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+/// Provides both inherent and trait impls for a field element type which are
+/// backed by a core set of arithmetic functions specified as macro arguments.
+///
+/// # Inherent impls
+/// - `const ZERO: Self`
+/// - `const ONE: Self` (multiplicative identity)
+/// - `pub fn from_be_bytes`
+/// - `pub fn from_be_slice`
+/// - `pub fn from_le_bytes`
+/// - `pub fn from_le_slice`
+/// - `pub fn from_uint`
+/// - `fn from_uint_unchecked`
+/// - `pub fn to_be_bytes`
+/// - `pub fn to_le_bytes`
+/// - `pub fn to_canonical`
+/// - `pub fn is_odd`
+/// - `pub fn is_zero`
+/// - `pub fn double`
+///
+/// NOTE: field implementations must provide their own inherent impls of
+/// the following methods in order for the code generated by this macro to
+/// compile:
+///
+/// - `pub fn invert`
+/// - `pub fn sqrt`
+///
+/// # Trait impls
+/// - `AsRef<$arr>`
+/// - `ConditionallySelectable`
+/// - `ConstantTimeEq`
+/// - `ConstantTimeGreater`
+/// - `ConstantTimeLess`
+/// - `Default`
+/// - `DefaultIsZeroes`
+/// - `Eq`
+/// - `Field`
+/// - `PartialEq`
+///
+/// ## Ops
+/// - `Add`
+/// - `AddAssign`
+/// - `Sub`
+/// - `SubAssign`
+/// - `Mul`
+/// - `MulAssign`
+/// - `Neg`
+#[macro_export]
+macro_rules! impl_field_element {
+ (
+ $fe:tt,
+ $bytes:ty,
+ $uint:ty,
+ $modulus:expr,
+ $arr:ty,
+ $from_mont:ident,
+ $to_mont:ident,
+ $add:ident,
+ $sub:ident,
+ $mul:ident,
+ $neg:ident,
+ $square:ident
+ ) => {
+ impl $fe {
+ /// Zero element.
+ pub const ZERO: Self = Self(<$uint>::ZERO);
+
+ /// Multiplicative identity.
+ pub const ONE: Self = Self::from_uint_unchecked(<$uint>::ONE);
+
+ /// Create a [`
+ #[doc = stringify!($fe)]
+ /// `] from a canonical big-endian representation.
+ pub fn from_be_bytes(repr: $bytes) -> $crate::subtle::CtOption<Self> {
+ use $crate::bigint::ArrayEncoding as _;
+ Self::from_uint(<$uint>::from_be_byte_array(repr))
+ }
+
+ /// Decode [`
+ #[doc = stringify!($fe)]
+ /// `] from a big endian byte slice.
+ pub fn from_be_slice(slice: &[u8]) -> $crate::Result<Self> {
+ <$uint as $crate::bigint::Encoding>::Repr::try_from(slice)
+ .ok()
+ .and_then(|array| Self::from_be_bytes(array.into()).into())
+ .ok_or($crate::Error)
+ }
+
+ /// Create a [`
+ #[doc = stringify!($fe)]
+ /// `] from a canonical little-endian representation.
+ pub fn from_le_bytes(repr: $bytes) -> $crate::subtle::CtOption<Self> {
+ use $crate::bigint::ArrayEncoding as _;
+ Self::from_uint(<$uint>::from_le_byte_array(repr))
+ }
+
+ /// Decode [`
+ #[doc = stringify!($fe)]
+ /// `] from a little endian byte slice.
+ pub fn from_le_slice(slice: &[u8]) -> $crate::Result<Self> {
+ <$uint as $crate::bigint::Encoding>::Repr::try_from(slice)
+ .ok()
+ .and_then(|array| Self::from_le_bytes(array.into()).into())
+ .ok_or($crate::Error)
+ }
+
+ /// Decode [`
+ #[doc = stringify!($fe)]
+ /// `]
+ /// from [`
+ #[doc = stringify!($uint)]
+ /// `] converting it into Montgomery form:
+ ///
+ /// ```text
+ /// w * R^2 * R^-1 mod p = wR mod p
+ /// ```
+ pub fn from_uint(uint: $uint) -> $crate::subtle::CtOption<Self> {
+ use $crate::subtle::ConstantTimeLess as _;
+ let is_some = uint.ct_lt(&$modulus);
+ $crate::subtle::CtOption::new(Self::from_uint_unchecked(uint), is_some)
+ }
+
+ /// Parse a [`
+ #[doc = stringify!($fe)]
+ /// `] from big endian hex-encoded bytes.
+ ///
+ /// Does *not* perform a check that the field element does not overflow the order.
+ ///
+ /// This method is primarily intended for defining internal constants.
+ #[allow(dead_code)]
+ pub(crate) const fn from_be_hex(hex: &str) -> Self {
+ Self::from_uint_unchecked(<$uint>::from_be_hex(hex))
+ }
+
+ /// Parse a [`
+ #[doc = stringify!($fe)]
+ /// `] from little endian hex-encoded bytes.
+ ///
+ /// Does *not* perform a check that the field element does not overflow the order.
+ ///
+ /// This method is primarily intended for defining internal constants.
+ #[allow(dead_code)]
+ pub(crate) const fn from_le_hex(hex: &str) -> Self {
+ Self::from_uint_unchecked(<$uint>::from_le_hex(hex))
+ }
+
+ /// Decode [`
+ #[doc = stringify!($fe)]
+ /// `] from [`
+ #[doc = stringify!($uint)]
+ /// `] converting it into Montgomery form.
+ ///
+ /// Does *not* perform a check that the field element does not overflow the order.
+ ///
+ /// Used incorrectly this can lead to invalid results!
+ pub(crate) const fn from_uint_unchecked(w: $uint) -> Self {
+ Self(<$uint>::from_words($to_mont(w.as_words())))
+ }
+
+ /// Returns the big-endian encoding of this [`
+ #[doc = stringify!($fe)]
+ /// `].
+ pub fn to_be_bytes(self) -> $bytes {
+ use $crate::bigint::ArrayEncoding as _;
+ self.to_canonical().to_be_byte_array()
+ }
+
+ /// Returns the little-endian encoding of this [`
+ #[doc = stringify!($fe)]
+ /// `].
+ pub fn to_le_bytes(self) -> $bytes {
+ use $crate::bigint::ArrayEncoding as _;
+ self.to_canonical().to_le_byte_array()
+ }
+
+ /// Translate [`
+ #[doc = stringify!($fe)]
+ /// `] out of the Montgomery domain, returning a [`
+ #[doc = stringify!($uint)]
+ /// `] in canonical form.
+ #[inline]
+ pub const fn to_canonical(self) -> $uint {
+ <$uint>::from_words($from_mont(self.0.as_words()))
+ }
+
+ /// Determine if this [`
+ #[doc = stringify!($fe)]
+ /// `] is odd in the SEC1 sense: `self mod 2 == 1`.
+ ///
+ /// # Returns
+ ///
+ /// If odd, return `Choice(1)`. Otherwise, return `Choice(0)`.
+ pub fn is_odd(&self) -> Choice {
+ use $crate::bigint::Integer;
+ self.to_canonical().is_odd()
+ }
+
+ /// Determine if this [`
+ #[doc = stringify!($fe)]
+ /// `] is even in the SEC1 sense: `self mod 2 == 0`.
+ ///
+ /// # Returns
+ ///
+ /// If even, return `Choice(1)`. Otherwise, return `Choice(0)`.
+ pub fn is_even(&self) -> Choice {
+ !self.is_odd()
+ }
+
+ /// Determine if this [`
+ #[doc = stringify!($fe)]
+ /// `] is zero.
+ ///
+ /// # Returns
+ ///
+ /// If zero, return `Choice(1)`. Otherwise, return `Choice(0)`.
+ pub fn is_zero(&self) -> Choice {
+ self.ct_eq(&Self::ZERO)
+ }
+
+ /// Add elements.
+ pub const fn add(&self, rhs: &Self) -> Self {
+ Self(<$uint>::from_words($add(
+ self.0.as_words(),
+ rhs.0.as_words(),
+ )))
+ }
+
+ /// Double element (add it to itself).
+ #[must_use]
+ pub const fn double(&self) -> Self {
+ self.add(self)
+ }
+
+ /// Subtract elements.
+ pub const fn sub(&self, rhs: &Self) -> Self {
+ Self(<$uint>::from_words($sub(
+ self.0.as_words(),
+ rhs.0.as_words(),
+ )))
+ }
+
+ /// Multiply elements.
+ pub const fn mul(&self, rhs: &Self) -> Self {
+ Self(<$uint>::from_words($mul(
+ self.0.as_words(),
+ rhs.0.as_words(),
+ )))
+ }
+
+ /// Negate element.
+ pub const fn neg(&self) -> Self {
+ Self(<$uint>::from_words($neg(self.0.as_words())))
+ }
+
+ /// Compute modular square.
+ #[must_use]
+ pub const fn square(&self) -> Self {
+ Self(<$uint>::from_words($square(self.0.as_words())))
+ }
+ }
+
+ impl AsRef<$arr> for $fe {
+ fn as_ref(&self) -> &$arr {
+ self.0.as_ref()
+ }
+ }
+
+ impl Default for $fe {
+ fn default() -> Self {
+ Self::ZERO
+ }
+ }
+
+ impl Eq for $fe {}
+
+ impl PartialEq for $fe {
+ fn eq(&self, rhs: &Self) -> bool {
+ self.0.ct_eq(&(rhs.0)).into()
+ }
+ }
+
+ impl $crate::subtle::ConditionallySelectable for $fe {
+ fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
+ Self(<$uint>::conditional_select(&a.0, &b.0, choice))
+ }
+ }
+
+ impl $crate::subtle::ConstantTimeEq for $fe {
+ fn ct_eq(&self, other: &Self) -> $crate::subtle::Choice {
+ self.0.ct_eq(&other.0)
+ }
+ }
+
+ impl $crate::subtle::ConstantTimeGreater for $fe {
+ fn ct_gt(&self, other: &Self) -> $crate::subtle::Choice {
+ self.0.ct_gt(&other.0)
+ }
+ }
+
+ impl $crate::subtle::ConstantTimeLess for $fe {
+ fn ct_lt(&self, other: &Self) -> $crate::subtle::Choice {
+ self.0.ct_lt(&other.0)
+ }
+ }
+
+ impl $crate::zeroize::DefaultIsZeroes for $fe {}
+
+ impl $crate::ff::Field for $fe {
+ fn random(mut rng: impl $crate::rand_core::RngCore) -> Self {
+ // NOTE: can't use ScalarCore::random due to CryptoRng bound
+ let mut bytes = <$bytes>::default();
+
+ loop {
+ rng.fill_bytes(&mut bytes);
+ if let Some(fe) = Self::from_be_bytes(bytes).into() {
+ return fe;
+ }
+ }
+ }
+
+ fn zero() -> Self {
+ Self::ZERO
+ }
+
+ fn one() -> Self {
+ Self::ONE
+ }
+
+ fn is_zero(&self) -> Choice {
+ Self::ZERO.ct_eq(self)
+ }
+
+ #[must_use]
+ fn square(&self) -> Self {
+ self.square()
+ }
+
+ #[must_use]
+ fn double(&self) -> Self {
+ self.double()
+ }
+
+ fn invert(&self) -> CtOption<Self> {
+ self.invert()
+ }
+
+ fn sqrt(&self) -> CtOption<Self> {
+ self.sqrt()
+ }
+ }
+
+ $crate::impl_field_op!($fe, $uint, Add, add, $add);
+ $crate::impl_field_op!($fe, $uint, Sub, sub, $sub);
+ $crate::impl_field_op!($fe, $uint, Mul, mul, $mul);
+
+ impl AddAssign<$fe> for $fe {
+ #[inline]
+ fn add_assign(&mut self, other: $fe) {
+ *self = *self + other;
+ }
+ }
+
+ impl AddAssign<&$fe> for $fe {
+ #[inline]
+ fn add_assign(&mut self, other: &$fe) {
+ *self = *self + other;
+ }
+ }
+
+ impl SubAssign<$fe> for $fe {
+ #[inline]
+ fn sub_assign(&mut self, other: $fe) {
+ *self = *self - other;
+ }
+ }
+
+ impl SubAssign<&$fe> for $fe {
+ #[inline]
+ fn sub_assign(&mut self, other: &$fe) {
+ *self = *self - other;
+ }
+ }
+
+ impl MulAssign<&$fe> for $fe {
+ #[inline]
+ fn mul_assign(&mut self, other: &$fe) {
+ *self = *self * other;
+ }
+ }
+
+ impl MulAssign for $fe {
+ #[inline]
+ fn mul_assign(&mut self, other: $fe) {
+ *self = *self * other;
+ }
+ }
+
+ impl Neg for $fe {
+ type Output = $fe;
+
+ #[inline]
+ fn neg(self) -> $fe {
+ Self($neg(self.as_ref()).into())
+ }
+ }
+ };
+}
+
+/// Emit impls for a `core::ops` trait for all combinations of reference types,
+/// which thunk to the given function.
+#[macro_export]
+macro_rules! impl_field_op {
+ ($fe:tt, $uint:ty, $op:tt, $op_fn:ident, $func:ident) => {
+ impl ::core::ops::$op for $fe {
+ type Output = $fe;
+
+ #[inline]
+ fn $op_fn(self, rhs: $fe) -> $fe {
+ $fe($func(self.as_ref(), rhs.as_ref()).into())
+ }
+ }
+
+ impl ::core::ops::$op<&$fe> for $fe {
+ type Output = $fe;
+
+ #[inline]
+ fn $op_fn(self, rhs: &$fe) -> $fe {
+ $fe($func(self.as_ref(), rhs.as_ref()).into())
+ }
+ }
+
+ impl ::core::ops::$op<&$fe> for &$fe {
+ type Output = $fe;
+
+ #[inline]
+ fn $op_fn(self, rhs: &$fe) -> $fe {
+ $fe($func(self.as_ref(), rhs.as_ref()).into())
+ }
+ }
+ };
+}