Merge pull request #52 from zcash/field-trait-changes
Migrate to `ff` revision with square root backports
This commit is contained in:
str4d
GitHub
commit
a5ac51d64e
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@ -6,6 +6,14 @@ and this project adheres to Rust's notion of
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[Semantic Versioning](https://semver.org/spec/v2.0.0.html).
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## [Unreleased]
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### Changed
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- Migrated to `ff 0.13`, `group 0.13`.
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### Removed
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- `pasta_curves::arithmetic::SqrtRatio` (use `ff::Field::{sqrt_ratio, sqrt_alt}`
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instead).
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- `pasta_curves::arithmetic::SqrtTables` (from public API, as it isn't suitable
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for generic usage).
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## [0.4.1] - 2022-10-13
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### Added
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@ -72,3 +72,6 @@ sqrt-table = ["alloc", "lazy_static"]
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repr-c = []
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uninline-portable = []
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serde = ["hex", "serde_crate"]
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[patch.crates-io]
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ff = { git = "https://github.com/zkcrypto/ff.git", rev = "c070ffbaea8cb17e57f817a91ed0e364ff679b7c" }
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@ -4,103 +4,39 @@
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use core::mem::size_of;
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use static_assertions::const_assert;
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use subtle::{Choice, ConditionallySelectable, CtOption};
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use super::Group;
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use core::assert;
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#[cfg(feature = "sqrt-table")]
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use alloc::{boxed::Box, vec::Vec};
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#[cfg(feature = "sqrt-table")]
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use core::marker::PhantomData;
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#[cfg(feature = "sqrt-table")]
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use subtle::Choice;
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const_assert!(size_of::<usize>() >= 4);
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/// A trait that exposes additional operations related to calculating square roots of
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/// An internal trait that exposes additional operations related to calculating square roots of
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/// prime-order finite fields.
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pub trait SqrtRatio: ff::PrimeField {
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/// The value $(T-1)/2$ such that $2^S \cdot T = p - 1$ with $T$ odd.
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const T_MINUS1_OVER2: [u64; 4];
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/// Raise this field element to the power [`Self::T_MINUS1_OVER2`].
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pub(crate) trait SqrtTableHelpers: ff::PrimeField {
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/// Raise this field element to the power $(t-1)/2$.
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///
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/// Field implementations may override this to use an efficient addition chain.
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fn pow_by_t_minus1_over2(&self) -> Self {
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ff::Field::pow_vartime(self, &Self::T_MINUS1_OVER2)
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}
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fn pow_by_t_minus1_over2(&self) -> Self;
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/// Gets the lower 32 bits of this field element when expressed
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/// canonically.
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fn get_lower_32(&self) -> u32;
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/// Computes:
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///
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/// - $(\textsf{true}, \sqrt{\textsf{num}/\textsf{div}})$, if $\textsf{num}$ and
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/// $\textsf{div}$ are nonzero and $\textsf{num}/\textsf{div}$ is a square in the
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/// field;
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/// - $(\textsf{true}, 0)$, if $\textsf{num}$ is zero;
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/// - $(\textsf{false}, 0)$, if $\textsf{num}$ is nonzero and $\textsf{div}$ is zero;
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/// - $(\textsf{false}, \sqrt{G_S \cdot \textsf{num}/\textsf{div}})$, if
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/// $\textsf{num}$ and $\textsf{div}$ are nonzero and $\textsf{num}/\textsf{div}$ is
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/// a nonsquare in the field;
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///
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/// where $G_S$ is a non-square.
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///
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/// For `pasta_curves`, $G_S$ is currently [`ff::PrimeField::root_of_unity`], a
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/// generator of the order $2^S$ subgroup. Users of this crate should not rely on this
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/// generator being fixed; it may be changed in future crate versions to simplify the
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/// implementation of the SSWU hash-to-curve algorithm.
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///
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/// The choice of root from sqrt is unspecified.
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fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
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// General implementation:
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//
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// a = num * inv0(div)
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// = { 0 if div is zero
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// { num/div otherwise
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//
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// b = G_S * a
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// = { 0 if div is zero
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// { G_S*num/div otherwise
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//
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// Since G_S is non-square, a and b are either both zero (and both square), or
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// only one of them is square. We can therefore choose the square root to return
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// based on whether a is square, but for the boolean output we need to handle the
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// num != 0 && div == 0 case specifically.
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let a = div.invert().unwrap_or_else(Self::zero) * num;
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let b = a * Self::root_of_unity();
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let sqrt_a = a.sqrt();
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let sqrt_b = b.sqrt();
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let num_is_zero = num.is_zero();
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let div_is_zero = div.is_zero();
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let is_square = sqrt_a.is_some();
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let is_nonsquare = sqrt_b.is_some();
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assert!(bool::from(
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num_is_zero | div_is_zero | (is_square ^ is_nonsquare)
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));
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(
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is_square & !(!num_is_zero & div_is_zero),
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CtOption::conditional_select(&sqrt_b, &sqrt_a, is_square).unwrap(),
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)
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}
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/// Equivalent to `Self::sqrt_ratio(self, one())`.
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fn sqrt_alt(&self) -> (Choice, Self) {
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Self::sqrt_ratio(self, &Self::one())
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}
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}
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/// This trait is a common interface for dealing with elements of a finite
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/// field.
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pub trait FieldExt: SqrtRatio + From<bool> + Ord + Group<Scalar = Self> {
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pub trait FieldExt: ff::PrimeField + From<bool> + Ord + Group<Scalar = Self> {
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/// Modulus of the field written as a string for display purposes
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const MODULUS: &'static str;
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/// Inverse of `PrimeField::root_of_unity()`
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/// Inverse of `PrimeField::ROOT_OF_UNITY`
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const ROOT_OF_UNITY_INV: Self;
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/// Generator of the $t-order$ multiplicative subgroup
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@ -119,77 +55,11 @@ pub trait FieldExt: SqrtRatio + From<bool> + Ord + Group<Scalar = Self> {
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/// byte representation of an integer.
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fn from_bytes_wide(bytes: &[u8; 64]) -> Self;
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/// Exponentiates `self` by `by`, where `by` is a little-endian order
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/// integer exponent.
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fn pow(&self, by: &[u64; 4]) -> Self {
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let mut res = Self::one();
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for e in by.iter().rev() {
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for i in (0..64).rev() {
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res = res.square();
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let mut tmp = res;
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tmp *= self;
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res.conditional_assign(&tmp, (((*e >> i) & 0x1) as u8).into());
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}
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}
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res
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}
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/// Gets the lower 128 bits of this field element when expressed
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/// canonically.
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fn get_lower_128(&self) -> u128;
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}
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/// Tonelli–Shanks' square-root algorithm for `p mod 16 = 1`.
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///
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/// https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
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///
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/// `tm1d2` should be set to `(t - 1) // 2`, where `t = (modulus - 1) >> F::S`.
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#[cfg(not(feature = "sqrt-table"))]
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#[cfg_attr(docsrs, doc(cfg(not(feature = "sqrt-table"))))]
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pub(crate) fn sqrt_tonelli_shanks<F: ff::PrimeField, S: AsRef<[u64]>>(
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f: &F,
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tm1d2: S,
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) -> CtOption<F> {
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use subtle::ConstantTimeEq;
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// w = self^((t - 1) // 2)
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let w = f.pow_vartime(tm1d2);
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let mut v = F::S;
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let mut x = w * f;
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let mut b = x * w;
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// Initialize z as the 2^S root of unity.
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let mut z = F::root_of_unity();
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for max_v in (1..=F::S).rev() {
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let mut k = 1;
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let mut tmp = b.square();
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let mut j_less_than_v: Choice = 1.into();
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for j in 2..max_v {
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let tmp_is_one = tmp.ct_eq(&F::one());
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let squared = F::conditional_select(&tmp, &z, tmp_is_one).square();
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tmp = F::conditional_select(&squared, &tmp, tmp_is_one);
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let new_z = F::conditional_select(&z, &squared, tmp_is_one);
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j_less_than_v &= !j.ct_eq(&v);
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k = u32::conditional_select(&j, &k, tmp_is_one);
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z = F::conditional_select(&z, &new_z, j_less_than_v);
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}
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let result = x * z;
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x = F::conditional_select(&result, &x, b.ct_eq(&F::one()));
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z = z.square();
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b *= z;
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v = k;
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}
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CtOption::new(
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x,
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(x * x).ct_eq(f), // Only return Some if it's the square root.
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)
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}
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/// Parameters for a perfect hash function used in square root computation.
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#[cfg(feature = "sqrt-table")]
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#[cfg_attr(docsrs, doc(cfg(feature = "sqrt-table")))]
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@ -201,7 +71,7 @@ struct SqrtHasher<F: FieldExt> {
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}
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#[cfg(feature = "sqrt-table")]
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impl<F: FieldExt> SqrtHasher<F> {
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impl<F: FieldExt + SqrtTableHelpers> SqrtHasher<F> {
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/// Returns a perfect hash of x for use with SqrtTables::inv.
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fn hash(&self, x: &F) -> usize {
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// This is just the simplest constant-time perfect hash construction that could
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@ -216,7 +86,7 @@ impl<F: FieldExt> SqrtHasher<F> {
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#[cfg(feature = "sqrt-table")]
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#[cfg_attr(docsrs, doc(cfg(feature = "sqrt-table")))]
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#[derive(Debug)]
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pub struct SqrtTables<F: FieldExt> {
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pub(crate) struct SqrtTables<F: FieldExt> {
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hasher: SqrtHasher<F>,
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inv: Vec<u8>,
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g0: Box<[F; 256]>,
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@ -226,7 +96,7 @@ pub struct SqrtTables<F: FieldExt> {
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}
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#[cfg(feature = "sqrt-table")]
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impl<F: FieldExt> SqrtTables<F> {
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impl<F: FieldExt + SqrtTableHelpers> SqrtTables<F> {
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/// Build tables given parameters for the perfect hash.
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pub fn new(hash_xor: u32, hash_mod: usize) -> Self {
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use alloc::vec;
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@ -237,10 +107,10 @@ impl<F: FieldExt> SqrtTables<F> {
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marker: PhantomData,
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};
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let mut gtab = (0..4).scan(F::root_of_unity(), |gi, _| {
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let mut gtab = (0..4).scan(F::ROOT_OF_UNITY, |gi, _| {
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// gi == ROOT_OF_UNITY^(256^i)
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let gtab_i: Vec<F> = (0..256)
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.scan(F::one(), |acc, _| {
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.scan(F::ONE, |acc, _| {
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let res = *acc;
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*acc *= *gi;
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Some(res)
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@ -335,7 +205,7 @@ impl<F: FieldExt> SqrtTables<F> {
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let sqdiv = res.square() * div;
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let is_square = (sqdiv - num).is_zero();
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let is_nonsquare = (sqdiv - F::root_of_unity() * num).is_zero();
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let is_nonsquare = (sqdiv - F::ROOT_OF_UNITY * num).is_zero();
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assert!(bool::from(
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num.is_zero() | div.is_zero() | (is_square ^ is_nonsquare)
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));
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@ -352,7 +222,7 @@ impl<F: FieldExt> SqrtTables<F> {
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let sq = res.square();
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let is_square = (sq - u).is_zero();
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let is_nonsquare = (sq - F::root_of_unity() * u).is_zero();
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let is_nonsquare = (sq - F::ROOT_OF_UNITY * u).is_zero();
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assert!(bool::from(u.is_zero() | (is_square ^ is_nonsquare)));
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(is_square, res)
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@ -897,7 +897,7 @@ macro_rules! impl_projective_curve_ext {
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use super::hashtocurve;
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Box::new(move |message| {
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let mut us = [Field::zero(); 2];
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let mut us = [Field::ZERO; 2];
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hashtocurve::hash_to_field($name::CURVE_ID, domain_prefix, message, &mut us);
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let q0 = hashtocurve::map_to_curve_simple_swu::<$base, $name, $iso>(
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&us[0],
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@ -1110,7 +1110,7 @@ impl Ep {
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0x4000000000000000,
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]);
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/// `(F::root_of_unity().invert().unwrap() * z).sqrt().unwrap()`
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/// `(F::ROOT_OF_UNITY.invert().unwrap() * z).sqrt().unwrap()`
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pub const THETA: Fp = Fp::from_raw([
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0xca330bcc09ac318e,
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0x51f64fc4dc888857,
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@ -1210,7 +1210,7 @@ impl Eq {
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0x4000000000000000,
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]);
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/// `(F::root_of_unity().invert().unwrap() * z).sqrt().unwrap()`
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/// `(F::ROOT_OF_UNITY.invert().unwrap() * z).sqrt().unwrap()`
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pub const THETA: Fq = Fq::from_raw([
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0x632cae9872df1b5d,
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0x38578ccadf03ac27,
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@ -1,7 +1,7 @@
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use core::fmt;
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use core::ops::{Add, Mul, Neg, Sub};
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use ff::PrimeField;
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use ff::{Field, PrimeField};
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use rand::RngCore;
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use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
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@ -11,7 +11,7 @@ use lazy_static::lazy_static;
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#[cfg(feature = "bits")]
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use ff::{FieldBits, PrimeFieldBits};
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use crate::arithmetic::{adc, mac, sbb, FieldExt, Group, SqrtRatio};
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use crate::arithmetic::{adc, mac, sbb, FieldExt, Group, SqrtTableHelpers};
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#[cfg(feature = "sqrt-table")]
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use crate::arithmetic::SqrtTables;
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@ -173,6 +173,18 @@ impl<'a, 'b> Mul<&'b Fp> for &'a Fp {
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impl_binops_additive!(Fp, Fp);
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impl_binops_multiplicative!(Fp, Fp);
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impl<T: ::core::borrow::Borrow<Fp>> ::core::iter::Sum<T> for Fp {
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fn sum<I: Iterator<Item = T>>(iter: I) -> Self {
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iter.fold(Self::ZERO, |acc, item| acc + item.borrow())
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}
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}
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impl<T: ::core::borrow::Borrow<Fp>> ::core::iter::Product<T> for Fp {
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fn product<I: Iterator<Item = T>>(iter: I) -> Self {
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iter.fold(Self::ONE, |acc, item| acc * item.borrow())
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}
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}
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/// INV = -(p^{-1} mod 2^64) mod 2^64
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const INV: u64 = 0x992d30ecffffffff;
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@ -232,6 +244,7 @@ const DELTA: Fp = Fp::from_raw([
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]);
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/// `(t - 1) // 2` where t * 2^s + 1 = p with t odd.
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#[cfg(any(test, not(feature = "sqrt-table")))]
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const T_MINUS1_OVER2: [u64; 4] = [
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0x04a6_7c8d_cc96_9876,
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0x0000_0000_1123_4c7e,
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@ -480,6 +493,9 @@ impl Group for Fp {
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}
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impl ff::Field for Fp {
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const ZERO: Self = Self::zero();
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const ONE: Self = Self::one();
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fn random(mut rng: impl RngCore) -> Self {
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Self::from_u512([
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rng.next_u64(),
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|
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@ -493,14 +509,6 @@ impl ff::Field for Fp {
|
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])
|
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}
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fn zero() -> Self {
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Self::zero()
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}
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fn one() -> Self {
|
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Self::one()
|
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}
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fn double(&self) -> Self {
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self.double()
|
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}
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@ -510,6 +518,21 @@ impl ff::Field for Fp {
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self.square()
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}
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fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
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#[cfg(feature = "sqrt-table")]
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{
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FP_TABLES.sqrt_ratio(num, div)
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}
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#[cfg(not(feature = "sqrt-table"))]
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ff::helpers::sqrt_ratio_generic(num, div)
|
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}
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#[cfg(feature = "sqrt-table")]
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fn sqrt_alt(&self) -> (Choice, Self) {
|
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FP_TABLES.sqrt_alt(self)
|
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}
|
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|
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/// Computes the square root of this element, if it exists.
|
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fn sqrt(&self) -> CtOption<Self> {
|
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#[cfg(feature = "sqrt-table")]
|
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|
|
@ -519,7 +542,7 @@ impl ff::Field for Fp {
|
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}
|
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|
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#[cfg(not(feature = "sqrt-table"))]
|
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crate::arithmetic::sqrt_tonelli_shanks(self, &T_MINUS1_OVER2)
|
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ff::helpers::sqrt_tonelli_shanks(self, &T_MINUS1_OVER2)
|
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}
|
||||
|
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/// Computes the multiplicative inverse of this element,
|
||||
|
|
@ -559,7 +582,9 @@ impl ff::PrimeField for Fp {
|
|||
|
||||
const NUM_BITS: u32 = 255;
|
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const CAPACITY: u32 = 254;
|
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const MULTIPLICATIVE_GENERATOR: Self = GENERATOR;
|
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const S: u32 = S;
|
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const ROOT_OF_UNITY: Self = ROOT_OF_UNITY;
|
||||
|
||||
fn from_repr(repr: Self::Repr) -> CtOption<Self> {
|
||||
let mut tmp = Fp([0, 0, 0, 0]);
|
||||
|
|
@ -604,14 +629,6 @@ impl ff::PrimeField for Fp {
|
|||
fn is_odd(&self) -> Choice {
|
||||
Choice::from(self.to_repr()[0] & 1)
|
||||
}
|
||||
|
||||
fn multiplicative_generator() -> Self {
|
||||
GENERATOR
|
||||
}
|
||||
|
||||
fn root_of_unity() -> Self {
|
||||
ROOT_OF_UNITY
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(all(feature = "bits", not(target_pointer_width = "64")))]
|
||||
|
|
@ -669,9 +686,7 @@ lazy_static! {
|
|||
static ref FP_TABLES: SqrtTables<Fp> = SqrtTables::new(0x11BE, 1098);
|
||||
}
|
||||
|
||||
impl SqrtRatio for Fp {
|
||||
const T_MINUS1_OVER2: [u64; 4] = T_MINUS1_OVER2;
|
||||
|
||||
impl SqrtTableHelpers for Fp {
|
||||
fn pow_by_t_minus1_over2(&self) -> Self {
|
||||
let sqr = |x: Fp, i: u32| (0..i).fold(x, |x, _| x.square());
|
||||
|
||||
|
|
@ -709,16 +724,6 @@ impl SqrtRatio for Fp {
|
|||
|
||||
tmp.0[0] as u32
|
||||
}
|
||||
|
||||
#[cfg(feature = "sqrt-table")]
|
||||
fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
|
||||
FP_TABLES.sqrt_ratio(num, div)
|
||||
}
|
||||
|
||||
#[cfg(feature = "sqrt-table")]
|
||||
fn sqrt_alt(&self) -> (Choice, Self) {
|
||||
FP_TABLES.sqrt_alt(self)
|
||||
}
|
||||
}
|
||||
|
||||
impl FieldExt for Fp {
|
||||
|
|
@ -792,9 +797,6 @@ impl ec_gpu::GpuField for Fp {
|
|||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
use ff::Field;
|
||||
|
||||
#[test]
|
||||
fn test_inv() {
|
||||
// Compute -(r^{-1} mod 2^64) mod 2^64 by exponentiating
|
||||
|
|
@ -840,8 +842,8 @@ fn test_sqrt_ratio_and_alt() {
|
|||
assert!(v_alt == v);
|
||||
|
||||
// (false, sqrt(ROOT_OF_UNITY * num/div)), if num and div are nonzero and num/div is a nonsquare in the field
|
||||
let num = num * Fp::root_of_unity();
|
||||
let expected = Fp::TWO_INV * Fp::root_of_unity() * Fp::from(5).invert().unwrap();
|
||||
let num = num * Fp::ROOT_OF_UNITY;
|
||||
let expected = Fp::TWO_INV * Fp::ROOT_OF_UNITY * Fp::from(5).invert().unwrap();
|
||||
let (is_square, v) = Fp::sqrt_ratio(&num, &div);
|
||||
assert!(!bool::from(is_square));
|
||||
assert!(v == expected || (-v) == expected);
|
||||
|
|
@ -888,14 +890,14 @@ fn test_zeta() {
|
|||
#[test]
|
||||
fn test_root_of_unity() {
|
||||
assert_eq!(
|
||||
Fp::root_of_unity().pow_vartime(&[1 << Fp::S, 0, 0, 0]),
|
||||
Fp::ROOT_OF_UNITY.pow_vartime(&[1 << Fp::S, 0, 0, 0]),
|
||||
Fp::one()
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_inv_root_of_unity() {
|
||||
assert_eq!(Fp::ROOT_OF_UNITY_INV, Fp::root_of_unity().invert().unwrap());
|
||||
assert_eq!(Fp::ROOT_OF_UNITY_INV, Fp::ROOT_OF_UNITY.invert().unwrap());
|
||||
}
|
||||
|
||||
#[test]
|
||||
|
|
@ -908,7 +910,7 @@ fn test_delta() {
|
|||
assert_eq!(Fp::DELTA, GENERATOR.pow(&[1u64 << Fp::S, 0, 0, 0]));
|
||||
assert_eq!(
|
||||
Fp::DELTA,
|
||||
Fp::multiplicative_generator().pow(&[1u64 << Fp::S, 0, 0, 0])
|
||||
Fp::MULTIPLICATIVE_GENERATOR.pow(&[1u64 << Fp::S, 0, 0, 0])
|
||||
);
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
use core::fmt;
|
||||
use core::ops::{Add, Mul, Neg, Sub};
|
||||
|
||||
use ff::PrimeField;
|
||||
use ff::{Field, PrimeField};
|
||||
use rand::RngCore;
|
||||
use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
|
||||
|
||||
|
|
@ -11,7 +11,7 @@ use lazy_static::lazy_static;
|
|||
#[cfg(feature = "bits")]
|
||||
use ff::{FieldBits, PrimeFieldBits};
|
||||
|
||||
use crate::arithmetic::{adc, mac, sbb, FieldExt, Group, SqrtRatio};
|
||||
use crate::arithmetic::{adc, mac, sbb, FieldExt, Group, SqrtTableHelpers};
|
||||
|
||||
#[cfg(feature = "sqrt-table")]
|
||||
use crate::arithmetic::SqrtTables;
|
||||
|
|
@ -173,6 +173,18 @@ impl<'a, 'b> Mul<&'b Fq> for &'a Fq {
|
|||
impl_binops_additive!(Fq, Fq);
|
||||
impl_binops_multiplicative!(Fq, Fq);
|
||||
|
||||
impl<T: ::core::borrow::Borrow<Fq>> ::core::iter::Sum<T> for Fq {
|
||||
fn sum<I: Iterator<Item = T>>(iter: I) -> Self {
|
||||
iter.fold(Self::ZERO, |acc, item| acc + item.borrow())
|
||||
}
|
||||
}
|
||||
|
||||
impl<T: ::core::borrow::Borrow<Fq>> ::core::iter::Product<T> for Fq {
|
||||
fn product<I: Iterator<Item = T>>(iter: I) -> Self {
|
||||
iter.fold(Self::ONE, |acc, item| acc * item.borrow())
|
||||
}
|
||||
}
|
||||
|
||||
/// INV = -(q^{-1} mod 2^64) mod 2^64
|
||||
const INV: u64 = 0x8c46eb20ffffffff;
|
||||
|
||||
|
|
@ -232,6 +244,7 @@ const DELTA: Fq = Fq::from_raw([
|
|||
]);
|
||||
|
||||
/// `(t - 1) // 2` where t * 2^s + 1 = p with t odd.
|
||||
#[cfg(any(test, not(feature = "sqrt-table")))]
|
||||
const T_MINUS1_OVER2: [u64; 4] = [
|
||||
0x04ca_546e_c623_7590,
|
||||
0x0000_0000_1123_4c7e,
|
||||
|
|
@ -480,6 +493,9 @@ impl Group for Fq {
|
|||
}
|
||||
|
||||
impl ff::Field for Fq {
|
||||
const ZERO: Self = Self::zero();
|
||||
const ONE: Self = Self::one();
|
||||
|
||||
fn random(mut rng: impl RngCore) -> Self {
|
||||
Self::from_u512([
|
||||
rng.next_u64(),
|
||||
|
|
@ -493,14 +509,6 @@ impl ff::Field for Fq {
|
|||
])
|
||||
}
|
||||
|
||||
fn zero() -> Self {
|
||||
Self::zero()
|
||||
}
|
||||
|
||||
fn one() -> Self {
|
||||
Self::one()
|
||||
}
|
||||
|
||||
fn double(&self) -> Self {
|
||||
self.double()
|
||||
}
|
||||
|
|
@ -510,6 +518,21 @@ impl ff::Field for Fq {
|
|||
self.square()
|
||||
}
|
||||
|
||||
fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
|
||||
#[cfg(feature = "sqrt-table")]
|
||||
{
|
||||
FQ_TABLES.sqrt_ratio(num, div)
|
||||
}
|
||||
|
||||
#[cfg(not(feature = "sqrt-table"))]
|
||||
ff::helpers::sqrt_ratio_generic(num, div)
|
||||
}
|
||||
|
||||
#[cfg(feature = "sqrt-table")]
|
||||
fn sqrt_alt(&self) -> (Choice, Self) {
|
||||
FQ_TABLES.sqrt_alt(self)
|
||||
}
|
||||
|
||||
/// Computes the square root of this element, if it exists.
|
||||
fn sqrt(&self) -> CtOption<Self> {
|
||||
#[cfg(feature = "sqrt-table")]
|
||||
|
|
@ -519,7 +542,7 @@ impl ff::Field for Fq {
|
|||
}
|
||||
|
||||
#[cfg(not(feature = "sqrt-table"))]
|
||||
crate::arithmetic::sqrt_tonelli_shanks(self, &T_MINUS1_OVER2)
|
||||
ff::helpers::sqrt_tonelli_shanks(self, &T_MINUS1_OVER2)
|
||||
}
|
||||
|
||||
/// Computes the multiplicative inverse of this element,
|
||||
|
|
@ -559,7 +582,9 @@ impl ff::PrimeField for Fq {
|
|||
|
||||
const NUM_BITS: u32 = 255;
|
||||
const CAPACITY: u32 = 254;
|
||||
const MULTIPLICATIVE_GENERATOR: Self = GENERATOR;
|
||||
const S: u32 = S;
|
||||
const ROOT_OF_UNITY: Self = ROOT_OF_UNITY;
|
||||
|
||||
fn from_repr(repr: Self::Repr) -> CtOption<Self> {
|
||||
let mut tmp = Fq([0, 0, 0, 0]);
|
||||
|
|
@ -604,14 +629,6 @@ impl ff::PrimeField for Fq {
|
|||
fn is_odd(&self) -> Choice {
|
||||
Choice::from(self.to_repr()[0] & 1)
|
||||
}
|
||||
|
||||
fn multiplicative_generator() -> Self {
|
||||
GENERATOR
|
||||
}
|
||||
|
||||
fn root_of_unity() -> Self {
|
||||
ROOT_OF_UNITY
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(all(feature = "bits", not(target_pointer_width = "64")))]
|
||||
|
|
@ -668,9 +685,7 @@ lazy_static! {
|
|||
static ref FQ_TABLES: SqrtTables<Fq> = SqrtTables::new(0x116A9E, 1206);
|
||||
}
|
||||
|
||||
impl SqrtRatio for Fq {
|
||||
const T_MINUS1_OVER2: [u64; 4] = T_MINUS1_OVER2;
|
||||
|
||||
impl SqrtTableHelpers for Fq {
|
||||
fn pow_by_t_minus1_over2(&self) -> Self {
|
||||
let sqr = |x: Fq, i: u32| (0..i).fold(x, |x, _| x.square());
|
||||
|
||||
|
|
@ -708,16 +723,6 @@ impl SqrtRatio for Fq {
|
|||
|
||||
tmp.0[0] as u32
|
||||
}
|
||||
|
||||
#[cfg(feature = "sqrt-table")]
|
||||
fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
|
||||
FQ_TABLES.sqrt_ratio(num, div)
|
||||
}
|
||||
|
||||
#[cfg(feature = "sqrt-table")]
|
||||
fn sqrt_alt(&self) -> (Choice, Self) {
|
||||
FQ_TABLES.sqrt_alt(self)
|
||||
}
|
||||
}
|
||||
|
||||
impl FieldExt for Fq {
|
||||
|
|
@ -791,9 +796,6 @@ impl ec_gpu::GpuField for Fq {
|
|||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
use ff::Field;
|
||||
|
||||
#[test]
|
||||
fn test_inv() {
|
||||
// Compute -(r^{-1} mod 2^64) mod 2^64 by exponentiating
|
||||
|
|
@ -839,8 +841,8 @@ fn test_sqrt_ratio_and_alt() {
|
|||
assert!(v_alt == v);
|
||||
|
||||
// (false, sqrt(ROOT_OF_UNITY * num/div)), if num and div are nonzero and num/div is a nonsquare in the field
|
||||
let num = num * Fq::root_of_unity();
|
||||
let expected = Fq::TWO_INV * Fq::root_of_unity() * Fq::from(5).invert().unwrap();
|
||||
let num = num * Fq::ROOT_OF_UNITY;
|
||||
let expected = Fq::TWO_INV * Fq::ROOT_OF_UNITY * Fq::from(5).invert().unwrap();
|
||||
let (is_square, v) = Fq::sqrt_ratio(&num, &div);
|
||||
assert!(!bool::from(is_square));
|
||||
assert!(v == expected || (-v) == expected);
|
||||
|
|
@ -886,14 +888,14 @@ fn test_zeta() {
|
|||
#[test]
|
||||
fn test_root_of_unity() {
|
||||
assert_eq!(
|
||||
Fq::root_of_unity().pow_vartime(&[1 << Fq::S, 0, 0, 0]),
|
||||
Fq::ROOT_OF_UNITY.pow_vartime(&[1 << Fq::S, 0, 0, 0]),
|
||||
Fq::one()
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_inv_root_of_unity() {
|
||||
assert_eq!(Fq::ROOT_OF_UNITY_INV, Fq::root_of_unity().invert().unwrap());
|
||||
assert_eq!(Fq::ROOT_OF_UNITY_INV, Fq::ROOT_OF_UNITY.invert().unwrap());
|
||||
}
|
||||
|
||||
#[test]
|
||||
|
|
@ -906,7 +908,7 @@ fn test_delta() {
|
|||
assert_eq!(Fq::DELTA, GENERATOR.pow(&[1u64 << Fq::S, 0, 0, 0]));
|
||||
assert_eq!(
|
||||
Fq::DELTA,
|
||||
Fq::multiplicative_generator().pow(&[1u64 << Fq::S, 0, 0, 0])
|
||||
Fq::MULTIPLICATIVE_GENERATOR.pow(&[1u64 << Fq::S, 0, 0, 0])
|
||||
);
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -136,7 +136,7 @@ pub fn map_to_curve_simple_swu<F: FieldExt, C: CurveExt<Base = F>, I: CurveExt<B
|
|||
let b = I::b();
|
||||
let z_u2 = z * u.square();
|
||||
let ta = z_u2.square() + z_u2;
|
||||
let num_x1 = b * (ta + F::one());
|
||||
let num_x1 = b * (ta + F::ONE);
|
||||
let div = a * F::conditional_select(&-ta, &z, ta.is_zero());
|
||||
let num2_x1 = num_x1.square();
|
||||
let div2 = div.square();
|
||||
|
|
|
|||
Loading…
Reference in New Issue