elliptic-curve 0.14.0

//! [`MockCurve`]: incomplete simulation of a curve implementation for testing.
//!
//! This module contains a family of mock types for use with the [`Curve`] and [`CurveArithmetic`]
//! traits which can be used to a limited degree for writing tests of algorithms implemented
//! generically over curves without having to pull in a complete curve implementation.

use crate::{
    BatchNormalize, Curve, CurveAffine, CurveArithmetic, CurveGroup, Generate, PrimeCurve,
    array::typenum::U32,
    bigint::{Limb, Odd, U256, modular::Retrieve},
    ctutils,
    error::{Error, Result},
    ops::{
        Add, AddAssign, Invert, LinearCombination, Mul, MulAssign, MulByGeneratorVartime,
        MulVartime, Neg, Reduce, ShrAssign, Sub, SubAssign,
    },
    point::{AffineCoordinates, NonIdentity},
    rand_core::{TryCryptoRng, TryRng},
    scalar::{FromUintUnchecked, IsHigh},
    sec1::{CompressedPoint, FromSec1Point, ToSec1Point},
    subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption},
    zeroize::DefaultIsZeroes,
};
use core::{
    array,
    iter::{Product, Sum},
};
use ff::{Field, PrimeField};
use hex_literal::hex;
use pkcs8::AssociatedOid;

#[cfg(feature = "alloc")]
use alloc::vec::Vec;

/// Pseudo-coordinate for fixed-based scalar mult output
pub const PSEUDO_COORDINATE_FIXED_BASE_MUL: [u8; 32] =
    hex!("deadbeef00000000000000000000000000000000000000000000000000000001");

/// SEC1 encoded point.
pub type Sec1Point = crate::sec1::Sec1Point<MockCurve>;

/// Field element bytes.
pub type FieldBytes = crate::FieldBytes<MockCurve>;

/// Non-zero scalar value.
pub type NonZeroScalar = crate::NonZeroScalar<MockCurve>;

/// Public key.
pub type PublicKey = crate::PublicKey<MockCurve>;

/// Secret key.
pub type SecretKey = crate::SecretKey<MockCurve>;

/// Scalar value type.
pub type ScalarValue = crate::ScalarValue<MockCurve>;

/// Mock elliptic curve type useful for writing tests which require a concrete
/// curve type.
///
/// Note: this type is roughly modeled off of NIST P-256, but does not provide
/// an actual cure arithmetic implementation.
#[derive(Copy, Clone, Debug, Default, Eq, PartialEq, PartialOrd, Ord)]
pub struct MockCurve;

impl Curve for MockCurve {
    type FieldBytesSize = U32;
    type Uint = U256;

    const ORDER: Odd<U256> = Odd::<U256>::from_be_hex(
        "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
    );
}

impl PrimeCurve for MockCurve {}

impl CurveArithmetic for MockCurve {
    type AffinePoint = AffinePoint;
    type ProjectivePoint = ProjectivePoint;
    type Scalar = Scalar;
}

impl AssociatedOid for MockCurve {
    /// OID for NIST P-256
    const OID: pkcs8::ObjectIdentifier = pkcs8::ObjectIdentifier::new_unwrap("1.2.840.10045.3.1.7");
}

/// Example scalar type
#[derive(Clone, Copy, Debug, Default, Eq, PartialEq, PartialOrd, Ord)]
pub struct Scalar(ScalarValue);

impl Field for Scalar {
    const ZERO: Self = Self(ScalarValue::ZERO);
    const ONE: Self = Self(ScalarValue::ONE);

    fn try_random<R: TryRng + ?Sized>(rng: &mut R) -> core::result::Result<Self, R::Error> {
        let mut bytes = FieldBytes::default();

        loop {
            rng.try_fill_bytes(&mut bytes)?;
            if let Some(scalar) = Self::from_repr(bytes).into() {
                return Ok(scalar);
            }
        }
    }

    fn is_zero(&self) -> Choice {
        self.0.is_zero()
    }

    fn square(&self) -> Self {
        unimplemented!();
    }

    fn double(&self) -> Self {
        self.add(self)
    }

    fn invert(&self) -> CtOption<Self> {
        unimplemented!();
    }

    fn sqrt(&self) -> CtOption<Self> {
        unimplemented!();
    }

    fn sqrt_ratio(_num: &Self, _div: &Self) -> (Choice, Self) {
        unimplemented!();
    }
}

impl PrimeField for Scalar {
    type Repr = FieldBytes;

    const MODULUS: &'static str =
        "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff";
    const NUM_BITS: u32 = 256;
    const CAPACITY: u32 = 255;
    const TWO_INV: Self = Self::ZERO; // BOGUS!
    const MULTIPLICATIVE_GENERATOR: Self = Self::ZERO; // BOGUS! Should be 7
    const S: u32 = 4;
    const ROOT_OF_UNITY: Self = Self::ZERO; // BOGUS! Should be 0xffc97f062a770992ba807ace842a3dfc1546cad004378daf0592d7fbb41e6602
    const ROOT_OF_UNITY_INV: Self = Self::ZERO; // BOGUS!
    const DELTA: Self = Self::ZERO; // BOGUS!

    fn from_repr(bytes: FieldBytes) -> CtOption<Self> {
        ScalarValue::from_bytes(&bytes).map(Self)
    }

    fn to_repr(&self) -> FieldBytes {
        self.0.to_bytes()
    }

    fn is_odd(&self) -> Choice {
        self.0.is_odd()
    }
}

impl Generate for Scalar {
    fn try_generate_from_rng<R: TryCryptoRng + ?Sized>(
        rng: &mut R,
    ) -> core::result::Result<Self, R::Error> {
        ScalarValue::try_generate_from_rng(rng).map(Self)
    }
}

impl AsRef<Scalar> for Scalar {
    fn as_ref(&self) -> &Scalar {
        self
    }
}

impl ConditionallySelectable for Scalar {
    fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
        Self(ScalarValue::conditional_select(&a.0, &b.0, choice))
    }
}

impl ConstantTimeEq for Scalar {
    fn ct_eq(&self, other: &Self) -> Choice {
        self.0.ct_eq(&other.0)
    }
}

impl ctutils::CtEq for Scalar {
    fn ct_eq(&self, other: &Self) -> ctutils::Choice {
        ctutils::CtEq::ct_eq(&self.0, &other.0)
    }
}

impl ctutils::CtSelect for Scalar {
    fn ct_select(&self, other: &Self, choice: ctutils::Choice) -> Self {
        Self(self.0.ct_select(&other.0, choice))
    }
}

impl DefaultIsZeroes for Scalar {}

impl Add<Scalar> for Scalar {
    type Output = Scalar;

    fn add(self, other: Scalar) -> Scalar {
        self.add(&other)
    }
}

impl Add<&Scalar> for Scalar {
    type Output = Scalar;

    fn add(self, other: &Scalar) -> Scalar {
        Self(self.0.add(&other.0))
    }
}

impl AddAssign<Scalar> for Scalar {
    fn add_assign(&mut self, other: Scalar) {
        *self = *self + other;
    }
}

impl AddAssign<&Scalar> for Scalar {
    fn add_assign(&mut self, other: &Scalar) {
        *self = *self + other;
    }
}

impl Sub<Scalar> for Scalar {
    type Output = Scalar;

    fn sub(self, other: Scalar) -> Scalar {
        self.sub(&other)
    }
}

impl Sub<&Scalar> for Scalar {
    type Output = Scalar;

    fn sub(self, other: &Scalar) -> Scalar {
        Self(self.0.sub(&other.0))
    }
}

impl SubAssign<Scalar> for Scalar {
    fn sub_assign(&mut self, other: Scalar) {
        *self = *self - other;
    }
}

impl SubAssign<&Scalar> for Scalar {
    fn sub_assign(&mut self, other: &Scalar) {
        *self = *self - other;
    }
}

crate::scalar_mul_impls!(MockCurve, Scalar);

impl Mul<Scalar> for Scalar {
    type Output = Scalar;
    fn mul(self, _other: Scalar) -> Scalar {
        unimplemented!();
    }
}

impl Mul<&Scalar> for Scalar {
    type Output = Scalar;

    fn mul(self, _other: &Scalar) -> Scalar {
        unimplemented!();
    }
}

impl MulAssign<Scalar> for Scalar {
    fn mul_assign(&mut self, _rhs: Scalar) {
        unimplemented!();
    }
}

impl MulAssign<&Scalar> for Scalar {
    fn mul_assign(&mut self, _rhs: &Scalar) {
        unimplemented!();
    }
}

impl Neg for Scalar {
    type Output = Scalar;

    fn neg(self) -> Scalar {
        Self(self.0.neg())
    }
}

impl ShrAssign<usize> for Scalar {
    fn shr_assign(&mut self, rhs: usize) {
        self.0 >>= rhs;
    }
}

impl Sum for Scalar {
    fn sum<I: Iterator<Item = Self>>(_iter: I) -> Self {
        unimplemented!();
    }
}

impl<'a> Sum<&'a Scalar> for Scalar {
    fn sum<I: Iterator<Item = &'a Scalar>>(_iter: I) -> Self {
        unimplemented!();
    }
}

impl Product for Scalar {
    fn product<I: Iterator<Item = Self>>(_iter: I) -> Self {
        unimplemented!();
    }
}

impl<'a> Product<&'a Scalar> for Scalar {
    fn product<I: Iterator<Item = &'a Scalar>>(_iter: I) -> Self {
        unimplemented!();
    }
}

impl Invert for Scalar {
    type Output = CtOption<Scalar>;

    fn invert(&self) -> CtOption<Scalar> {
        unimplemented!();
    }
}

impl Reduce<U256> for Scalar {
    fn reduce(w: &U256) -> Self {
        let (r, underflow) = w.borrowing_sub(&MockCurve::ORDER, Limb::ZERO);
        let underflow = Choice::from((underflow.0 >> (Limb::BITS - 1)) as u8);
        let reduced = U256::conditional_select(w, &r, !underflow);
        Self(ScalarValue::new(reduced).unwrap())
    }
}

impl Reduce<FieldBytes> for Scalar {
    fn reduce(_w: &FieldBytes) -> Self {
        todo!()
    }
}

impl Retrieve for Scalar {
    type Output = U256;

    fn retrieve(&self) -> U256 {
        self.0.to_uint()
    }
}

impl From<u64> for Scalar {
    fn from(n: u64) -> Scalar {
        Self(n.into())
    }
}

impl From<NonZeroScalar> for Scalar {
    fn from(scalar: NonZeroScalar) -> Self {
        scalar.0.into()
    }
}

impl From<ScalarValue> for Scalar {
    fn from(scalar: ScalarValue) -> Scalar {
        Self(scalar)
    }
}

impl From<Scalar> for ScalarValue {
    fn from(scalar: Scalar) -> ScalarValue {
        scalar.0
    }
}

impl From<Scalar> for U256 {
    fn from(scalar: Scalar) -> U256 {
        scalar.0.to_uint()
    }
}

impl TryFrom<Scalar> for NonZeroScalar {
    type Error = Error;

    fn try_from(scalar: Scalar) -> Result<Self> {
        NonZeroScalar::new(scalar).into_option().ok_or(Error)
    }
}

impl TryFrom<U256> for Scalar {
    type Error = Error;

    fn try_from(w: U256) -> Result<Self> {
        ScalarValue::new(w).into_option().map(Self).ok_or(Error)
    }
}

impl FromUintUnchecked for Scalar {
    type Uint = U256;

    fn from_uint_unchecked(uint: U256) -> Self {
        Self(ScalarValue::from_uint_unchecked(uint))
    }
}

impl From<Scalar> for FieldBytes {
    fn from(scalar: Scalar) -> Self {
        Self::from(&scalar)
    }
}

impl From<&Scalar> for FieldBytes {
    fn from(scalar: &Scalar) -> Self {
        scalar.to_repr()
    }
}

impl IsHigh for Scalar {
    fn is_high(&self) -> Choice {
        self.0.is_high()
    }
}

/// Example affine point type
#[derive(Clone, Copy, Default, Debug, Eq, PartialEq)]
pub enum AffinePoint {
    /// Result of fixed-based scalar multiplication.
    FixedBaseOutput(Scalar),

    /// Identity.
    #[default]
    Identity,

    /// Base point.
    Generator,

    /// Point corresponding to a given [`Sec1Point`].
    Other(Sec1Point),
}

impl AffineCoordinates for AffinePoint {
    type FieldRepr = FieldBytes;

    fn from_coordinates(_: &FieldBytes, _: &FieldBytes) -> CtOption<Self> {
        unimplemented!();
    }

    fn x(&self) -> FieldBytes {
        unimplemented!();
    }

    fn y(&self) -> FieldBytes {
        unimplemented!();
    }

    fn x_is_odd(&self) -> Choice {
        unimplemented!();
    }

    fn y_is_odd(&self) -> Choice {
        unimplemented!();
    }
}

impl CurveAffine for AffinePoint {
    type Curve = ProjectivePoint;
    type Scalar = Scalar;

    fn identity() -> Self {
        Self::Identity
    }

    fn generator() -> Self {
        Self::Generator
    }

    fn is_identity(&self) -> Choice {
        unimplemented!();
    }

    fn to_curve(&self) -> ProjectivePoint {
        unimplemented!();
    }
}

impl ConstantTimeEq for AffinePoint {
    fn ct_eq(&self, other: &Self) -> Choice {
        match (self, other) {
            (Self::FixedBaseOutput(scalar), Self::FixedBaseOutput(other_scalar)) => {
                scalar.ct_eq(other_scalar)
            }
            (Self::Identity, Self::Identity) | (Self::Generator, Self::Generator) => 1.into(),
            (Self::Other(point), Self::Other(other_point)) => u8::from(point == other_point).into(),
            _ => 0.into(),
        }
    }
}

impl ConditionallySelectable for AffinePoint {
    fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
        ctutils::CtSelect::ct_select(a, b, choice.into())
    }
}

impl ctutils::CtEq for AffinePoint {
    fn ct_eq(&self, other: &Self) -> ctutils::Choice {
        ConstantTimeEq::ct_eq(self, other).into()
    }
}

impl ctutils::CtSelect for AffinePoint {
    fn ct_select(&self, other: &Self, choice: ctutils::Choice) -> Self {
        // Not really constant time, but this is dev code
        if choice.to_bool() { *other } else { *self }
    }
}

impl DefaultIsZeroes for AffinePoint {}

impl From<NonIdentity<AffinePoint>> for AffinePoint {
    fn from(affine: NonIdentity<AffinePoint>) -> Self {
        affine.to_point()
    }
}

impl Generate for AffinePoint {
    fn try_generate_from_rng<R: TryCryptoRng + ?Sized>(
        _rng: &mut R,
    ) -> core::result::Result<Self, R::Error> {
        unimplemented!()
    }
}

impl FromSec1Point<MockCurve> for AffinePoint {
    fn from_sec1_point(encoded_point: &Sec1Point) -> ctutils::CtOption<Self> {
        let point = if encoded_point.is_identity() {
            Self::Identity
        } else {
            Self::Other(*encoded_point)
        };

        ctutils::CtOption::new(point, ctutils::Choice::TRUE)
    }
}

impl ToSec1Point<MockCurve> for AffinePoint {
    fn to_sec1_point(&self, compress: bool) -> Sec1Point {
        match self {
            Self::FixedBaseOutput(scalar) => Sec1Point::from_affine_coordinates(
                &scalar.to_repr(),
                &PSEUDO_COORDINATE_FIXED_BASE_MUL.into(),
                false,
            ),
            Self::Other(point) => {
                if compress == point.is_compressed() {
                    *point
                } else {
                    unimplemented!();
                }
            }
            _ => unimplemented!(),
        }
    }
}

impl Mul<Scalar> for AffinePoint {
    type Output = ProjectivePoint;

    fn mul(self, _scalar: Scalar) -> ProjectivePoint {
        unimplemented!();
    }
}

impl Mul<&Scalar> for AffinePoint {
    type Output = ProjectivePoint;

    fn mul(self, _scalar: &Scalar) -> ProjectivePoint {
        unimplemented!();
    }
}

impl MulVartime<Scalar> for AffinePoint {
    fn mul_vartime(self, _scalar: Scalar) -> ProjectivePoint {
        unimplemented!()
    }
}

impl MulVartime<&Scalar> for AffinePoint {
    fn mul_vartime(self, _scalar: &Scalar) -> ProjectivePoint {
        unimplemented!()
    }
}

impl Mul<NonZeroScalar> for AffinePoint {
    type Output = AffinePoint;

    fn mul(self, _scalar: NonZeroScalar) -> Self {
        unimplemented!();
    }
}

impl Neg for AffinePoint {
    type Output = Self;

    fn neg(self) -> Self {
        unimplemented!();
    }
}

impl TryFrom<AffinePoint> for NonIdentity<AffinePoint> {
    type Error = Error;

    fn try_from(affine: AffinePoint) -> Result<Self> {
        NonIdentity::new(affine).into_option().ok_or(Error)
    }
}

/// Example projective point type
#[derive(Clone, Copy, Default, Debug, Eq, PartialEq)]
pub enum ProjectivePoint {
    /// Result of fixed-based scalar multiplication
    FixedBaseOutput(Scalar),

    /// Is this point the identity point?
    #[default]
    Identity,

    /// Is this point the generator point?
    Generator,

    /// Is this point a different point corresponding to a given [`AffinePoint`]
    Other(AffinePoint),
}

impl<const N: usize> BatchNormalize<[ProjectivePoint; N]> for ProjectivePoint {
    type Output = [AffinePoint; N];

    fn batch_normalize(points: &[ProjectivePoint; N]) -> [AffinePoint; N] {
        array::from_fn(|index| points[index].into())
    }
}

#[cfg(feature = "alloc")]
impl BatchNormalize<[ProjectivePoint]> for ProjectivePoint {
    type Output = Vec<AffinePoint>;

    fn batch_normalize(points: &[ProjectivePoint]) -> Vec<AffinePoint> {
        points.iter().copied().map(AffinePoint::from).collect()
    }
}

impl ConstantTimeEq for ProjectivePoint {
    fn ct_eq(&self, other: &Self) -> Choice {
        match (self, other) {
            (Self::FixedBaseOutput(scalar), Self::FixedBaseOutput(other_scalar)) => {
                scalar.ct_eq(other_scalar)
            }
            (Self::Identity, Self::Identity) | (Self::Generator, Self::Generator) => 1.into(),
            (Self::Other(point), Self::Other(other_point)) => point.ct_eq(other_point),
            _ => 0.into(),
        }
    }
}

impl ConditionallySelectable for ProjectivePoint {
    fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
        ctutils::CtSelect::ct_select(a, b, choice.into())
    }
}

impl ctutils::CtEq for ProjectivePoint {
    fn ct_eq(&self, other: &Self) -> ctutils::Choice {
        ConstantTimeEq::ct_eq(self, other).into()
    }
}

impl ctutils::CtSelect for ProjectivePoint {
    fn ct_select(&self, other: &Self, choice: ctutils::Choice) -> Self {
        if choice.to_bool() { *other } else { *self }
    }
}

impl DefaultIsZeroes for ProjectivePoint {}

impl From<AffinePoint> for ProjectivePoint {
    fn from(point: AffinePoint) -> ProjectivePoint {
        match point {
            AffinePoint::FixedBaseOutput(scalar) => ProjectivePoint::FixedBaseOutput(scalar),
            AffinePoint::Identity => ProjectivePoint::Identity,
            AffinePoint::Generator => ProjectivePoint::Generator,
            other => ProjectivePoint::Other(other),
        }
    }
}

impl From<NonIdentity<ProjectivePoint>> for ProjectivePoint {
    fn from(point: NonIdentity<ProjectivePoint>) -> Self {
        point.to_point()
    }
}

impl From<ProjectivePoint> for AffinePoint {
    fn from(point: ProjectivePoint) -> AffinePoint {
        CurveGroup::to_affine(&point)
    }
}

impl Generate for ProjectivePoint {
    fn try_generate_from_rng<R: TryCryptoRng + ?Sized>(
        _rng: &mut R,
    ) -> core::result::Result<Self, R::Error> {
        unimplemented!()
    }
}

impl FromSec1Point<MockCurve> for ProjectivePoint {
    fn from_sec1_point(_point: &Sec1Point) -> ctutils::CtOption<Self> {
        unimplemented!();
    }
}

impl ToSec1Point<MockCurve> for ProjectivePoint {
    fn to_sec1_point(&self, _compress: bool) -> Sec1Point {
        unimplemented!();
    }
}

impl TryFrom<ProjectivePoint> for NonIdentity<ProjectivePoint> {
    type Error = Error;

    fn try_from(point: ProjectivePoint) -> Result<Self> {
        NonIdentity::new(point).into_option().ok_or(Error)
    }
}

impl group::Group for ProjectivePoint {
    type Scalar = Scalar;

    fn try_random<R: TryRng + ?Sized>(_rng: &mut R) -> core::result::Result<Self, R::Error> {
        unimplemented!();
    }

    fn identity() -> Self {
        Self::Identity
    }

    fn generator() -> Self {
        Self::Generator
    }

    fn is_identity(&self) -> Choice {
        Choice::from(u8::from(self == &Self::Identity))
    }

    fn double(&self) -> Self {
        unimplemented!();
    }
}

impl group::GroupEncoding for AffinePoint {
    type Repr = CompressedPoint<MockCurve>;

    #[allow(clippy::map_unwrap_or)]
    fn from_bytes(bytes: &Self::Repr) -> CtOption<Self> {
        Sec1Point::from_bytes(bytes)
            .map(|point| ctutils::CtOption::new(point, ctutils::Choice::TRUE))
            .unwrap_or_else(|_| {
                let is_identity =
                    ctutils::CtEq::ct_eq(bytes.as_slice(), Self::Repr::default().as_slice());
                ctutils::CtOption::new(Sec1Point::identity(), is_identity)
            })
            .and_then(|point| Self::from_sec1_point(&point))
            .into()
    }

    fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self> {
        Self::from_bytes(bytes)
    }

    fn to_bytes(&self) -> Self::Repr {
        let encoded = self.to_sec1_point(true);
        let mut result = CompressedPoint::<MockCurve>::default();
        result[..encoded.len()].copy_from_slice(encoded.as_bytes());
        result
    }
}

impl group::GroupEncoding for ProjectivePoint {
    type Repr = CompressedPoint<MockCurve>;

    fn from_bytes(bytes: &Self::Repr) -> CtOption<Self> {
        <AffinePoint as group::GroupEncoding>::from_bytes(bytes).map(Into::into)
    }

    fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self> {
        Self::from_bytes(bytes)
    }

    fn to_bytes(&self) -> Self::Repr {
        CurveGroup::to_affine(self).to_bytes()
    }
}

impl CurveGroup for ProjectivePoint {
    type Affine = AffinePoint;

    fn to_affine(&self) -> AffinePoint {
        match self {
            Self::FixedBaseOutput(scalar) => AffinePoint::FixedBaseOutput(*scalar),
            Self::Other(affine) => *affine,
            _ => unimplemented!(),
        }
    }
}

impl LinearCombination<[(ProjectivePoint, Scalar)]> for ProjectivePoint {}
impl<const N: usize> LinearCombination<[(ProjectivePoint, Scalar); N]> for ProjectivePoint {}

impl Add<ProjectivePoint> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn add(self, _other: ProjectivePoint) -> ProjectivePoint {
        unimplemented!();
    }
}

impl Add<&ProjectivePoint> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn add(self, _other: &ProjectivePoint) -> ProjectivePoint {
        unimplemented!();
    }
}

impl AddAssign<ProjectivePoint> for ProjectivePoint {
    fn add_assign(&mut self, _rhs: ProjectivePoint) {
        unimplemented!();
    }
}

impl AddAssign<&ProjectivePoint> for ProjectivePoint {
    fn add_assign(&mut self, _rhs: &ProjectivePoint) {
        unimplemented!();
    }
}

impl Sub<ProjectivePoint> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn sub(self, _other: ProjectivePoint) -> ProjectivePoint {
        unimplemented!();
    }
}

impl Sub<&ProjectivePoint> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn sub(self, _other: &ProjectivePoint) -> ProjectivePoint {
        unimplemented!();
    }
}

impl SubAssign<ProjectivePoint> for ProjectivePoint {
    fn sub_assign(&mut self, _rhs: ProjectivePoint) {
        unimplemented!();
    }
}

impl SubAssign<&ProjectivePoint> for ProjectivePoint {
    fn sub_assign(&mut self, _rhs: &ProjectivePoint) {
        unimplemented!();
    }
}

impl Add<AffinePoint> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn add(self, _other: AffinePoint) -> ProjectivePoint {
        unimplemented!();
    }
}

impl Add<&AffinePoint> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn add(self, _other: &AffinePoint) -> ProjectivePoint {
        unimplemented!();
    }
}

impl AddAssign<AffinePoint> for ProjectivePoint {
    fn add_assign(&mut self, _rhs: AffinePoint) {
        unimplemented!();
    }
}

impl AddAssign<&AffinePoint> for ProjectivePoint {
    fn add_assign(&mut self, _rhs: &AffinePoint) {
        unimplemented!();
    }
}

impl Sum for ProjectivePoint {
    fn sum<I: Iterator<Item = Self>>(_iter: I) -> Self {
        unimplemented!();
    }
}

impl<'a> Sum<&'a ProjectivePoint> for ProjectivePoint {
    fn sum<I: Iterator<Item = &'a ProjectivePoint>>(_iter: I) -> Self {
        unimplemented!();
    }
}

impl Sub<AffinePoint> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn sub(self, _other: AffinePoint) -> ProjectivePoint {
        unimplemented!();
    }
}

impl Sub<&AffinePoint> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn sub(self, _other: &AffinePoint) -> ProjectivePoint {
        unimplemented!();
    }
}

impl SubAssign<AffinePoint> for ProjectivePoint {
    fn sub_assign(&mut self, _rhs: AffinePoint) {
        unimplemented!();
    }
}

impl SubAssign<&AffinePoint> for ProjectivePoint {
    fn sub_assign(&mut self, _rhs: &AffinePoint) {
        unimplemented!();
    }
}

impl Mul<Scalar> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn mul(self, scalar: Scalar) -> ProjectivePoint {
        match self {
            Self::Generator => Self::FixedBaseOutput(scalar),
            _ => unimplemented!(),
        }
    }
}

impl Mul<&Scalar> for ProjectivePoint {
    type Output = ProjectivePoint;

    fn mul(self, scalar: &Scalar) -> ProjectivePoint {
        self * *scalar
    }
}

impl Mul<&Scalar> for &ProjectivePoint {
    type Output = ProjectivePoint;

    fn mul(self, _scalar: &Scalar) -> ProjectivePoint {
        unimplemented!();
    }
}

impl MulByGeneratorVartime for ProjectivePoint {}

impl MulVartime<Scalar> for ProjectivePoint {
    fn mul_vartime(self, _scalar: Scalar) -> ProjectivePoint {
        unimplemented!()
    }
}

impl MulVartime<&Scalar> for ProjectivePoint {
    fn mul_vartime(self, _scalar: &Scalar) -> ProjectivePoint {
        unimplemented!()
    }
}

impl MulAssign<Scalar> for ProjectivePoint {
    fn mul_assign(&mut self, _rhs: Scalar) {
        unimplemented!();
    }
}

impl MulAssign<&Scalar> for ProjectivePoint {
    fn mul_assign(&mut self, _rhs: &Scalar) {
        unimplemented!();
    }
}

impl Neg for ProjectivePoint {
    type Output = ProjectivePoint;

    fn neg(self) -> ProjectivePoint {
        unimplemented!();
    }
}

#[cfg(test)]
mod tests {
    use super::Scalar;
    use ff::PrimeField;
    use hex_literal::hex;

    #[test]
    fn round_trip() {
        let bytes = hex!("c9afa9d845ba75166b5c215767b1d6934e50c3db36e89b127b8a622b120f6721");
        let scalar = Scalar::from_repr(bytes.into()).unwrap();
        assert_eq!(&bytes, scalar.to_repr().as_slice());
    }
}