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use super::{FieldElement, ProjectivePoint, CURVE_EQUATION_B};
use crate::{EncodedPoint, FieldBytes, NonZeroScalar, Secp256k1};
use core::ops::{Mul, Neg};
use elliptic_curve::{
generic_array::arr,
sec1::{self, FromEncodedPoint, ToEncodedPoint},
subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption},
weierstrass::point::Decompress,
};
#[cfg(feature = "zeroize")]
use elliptic_curve::zeroize::Zeroize;
#[derive(Clone, Copy, Debug)]
#[cfg_attr(docsrs, doc(cfg(feature = "arithmetic")))]
pub struct AffinePoint {
pub(crate) x: FieldElement,
pub(crate) y: FieldElement,
pub(super) infinity: Choice,
}
impl AffinePoint {
pub fn generator() -> AffinePoint {
AffinePoint {
x: FieldElement::from_bytes(&arr![u8;
0x79, 0xbe, 0x66, 0x7e, 0xf9, 0xdc, 0xbb, 0xac, 0x55, 0xa0, 0x62, 0x95, 0xce, 0x87,
0x0b, 0x07, 0x02, 0x9b, 0xfc, 0xdb, 0x2d, 0xce, 0x28, 0xd9, 0x59, 0xf2, 0x81, 0x5b,
0x16, 0xf8, 0x17, 0x98
])
.unwrap(),
y: FieldElement::from_bytes(&arr![u8;
0x48, 0x3a, 0xda, 0x77, 0x26, 0xa3, 0xc4, 0x65, 0x5d, 0xa4, 0xfb, 0xfc, 0x0e, 0x11,
0x08, 0xa8, 0xfd, 0x17, 0xb4, 0x48, 0xa6, 0x85, 0x54, 0x19, 0x9c, 0x47, 0xd0, 0x8f,
0xfb, 0x10, 0xd4, 0xb8
])
.unwrap(),
infinity: Choice::from(0),
}
}
pub fn identity() -> AffinePoint {
Self {
x: FieldElement::zero(),
y: FieldElement::zero(),
infinity: Choice::from(1),
}
}
pub fn is_identity(&self) -> Choice {
self.infinity
}
}
impl ConditionallySelectable for AffinePoint {
fn conditional_select(a: &AffinePoint, b: &AffinePoint, choice: Choice) -> AffinePoint {
AffinePoint {
x: FieldElement::conditional_select(&a.x, &b.x, choice),
y: FieldElement::conditional_select(&a.y, &b.y, choice),
infinity: Choice::conditional_select(&a.infinity, &b.infinity, choice),
}
}
}
impl ConstantTimeEq for AffinePoint {
fn ct_eq(&self, other: &AffinePoint) -> Choice {
(self.x.negate(1) + &other.x).normalizes_to_zero()
& (self.y.negate(1) + &other.y).normalizes_to_zero()
& self.infinity.ct_eq(&other.infinity)
}
}
impl Default for AffinePoint {
fn default() -> Self {
Self::identity()
}
}
impl PartialEq for AffinePoint {
fn eq(&self, other: &AffinePoint) -> bool {
self.ct_eq(other).into()
}
}
impl Eq for AffinePoint {}
impl Decompress<Secp256k1> for AffinePoint {
fn decompress(x_bytes: &FieldBytes, y_is_odd: Choice) -> CtOption<Self> {
FieldElement::from_bytes(x_bytes).and_then(|x| {
let alpha = (x * &x * &x) + &CURVE_EQUATION_B;
let beta = alpha.sqrt();
beta.map(|beta| {
let y = FieldElement::conditional_select(
&beta.negate(1),
&beta,
beta.normalize().is_odd().ct_eq(&y_is_odd),
);
Self {
x,
y: y.normalize(),
infinity: Choice::from(0),
}
})
})
}
}
impl FromEncodedPoint<Secp256k1> for AffinePoint {
fn from_encoded_point(encoded_point: &EncodedPoint) -> Option<Self> {
match encoded_point.coordinates() {
sec1::Coordinates::Identity => Some(Self::identity()),
sec1::Coordinates::Compressed { x, y_is_odd } => {
AffinePoint::decompress(x, Choice::from(y_is_odd as u8)).into()
}
sec1::Coordinates::Uncompressed { x, y } => {
let x = FieldElement::from_bytes(x);
let y = FieldElement::from_bytes(y);
x.and_then(|x| {
y.and_then(|y| {
let lhs = (y * &y).negate(1);
let rhs = x * &x * &x + &CURVE_EQUATION_B;
let point = AffinePoint {
x,
y,
infinity: Choice::from(0),
};
CtOption::new(point, (lhs + &rhs).normalizes_to_zero())
})
})
.into()
}
}
}
}
impl ToEncodedPoint<Secp256k1> for AffinePoint {
fn to_encoded_point(&self, compress: bool) -> EncodedPoint {
EncodedPoint::conditional_select(
&EncodedPoint::from_affine_coordinates(
&self.x.to_bytes(),
&self.y.to_bytes(),
compress,
),
&EncodedPoint::identity(),
self.infinity,
)
}
}
impl From<AffinePoint> for EncodedPoint {
fn from(affine_point: AffinePoint) -> EncodedPoint {
affine_point.to_encoded_point(true)
}
}
impl Mul<NonZeroScalar> for AffinePoint {
type Output = AffinePoint;
fn mul(self, scalar: NonZeroScalar) -> Self {
(ProjectivePoint::from(self) * scalar.as_ref()).to_affine()
}
}
impl Neg for AffinePoint {
type Output = AffinePoint;
fn neg(self) -> Self::Output {
AffinePoint {
x: self.x,
y: self.y.negate(1).normalize_weak(),
infinity: self.infinity,
}
}
}
#[cfg(feature = "zeroize")]
impl Zeroize for AffinePoint {
fn zeroize(&mut self) {
self.x.zeroize();
self.y.zeroize();
}
}
#[cfg(test)]
mod tests {
use super::AffinePoint;
use crate::EncodedPoint;
use elliptic_curve::sec1::{FromEncodedPoint, ToEncodedPoint};
use hex_literal::hex;
const UNCOMPRESSED_BASEPOINT: &[u8] = &hex!(
"0479BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8"
);
const COMPRESSED_BASEPOINT: &[u8] =
&hex!("0279BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798");
#[test]
fn uncompressed_round_trip() {
let pubkey = EncodedPoint::from_bytes(UNCOMPRESSED_BASEPOINT).unwrap();
let res: EncodedPoint = AffinePoint::from_encoded_point(&pubkey)
.unwrap()
.to_encoded_point(false);
assert_eq!(res, pubkey);
}
#[test]
fn compressed_round_trip() {
let pubkey = EncodedPoint::from_bytes(COMPRESSED_BASEPOINT).unwrap();
let res: EncodedPoint = AffinePoint::from_encoded_point(&pubkey)
.unwrap()
.to_encoded_point(true);
assert_eq!(res, pubkey);
}
#[test]
fn uncompressed_to_compressed() {
let encoded = EncodedPoint::from_bytes(UNCOMPRESSED_BASEPOINT).unwrap();
let res = AffinePoint::from_encoded_point(&encoded)
.unwrap()
.to_encoded_point(true);
assert_eq!(res.as_bytes(), COMPRESSED_BASEPOINT);
}
#[test]
fn compressed_to_uncompressed() {
let encoded = EncodedPoint::from_bytes(COMPRESSED_BASEPOINT).unwrap();
let res = AffinePoint::from_encoded_point(&encoded)
.unwrap()
.to_encoded_point(false);
assert_eq!(res.as_bytes(), UNCOMPRESSED_BASEPOINT);
}
#[test]
fn decompress() {
let encoded = EncodedPoint::from_bytes(COMPRESSED_BASEPOINT).unwrap();
let decompressed = encoded.decompress().unwrap();
assert_eq!(decompressed.as_bytes(), UNCOMPRESSED_BASEPOINT);
}
#[test]
fn affine_negation() {
let basepoint = AffinePoint::generator();
assert_eq!((-(-basepoint)), basepoint);
}
}