Move secq256k1 to short-weierstrass

Cargo.lock

@@ -9542,14 +9542,15 @@ version = "0.1.0"
 dependencies = [
  "blake2",
  "ciphersuite 0.4.2",
- "ec-divisors",
  "ff-group-tests",
  "generalized-bulletproofs-ec-gadgets",
+ "generic-array 1.2.0",
  "hex",
  "hex-literal",
  "k256",
  "prime-field",
  "rand_core 0.6.4",
+ "short-weierstrass",
  "std-shims",
 ]
 
@@ -10928,7 +10929,6 @@ version = "0.1.0"
 dependencies = [
  "ec-divisors",
  "ff",
- "generic-array 1.2.0",
  "group",
  "rand_core 0.6.4",
  "subtle",

crypto/evrf/secq256k1/Cargo.toml

@@ -18,13 +18,14 @@ hex-literal = { version = "0.4", default-features = false }
 
 std-shims = { version = "0.1", path = "../../../common/std-shims", default-features = false, optional = true }
 
+generic-array = { version = "1", default-features = false }
 k256 = { version = "0.13", default-features = false, features = ["arithmetic"] }
 prime-field = { path = "../../prime-field", default-features = false }
+short-weierstrass = { path = "../../short-weierstrass", default-features = false }
 
 blake2 = { version = "0.10", default-features = false }
 ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false }
-ec-divisors = { git = "https://github.com/monero-oxide/monero-oxide", rev = "a6f8797007e768488568b821435cf5006517a962", default-features = false }
+generalized-bulletproofs-ec-gadgets = { git = "https://github.com/monero-oxide/monero-oxide", rev = "a6f8797007e768488568b821435cf5006517a962", default-features = false, optional = true }
-generalized-bulletproofs-ec-gadgets = { git = "https://github.com/monero-oxide/monero-oxide", rev = "a6f8797007e768488568b821435cf5006517a962", default-features = false }
 
 [dev-dependencies]
 hex = "0.4"
@@ -34,6 +35,6 @@ rand_core = { version = "0.6", features = ["std"] }
 ff-group-tests = { path = "../../ff-group-tests" }
 
 [features]
-alloc = ["std-shims", "k256/alloc", "prime-field/alloc", "ciphersuite/alloc"]
+alloc = ["std-shims", "generic-array/alloc", "k256/alloc", "prime-field/alloc", "short-weierstrass/alloc", "ciphersuite/alloc", "generalized-bulletproofs-ec-gadgets"]
-std = ["std-shims/std", "k256/std", "prime-field/std", "blake2/std", "ciphersuite/std", "ec-divisors/std", "generalized-bulletproofs-ec-gadgets/std"]
+std = ["alloc", "std-shims/std", "k256/std", "prime-field/std", "blake2/std", "ciphersuite/std", "generalized-bulletproofs-ec-gadgets/std"]
 default = ["std"]

crypto/evrf/secq256k1/src/lib.rs

@@ -4,12 +4,17 @@
 
 #[allow(unused_imports)]
 use std_shims::prelude::*;
-#[cfg(any(feature = "alloc", feature = "std"))]
+#[cfg(feature = "alloc")]
 use std_shims::io::{self, Read};
 
+// Doesn't use the `generic-array 0.14` exported by `k256::elliptic_curve` as we need `1.0`
+use generic_array::{
+  typenum::{U, U33},
+  GenericArray,
+};
 use k256::elliptic_curve::{
+  subtle::{Choice, ConstantTimeEq, ConditionallySelectable},
   zeroize::Zeroize,
-  generic_array::typenum::U,
   group::{
     ff::{PrimeField, FromUniformBytes},
     Group,
@@ -25,34 +30,85 @@ prime_field::odd_prime_field!(
 
 pub use k256::Scalar as FieldElement;
 
-mod point;
+use short_weierstrass::{ShortWeierstrass, Affine, Projective};
-pub use point::Point;
 
-pub(crate) fn u8_from_bool(bit_ref: &mut bool) -> u8 {
-  use core::hint::black_box;
-  use prime_field::zeroize::Zeroize;
-
-  let bit_ref = black_box(bit_ref);
-
-  let mut bit = black_box(*bit_ref);
-  let res = black_box(u8::from(bit));
-  bit.zeroize();
-  debug_assert!((res | 1) == 1);
-
-  bit_ref.zeroize();
-  res
-}
-
-/// Ciphersuite for Secq256k1.
-///
-/// hash_to_F is implemented with a naive concatenation of the dst and data, allowing transposition
-/// between the two. This means `dst: b"abc", data: b"def"`, will produce the same scalar as
-/// `dst: "abcdef", data: b""`. Please use carefully, not letting dsts be substrings of each other.
 #[derive(Clone, Copy, PartialEq, Eq, Debug)]
 pub struct Secq256k1;
 impl Zeroize for Secq256k1 {
   fn zeroize(&mut self) {}
 }
+
+impl ShortWeierstrass for Secq256k1 {
+  type FieldElement = FieldElement;
+  const A: FieldElement = FieldElement::ZERO;
+  const B: FieldElement = {
+    let two = FieldElement::ONE.add(&FieldElement::ONE);
+    let four = two.add(&two);
+    let six = four.add(&two);
+    six.add(&FieldElement::ONE)
+  };
+  const GENERATOR: Affine<Self> = Affine::from_xy_unchecked(FieldElement::ONE, {
+    let y_be =
+      hex_literal::hex!("0c7c97045a2074634909abdf82c9bd0248916189041f2af0c1b800d1ffc278c0");
+    let mut res = FieldElement::ZERO;
+    let mut i = 0;
+    while i < 32 {
+      let mut j = 0;
+      while j < 8 {
+        // Shift over the existing result
+        res = res.add(&res);
+        // Add this bit, if set
+        if ((y_be[i] >> (8 - 1 - j)) & 1) == 1 {
+          res = res.add(&FieldElement::ONE);
+        }
+        j += 1;
+      }
+      i += 1;
+    }
+    res
+  });
+  type Scalar = Scalar;
+
+  type Repr = GenericArray<u8, U33>;
+  // Use an all-zero encoding for the identity as `0` isn't the `x` coordinate of an on-curve point
+  // This uses `unsafe` to construct a `GenericArray` at compile-time as ``
+  const IDENTITY: Self::Repr = GenericArray::from_array([0; 33]);
+  fn compress(x: Self::FieldElement, odd_y: Choice) -> Self::Repr {
+    // If `y` is odd, followed by the big-endian `x` coordinate
+    let mut res = GenericArray::default();
+    res[0] = odd_y.unwrap_u8();
+    {
+      let res: &mut [u8] = res.as_mut();
+      res[1 ..].copy_from_slice(x.to_repr().as_ref());
+    }
+    res
+  }
+  fn decode_compressed(bytes: &Self::Repr) -> (<Self::FieldElement as PrimeField>::Repr, Choice) {
+    // Parse out if `y` is odd
+    let odd_y = Choice::from(bytes[0] & 1);
+    // Check if the extra byte was malleated
+    let invalid = !bytes[0].ct_eq(&odd_y.unwrap_u8());
+
+    // Copy the alleged `x` coordinate, overwriting with `0xffffff...` if the sign byte was
+    // malleated (causing the `x` coordinate to be invalid)
+    let mut x = <Self::FieldElement as PrimeField>::Repr::default();
+    {
+      let x: &mut [u8] = x.as_mut();
+      for i in 0 .. 32 {
+        x[i] = <_>::conditional_select(&bytes[1 + i], &u8::MAX, invalid);
+      }
+    }
+
+    (x, odd_y)
+  }
+  // No points have a torsion element as this a prime-order curve
+  fn has_torsion_element(_point: Projective<Self>) -> Choice {
+    0.into()
+  }
+}
+
+pub type Point = Projective<Secq256k1>;
+
 impl ciphersuite::Ciphersuite for Secq256k1 {
   type F = Scalar;
   type G = Point;
@@ -64,6 +120,10 @@ impl ciphersuite::Ciphersuite for Secq256k1 {
     Point::generator()
   }
 
+  /// `hash_to_F` is implemented with a naive concatenation of the `dst` and `data`, allowing
+  /// transposition between the two. This means `dst: b"abc", data: b"def"`, will produce the same
+  /// scalar as `dst: "abcdef", data: b""`. Please use carefully, not letting `dst` valuess be
+  /// substrings of each other.
   fn hash_to_F(dst: &[u8], data: &[u8]) -> Self::F {
     use blake2::Digest;
     <Scalar as FromUniformBytes<64>>::from_uniform_bytes(
@@ -73,7 +133,7 @@ impl ciphersuite::Ciphersuite for Secq256k1 {
 
   // We override the provided impl, which compares against the reserialization, because
   // we already require canonicity
-  #[cfg(any(feature = "alloc", feature = "std"))]
+  #[cfg(feature = "alloc")]
   #[allow(non_snake_case)]
   fn read_G<R: Read>(reader: &mut R) -> io::Result<Self::G> {
     use ciphersuite::group::GroupEncoding;
@@ -87,6 +147,35 @@ impl ciphersuite::Ciphersuite for Secq256k1 {
   }
 }
 
+#[cfg(feature = "alloc")]
 impl generalized_bulletproofs_ec_gadgets::DiscreteLogParameter for Secq256k1 {
   type ScalarBits = U<{ Scalar::NUM_BITS as usize }>;
 }
+
+#[test]
+fn test_curve() {
+  ff_group_tests::group::test_prime_group_bits::<_, Point>(&mut rand_core::OsRng);
+}
+
+#[test]
+fn generator() {
+  use ciphersuite::group::GroupEncoding;
+  assert_eq!(
+    Point::generator(),
+    Point::from_bytes(GenericArray::from_slice(&hex_literal::hex!(
+      "000000000000000000000000000000000000000000000000000000000000000001"
+    )))
+    .unwrap()
+  );
+}
+
+#[test]
+fn zero_x_is_off_curve() {
+  assert!(bool::from(Affine::<Secq256k1>::decompress(FieldElement::ZERO, 1.into()).is_none()));
+}
+
+// Checks random won't infinitely loop
+#[test]
+fn random() {
+  Point::random(&mut rand_core::OsRng);
+}

crypto/evrf/secq256k1/src/point.rs

@@ -1,439 +0,0 @@
-use core::{
-  borrow::Borrow,
-  ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
-  iter::Sum,
-};
-
-use k256::elliptic_curve::{
-  zeroize::Zeroize,
-  subtle::{Choice, CtOption, ConstantTimeEq, ConditionallySelectable, ConditionallyNegatable},
-  generic_array::{typenum::U33, GenericArray},
-  rand_core::RngCore,
-  group::{
-    ff::{Field, PrimeField, PrimeFieldBits},
-    Group, GroupEncoding,
-    prime::PrimeGroup,
-  },
-};
-
-use crate::{u8_from_bool, Scalar, FieldElement};
-
-fn recover_y(x: FieldElement) -> CtOption<FieldElement> {
-  // x**3 + B since a = 0
-  ((x.square() * x) + FieldElement::from(7u64)).sqrt()
-}
-
-/// Point.
-#[derive(Clone, Copy, Debug)]
-#[repr(C)]
-pub struct Point {
-  x: FieldElement, // / Z
-  y: FieldElement, // / Z
-  z: FieldElement,
-}
-
-impl Zeroize for Point {
-  fn zeroize(&mut self) {
-    self.x.zeroize();
-    self.y.zeroize();
-    self.z.zeroize();
-    let identity = Self::identity();
-    self.x = identity.x;
-    self.y = identity.y;
-    self.z = identity.z;
-  }
-}
-
-impl ConstantTimeEq for Point {
-  fn ct_eq(&self, other: &Self) -> Choice {
-    let x1 = self.x * other.z;
-    let x2 = other.x * self.z;
-
-    let y1 = self.y * other.z;
-    let y2 = other.y * self.z;
-
-    // Identity or equivalent
-    (self.z.is_zero() & other.z.is_zero()) | (x1.ct_eq(&x2) & y1.ct_eq(&y2))
-  }
-}
-
-impl PartialEq for Point {
-  fn eq(&self, other: &Point) -> bool {
-    self.ct_eq(other).into()
-  }
-}
-
-impl Eq for Point {}
-
-impl ConditionallySelectable for Point {
-  fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
-    Point {
-      x: FieldElement::conditional_select(&a.x, &b.x, choice),
-      y: FieldElement::conditional_select(&a.y, &b.y, choice),
-      z: FieldElement::conditional_select(&a.z, &b.z, choice),
-    }
-  }
-}
-
-impl Add for Point {
-  type Output = Point;
-  #[allow(non_snake_case)]
-  fn add(self, other: Self) -> Self {
-    // add-2015-rcb
-
-    let a = FieldElement::ZERO;
-    let B = FieldElement::from(7u64);
-    let b3 = B + B + B;
-
-    let X1 = self.x;
-    let Y1 = self.y;
-    let Z1 = self.z;
-    let X2 = other.x;
-    let Y2 = other.y;
-    let Z2 = other.z;
-
-    let t0 = X1 * X2;
-    let t1 = Y1 * Y2;
-    let t2 = Z1 * Z2;
-    let t3 = X1 + Y1;
-    let t4 = X2 + Y2;
-    let t3 = t3 * t4;
-    let t4 = t0 + t1;
-    let t3 = t3 - t4;
-    let t4 = X1 + Z1;
-    let t5 = X2 + Z2;
-    let t4 = t4 * t5;
-    let t5 = t0 + t2;
-    let t4 = t4 - t5;
-    let t5 = Y1 + Z1;
-    let X3 = Y2 + Z2;
-    let t5 = t5 * X3;
-    let X3 = t1 + t2;
-    let t5 = t5 - X3;
-    let Z3 = a * t4;
-    let X3 = b3 * t2;
-    let Z3 = X3 + Z3;
-    let X3 = t1 - Z3;
-    let Z3 = t1 + Z3;
-    let Y3 = X3 * Z3;
-    let t1 = t0 + t0;
-    let t1 = t1 + t0;
-    let t2 = a * t2;
-    let t4 = b3 * t4;
-    let t1 = t1 + t2;
-    let t2 = t0 - t2;
-    let t2 = a * t2;
-    let t4 = t4 + t2;
-    let t0 = t1 * t4;
-    let Y3 = Y3 + t0;
-    let t0 = t5 * t4;
-    let X3 = t3 * X3;
-    let X3 = X3 - t0;
-    let t0 = t3 * t1;
-    let Z3 = t5 * Z3;
-    let Z3 = Z3 + t0;
-    Point { x: X3, y: Y3, z: Z3 }
-  }
-}
-
-impl AddAssign for Point {
-  fn add_assign(&mut self, other: Point) {
-    *self = *self + other;
-  }
-}
-
-impl Add<&Point> for Point {
-  type Output = Point;
-  fn add(self, other: &Point) -> Point {
-    self + *other
-  }
-}
-
-impl AddAssign<&Point> for Point {
-  fn add_assign(&mut self, other: &Point) {
-    *self += *other;
-  }
-}
-
-impl Neg for Point {
-  type Output = Point;
-  fn neg(self) -> Self {
-    Point { x: self.x, y: -self.y, z: self.z }
-  }
-}
-
-impl Sub for Point {
-  type Output = Point;
-  #[allow(clippy::suspicious_arithmetic_impl)]
-  fn sub(self, other: Self) -> Self {
-    self + other.neg()
-  }
-}
-
-impl SubAssign for Point {
-  fn sub_assign(&mut self, other: Point) {
-    *self = *self - other;
-  }
-}
-
-impl Sub<&Point> for Point {
-  type Output = Point;
-  fn sub(self, other: &Point) -> Point {
-    self - *other
-  }
-}
-
-impl SubAssign<&Point> for Point {
-  fn sub_assign(&mut self, other: &Point) {
-    *self -= *other;
-  }
-}
-
-impl Group for Point {
-  type Scalar = Scalar;
-  fn random(mut rng: impl RngCore) -> Self {
-    loop {
-      let mut bytes = GenericArray::default();
-      rng.fill_bytes(bytes.as_mut());
-      let opt = Self::from_bytes(&bytes);
-      if opt.is_some().into() {
-        return opt.unwrap();
-      }
-    }
-  }
-  fn identity() -> Self {
-    Point { x: FieldElement::ZERO, y: FieldElement::ONE, z: FieldElement::ZERO }
-  }
-  fn generator() -> Self {
-    // Point with the lowest valid x-coordinate
-    Point {
-      x: FieldElement::from_repr(
-        hex_literal::hex!("0000000000000000000000000000000000000000000000000000000000000001")
-          .into(),
-      )
-      .unwrap(),
-      y: FieldElement::from_repr(
-        hex_literal::hex!("0C7C97045A2074634909ABDF82C9BD0248916189041F2AF0C1B800D1FFC278C0")
-          .into(),
-      )
-      .unwrap(),
-      z: FieldElement::ONE,
-    }
-  }
-  fn is_identity(&self) -> Choice {
-    self.z.ct_eq(&FieldElement::ZERO)
-  }
-  #[allow(non_snake_case)]
-  fn double(&self) -> Self {
-    // dbl-2007-bl
-
-    let a = FieldElement::ZERO;
-
-    let X1 = self.x;
-    let Y1 = self.y;
-    let Z1 = self.z;
-
-    let XX = X1 * X1;
-    let ZZ = Z1 * Z1;
-    let w = (a * ZZ) + XX.double() + XX;
-    let s = (Y1 * Z1).double();
-    let ss = s * s;
-    let sss = s * ss;
-    let R = Y1 * s;
-    let RR = R * R;
-    let B = X1 + R;
-    let B = (B * B) - XX - RR;
-    let h = (w * w) - B.double();
-    let X3 = h * s;
-    let Y3 = w * (B - h) - RR.double();
-    let Z3 = sss;
-
-    let res = Self { x: X3, y: Y3, z: Z3 };
-    // If self is identity, res will not be well-formed
-    // Accordingly, we return self if self was the identity
-    Self::conditional_select(&res, self, self.is_identity())
-  }
-}
-
-impl Sum<Point> for Point {
-  fn sum<I: Iterator<Item = Point>>(iter: I) -> Point {
-    let mut res = Self::identity();
-    for i in iter {
-      res += i;
-    }
-    res
-  }
-}
-
-impl<'a> Sum<&'a Point> for Point {
-  fn sum<I: Iterator<Item = &'a Point>>(iter: I) -> Point {
-    Point::sum(iter.cloned())
-  }
-}
-
-impl Mul<Scalar> for Point {
-  type Output = Point;
-  fn mul(self, mut other: Scalar) -> Point {
-    // Precompute the optimal amount that's a multiple of 2
-    let mut table = [Point::identity(); 16];
-    table[1] = self;
-    for i in 2 .. 16 {
-      table[i] = table[i - 1] + self;
-    }
-
-    let mut res = Self::identity();
-    let mut bits = 0;
-    for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
-      bits <<= 1;
-      let mut bit = u8_from_bool(bit.deref_mut());
-      bits |= bit;
-      bit.zeroize();
-
-      if ((i + 1) % 4) == 0 {
-        if i != 3 {
-          for _ in 0 .. 4 {
-            res = res.double();
-          }
-        }
-
-        let mut term = table[0];
-        for (j, candidate) in table[1 ..].iter().enumerate() {
-          let j = j + 1;
-          term = Self::conditional_select(&term, candidate, usize::from(bits).ct_eq(&j));
-        }
-        res += term;
-        bits = 0;
-      }
-    }
-    other.zeroize();
-    res
-  }
-}
-
-impl MulAssign<Scalar> for Point {
-  fn mul_assign(&mut self, other: Scalar) {
-    *self = *self * other;
-  }
-}
-
-impl Mul<&Scalar> for Point {
-  type Output = Point;
-  fn mul(self, other: &Scalar) -> Point {
-    self * *other
-  }
-}
-
-impl MulAssign<&Scalar> for Point {
-  fn mul_assign(&mut self, other: &Scalar) {
-    *self *= *other;
-  }
-}
-
-impl GroupEncoding for Point {
-  type Repr = GenericArray<u8, U33>;
-
-  fn from_bytes(bytes: &Self::Repr) -> CtOption<Self> {
-    // Extract and clear the sign bit
-    let sign = Choice::from(bytes[0] & 1);
-
-    // Parse x, recover y
-    FieldElement::from_repr(*GenericArray::from_slice(&bytes[1 ..])).and_then(|x| {
-      let is_identity = x.is_zero();
-
-      let y = recover_y(x).map(|mut y| {
-        y.conditional_negate(y.is_odd().ct_eq(&!sign));
-        y
-      });
-
-      // If this the identity, set y to 1
-      let y =
-        CtOption::conditional_select(&y, &CtOption::new(FieldElement::ONE, 1.into()), is_identity);
-      // If this the identity, set y to 1 and z to 0 (instead of 1)
-      let z = <_>::conditional_select(&FieldElement::ONE, &FieldElement::ZERO, is_identity);
-      // Create the point if we have a y solution
-      let point = y.map(|y| Point { x, y, z });
-
-      let not_negative_zero = !(is_identity & sign);
-      // Only return the point if it isn't -0 and the sign byte wasn't malleated
-      CtOption::conditional_select(
-        &CtOption::new(Point::identity(), 0.into()),
-        &point,
-        not_negative_zero & ((bytes[0] & 1).ct_eq(&bytes[0])),
-      )
-    })
-  }
-
-  fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self> {
-    Point::from_bytes(bytes)
-  }
-
-  fn to_bytes(&self) -> Self::Repr {
-    let Some(z) = Option::<FieldElement>::from(self.z.invert()) else {
-      return *GenericArray::from_slice(&[0; 33]);
-    };
-    let x = self.x * z;
-    let y = self.y * z;
-
-    let mut res = *GenericArray::from_slice(&[0; 33]);
-    res[1 ..].as_mut().copy_from_slice(&x.to_repr());
-
-    // The following conditional select normalizes the sign to 0 when x is 0
-    let y_sign = u8::conditional_select(&y.is_odd().unwrap_u8(), &0, x.ct_eq(&FieldElement::ZERO));
-    res[0] |= y_sign;
-    res
-  }
-}
-
-impl PrimeGroup for Point {}
-
-impl ec_divisors::DivisorCurve for Point {
-  type FieldElement = FieldElement;
-  type XyPoint = ec_divisors::Projective<Self>;
-
-  fn interpolator_for_scalar_mul() -> impl Borrow<ec_divisors::Interpolator<Self::FieldElement>> {
-    static PRECOMPUTE: std_shims::sync::LazyLock<ec_divisors::Interpolator<FieldElement>> =
-      std_shims::sync::LazyLock::new(|| {
-        ec_divisors::Interpolator::new(usize::try_from(130).unwrap())
-      });
-    &*PRECOMPUTE
-  }
-
-  fn a() -> Self::FieldElement {
-    FieldElement::from(0u64)
-  }
-  fn b() -> Self::FieldElement {
-    FieldElement::from(7u64)
-  }
-
-  fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
-    let z: Self::FieldElement = Option::from(point.z.invert())?;
-    Some((point.x * z, point.y * z))
-  }
-}
-
-#[test]
-fn test_curve() {
-  ff_group_tests::group::test_prime_group_bits::<_, Point>(&mut rand_core::OsRng);
-}
-
-#[test]
-fn generator() {
-  assert_eq!(
-    Point::generator(),
-    Point::from_bytes(GenericArray::from_slice(&hex_literal::hex!(
-      "000000000000000000000000000000000000000000000000000000000000000001"
-    )))
-    .unwrap()
-  );
-}
-
-#[test]
-fn zero_x_is_invalid() {
-  assert!(Option::<FieldElement>::from(recover_y(FieldElement::ZERO)).is_none());
-}
-
-// Checks random won't infinitely loop
-#[test]
-fn random() {
-  Point::random(&mut rand_core::OsRng);
-}

crypto/short-weierstrass/Cargo.toml

@@ -21,10 +21,9 @@ rand_core = { version = "0.6", default-features = false }
 ff = { version = "0.13", default-features = false, features = ["bits"] }
 group = { version = "0.13", default-features = false }
 
-generic-array = { version = "1", default-features = false, optional = true }
 ec-divisors = { git = "https://github.com/monero-oxide/monero-oxide", rev = "a6f8797007e768488568b821435cf5006517a962", default-features = false, optional = true }
 
 [features]
-alloc = ["zeroize/alloc", "rand_core/alloc", "ff/alloc", "group/alloc", "generic-array", "ec-divisors"]
+alloc = ["zeroize/alloc", "rand_core/alloc", "ff/alloc", "group/alloc", "ec-divisors"]
 std = ["alloc", "zeroize/std", "subtle/std", "rand_core/std", "ff/std"]
 default = ["std"]