
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)
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}
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/// Returns the inner point.
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pub fn inner(&self) -> &EccChip::Point {
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&self.inner
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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` using complete addition.
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pub fn add<Other: Into<Point<C, EccChip>> + Clone>(
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&self,
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mut layouter: impl Layouter<C::Base>,
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other: &Other,
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) -> Result<Point<C, EccChip>, Error> {
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let other: Point<C, EccChip> = (other.clone()).into();
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assert_eq!(self.chip, other.chip);
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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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}
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/// The affine short Weierstrass x-coordinate of an elliptic curve point over the
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/// given curve.
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#[derive(Debug)]
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pub struct X<C: CurveAffine, EccChip: EccInstructions<C> + Clone + Debug + Eq> {
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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 + Debug + Eq> 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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/// Returns the inner x-coordinate.
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pub fn inner(&self) -> &EccChip::X {
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&self.inner
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}
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}
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/// A constant elliptic curve point over the given curve, for which window tables have
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/// been provided to make scalar multiplication more efficient.
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///
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/// Used in scalar multiplication with full-width scalars.
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#[derive(Clone, Debug)]
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pub struct FixedPoint<C: CurveAffine, EccChip>
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where
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EccChip: EccInstructions<C> + Clone + Debug + Eq,
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{
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chip: EccChip,
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inner: EccChip::FixedPoints,
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}
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impl<C: CurveAffine, EccChip> FixedPoint<C, EccChip>
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where
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EccChip: EccInstructions<C> + Clone + Debug + Eq,
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{
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#[allow(clippy::type_complexity)]
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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: Option<C::Scalar>,
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) -> Result<(Point<C, EccChip>, ScalarFixed<C, EccChip>), Error> {
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self.chip
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.mul_fixed(&mut layouter, by, &self.inner)
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.map(|(point, scalar)| {
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(
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Point {
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chip: self.chip.clone(),
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inner: point,
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},
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ScalarFixed {
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chip: self.chip.clone(),
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inner: scalar,
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},
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)
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})
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}
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/// Wraps the given fixed base (obtained directly from an instruction) in a gadget.
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pub fn from_inner(chip: EccChip, inner: EccChip::FixedPoints) -> Self {
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FixedPoint { chip, inner }
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}
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}
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/// A constant elliptic curve point over the given curve, used in scalar multiplication
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/// with a base field element
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#[derive(Clone, Debug)]
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pub struct FixedPointBaseField<C: CurveAffine, EccChip>
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where
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EccChip: EccInstructions<C> + Clone + Debug + Eq,
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{
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chip: EccChip,
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inner: EccChip::FixedPointsBaseField,
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}
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impl<C: CurveAffine, EccChip> FixedPointBaseField<C, EccChip>
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where
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EccChip: EccInstructions<C> + Clone + Debug + Eq,
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{
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#[allow(clippy::type_complexity)]
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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: EccChip::Var,
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) -> Result<Point<C, EccChip>, Error> {
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self.chip
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.mul_fixed_base_field_elem(&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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/// Wraps the given fixed base (obtained directly from an instruction) in a gadget.
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pub fn from_inner(chip: EccChip, inner: EccChip::FixedPointsBaseField) -> Self {
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FixedPointBaseField { chip, inner }
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}
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}
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/// A constant elliptic curve point over the given curve, used in scalar multiplication
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/// with a short signed exponent
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#[derive(Clone, Debug)]
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pub struct FixedPointShort<C: CurveAffine, EccChip>
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where
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EccChip: EccInstructions<C> + Clone + Debug + Eq,
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{
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chip: EccChip,
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inner: EccChip::FixedPointsShort,
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}
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impl<C: CurveAffine, EccChip> FixedPointShort<C, EccChip>
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where
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EccChip: EccInstructions<C> + Clone + Debug + Eq,
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{
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#[allow(clippy::type_complexity)]
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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>,
|
||
magnitude_sign: (EccChip::Var, EccChip::Var),
|
||
) -> Result<(Point<C, EccChip>, ScalarFixedShort<C, EccChip>), Error> {
|
||
self.chip
|
||
.mul_fixed_short(&mut layouter, magnitude_sign, &self.inner)
|
||
.map(|(point, scalar)| {
|
||
(
|
||
Point {
|
||
chip: self.chip.clone(),
|
||
inner: point,
|
||
},
|
||
ScalarFixedShort {
|
||
chip: self.chip.clone(),
|
||
inner: scalar,
|
||
},
|
||
)
|
||
})
|
||
}
|
||
|
||
/// Wraps the given fixed base (obtained directly from an instruction) in a gadget.
|
||
pub fn from_inner(chip: EccChip, inner: EccChip::FixedPointsShort) -> Self {
|
||
FixedPointShort { chip, inner }
|
||
}
|
||
}
|
||
|
||
#[cfg(test)]
|
||
mod tests {
|
||
use group::{prime::PrimeCurveAffine, Curve, Group};
|
||
|
||
use halo2::{
|
||
circuit::{Layouter, SimpleFloorPlanner},
|
||
dev::MockProver,
|
||
plonk::{Circuit, ConstraintSystem, Error},
|
||
};
|
||
use pasta_curves::pallas;
|
||
|
||
use super::chip::{EccChip, EccConfig};
|
||
use crate::circuit::gadget::utilities::lookup_range_check::LookupRangeCheckConfig;
|
||
|
||
struct MyCircuit {}
|
||
|
||
#[allow(non_snake_case)]
|
||
impl Circuit<pallas::Base> for MyCircuit {
|
||
type Config = EccConfig;
|
||
type FloorPlanner = SimpleFloorPlanner;
|
||
|
||
fn without_witnesses(&self) -> Self {
|
||
MyCircuit {}
|
||
}
|
||
|
||
fn configure(meta: &mut ConstraintSystem<pallas::Base>) -> Self::Config {
|
||
let advices = [
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
meta.advice_column(),
|
||
];
|
||
let lookup_table = meta.lookup_table_column();
|
||
let lagrange_coeffs = [
|
||
meta.fixed_column(),
|
||
meta.fixed_column(),
|
||
meta.fixed_column(),
|
||
meta.fixed_column(),
|
||
meta.fixed_column(),
|
||
meta.fixed_column(),
|
||
meta.fixed_column(),
|
||
meta.fixed_column(),
|
||
];
|
||
// Shared fixed column for loading constants
|
||
let constants = meta.fixed_column();
|
||
meta.enable_constant(constants);
|
||
|
||
let range_check = LookupRangeCheckConfig::configure(meta, advices[9], lookup_table);
|
||
EccChip::configure(meta, advices, lagrange_coeffs, range_check)
|
||
}
|
||
|
||
fn synthesize(
|
||
&self,
|
||
config: Self::Config,
|
||
mut layouter: impl Layouter<pallas::Base>,
|
||
) -> Result<(), Error> {
|
||
let chip = EccChip::construct(config.clone());
|
||
|
||
// Load 10-bit lookup table. In the Action circuit, this will be
|
||
// provided by the Sinsemilla chip.
|
||
config.lookup_config.load(&mut layouter)?;
|
||
|
||
// Generate a random non-identity point P
|
||
let p_val = pallas::Point::random(rand::rngs::OsRng).to_affine(); // P
|
||
let p = super::NonIdentityPoint::new(
|
||
chip.clone(),
|
||
layouter.namespace(|| "P"),
|
||
Some(p_val),
|
||
)?;
|
||
let p_neg = -p_val;
|
||
let p_neg = super::NonIdentityPoint::new(
|
||
chip.clone(),
|
||
layouter.namespace(|| "-P"),
|
||
Some(p_neg),
|
||
)?;
|
||
|
||
// Generate a random non-identity point Q
|
||
let q_val = pallas::Point::random(rand::rngs::OsRng).to_affine(); // Q
|
||
let q = super::NonIdentityPoint::new(
|
||
chip.clone(),
|
||
layouter.namespace(|| "Q"),
|
||
Some(q_val),
|
||
)?;
|
||
|
||
// Make sure P and Q are not the same point.
|
||
assert_ne!(p_val, q_val);
|
||
|
||
// Generate a (0,0) point to be used in other tests.
|
||
let zero = {
|
||
super::Point::new(
|
||
chip.clone(),
|
||
layouter.namespace(|| "identity"),
|
||
Some(pallas::Affine::identity()),
|
||
)?
|
||
};
|
||
|
||
// Test complete addition
|
||
{
|
||
super::chip::add::tests::test_add(
|
||
chip.clone(),
|
||
layouter.namespace(|| "complete addition"),
|
||
&zero,
|
||
p_val,
|
||
&p,
|
||
q_val,
|
||
&q,
|
||
&p_neg,
|
||
)?;
|
||
}
|
||
|
||
// Test incomplete addition
|
||
{
|
||
super::chip::add_incomplete::tests::test_add_incomplete(
|
||
chip.clone(),
|
||
layouter.namespace(|| "incomplete addition"),
|
||
&zero,
|
||
p_val,
|
||
&p,
|
||
q_val,
|
||
&q,
|
||
&p_neg,
|
||
)?;
|
||
}
|
||
|
||
// Test variable-base scalar multiplication
|
||
{
|
||
super::chip::mul::tests::test_mul(
|
||
chip.clone(),
|
||
layouter.namespace(|| "variable-base scalar mul"),
|
||
&zero,
|
||
&p,
|
||
p_val,
|
||
)?;
|
||
}
|
||
|
||
// Test full-width fixed-base scalar multiplication
|
||
{
|
||
super::chip::mul_fixed::full_width::tests::test_mul_fixed(
|
||
chip.clone(),
|
||
layouter.namespace(|| "full-width fixed-base scalar mul"),
|
||
)?;
|
||
}
|
||
|
||
// Test signed short fixed-base scalar multiplication
|
||
{
|
||
super::chip::mul_fixed::short::tests::test_mul_fixed_short(
|
||
chip.clone(),
|
||
layouter.namespace(|| "signed short fixed-base scalar mul"),
|
||
)?;
|
||
}
|
||
|
||
// Test fixed-base scalar multiplication with a base field element
|
||
{
|
||
super::chip::mul_fixed::base_field_elem::tests::test_mul_fixed_base_field(
|
||
chip,
|
||
layouter.namespace(|| "fixed-base scalar mul with base field element"),
|
||
)?;
|
||
}
|
||
|
||
Ok(())
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn ecc_chip() {
|
||
let k = 13;
|
||
let circuit = MyCircuit {};
|
||
let prover = MockProver::run(k, &circuit, vec![]).unwrap();
|
||
assert_eq!(prover.verify(), Ok(()))
|
||
}
|
||
|
||
#[cfg(feature = "dev-graph")]
|
||
#[test]
|
||
fn print_ecc_chip() {
|
||
use plotters::prelude::*;
|
||
|
||
let root = BitMapBackend::new("ecc-chip-layout.png", (1024, 7680)).into_drawing_area();
|
||
root.fill(&WHITE).unwrap();
|
||
let root = root.titled("Ecc Chip Layout", ("sans-serif", 60)).unwrap();
|
||
|
||
let circuit = MyCircuit {};
|
||
halo2::dev::CircuitLayout::default()
|
||
.render(13, &circuit, &root)
|
||
.unwrap();
|
||
}
|
||
}
|