Unify SquareRootField and Field

ec/src/lib.rs

@@ -21,7 +21,7 @@ extern crate ark_std;
 
 use ark_ff::{
     bytes::{FromBytes, ToBytes},
-    fields::{BitIteratorBE, Field, PrimeField, SquareRootField},
+    fields::{BitIteratorBE, Field, PrimeField},
     UniformRand,
 };
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
@@ -47,7 +47,7 @@ pub mod wnaf;
 
 pub trait PairingEngine: Sized + 'static + Copy + Debug + Sync + Send + Eq + PartialEq {
     /// This is the scalar field of the G1/G2 groups.
-    type Fr: PrimeField + SquareRootField;
+    type Fr: PrimeField;
 
     /// The projective representation of an element in G1.
     type G1Projective: ProjectiveCurve<BaseField = Self::Fq, ScalarField = Self::Fr, Affine = Self::G1Affine>
@@ -80,10 +80,10 @@ pub trait PairingEngine: Sized + 'static + Copy + Debug + Sync + Send + Eq + Par
     type G2Prepared: ToBytes + Default + Clone + Send + Sync + Debug + From<Self::G2Affine>;
 
     /// The base field that hosts G1.
-    type Fq: PrimeField + SquareRootField;
+    type Fq: PrimeField;
 
     /// The extension field that hosts G2.
-    type Fqe: SquareRootField;
+    type Fqe: Field;
 
     /// The extension field that hosts the target group of the pairing.
     type Fqk: Field;
@@ -156,7 +156,7 @@ pub trait ProjectiveCurve:
     + From<<Self as ProjectiveCurve>::Affine>
 {
     type Parameters: ModelParameters<ScalarField = Self::ScalarField, BaseField = Self::BaseField>;
-    type ScalarField: PrimeField + SquareRootField;
+    type ScalarField: PrimeField;
     type BaseField: Field;
     type Affine: AffineCurve<
             Parameters = Self::Parameters,
@@ -256,7 +256,7 @@ pub trait AffineCurve:
     + From<<Self as AffineCurve>::Projective>
 {
     type Parameters: ModelParameters<ScalarField = Self::ScalarField, BaseField = Self::BaseField>;
-    type ScalarField: PrimeField + SquareRootField + Into<<Self::ScalarField as PrimeField>::BigInt>;
+    type ScalarField: PrimeField + Into<<Self::ScalarField as PrimeField>::BigInt>;
     type BaseField: Field;
     type Projective: ProjectiveCurve<
             Parameters = Self::Parameters,

ec/src/models/bls12/mod.rs

@@ -6,7 +6,7 @@ use ark_ff::fields::{
     fp12_2over3over2::{Fp12, Fp12Parameters},
     fp2::Fp2Config,
     fp6_3over2::Fp6Config,
-    BitIteratorBE, Field, Fp2, PrimeField, SquareRootField,
+    BitIteratorBE, Field, Fp2, PrimeField,
 };
 use core::marker::PhantomData;
 use num_traits::{One, Zero};
@@ -33,7 +33,7 @@ pub trait Bls12Parameters: 'static {
     /// What kind of twist is this?
     const TWIST_TYPE: TwistType;
 
-    type Fp: PrimeField + SquareRootField + Into<<Self::Fp as PrimeField>::BigInt>;
+    type Fp: PrimeField + Into<<Self::Fp as PrimeField>::BigInt>;
     type Fp2Params: Fp2Config<Fp = Self::Fp>;
     type Fp6Params: Fp6Config<Fp2Params = Self::Fp2Params>;
     type Fp12Params: Fp12Parameters<Fp6Params = Self::Fp6Params>;

ec/src/models/bn/mod.rs

@@ -6,7 +6,7 @@ use ark_ff::fields::{
     fp12_2over3over2::{Fp12, Fp12Parameters},
     fp2::Fp2Config,
     fp6_3over2::Fp6Config,
-    Field, Fp2, PrimeField, SquareRootField,
+    Field, Fp2, PrimeField,
 };
 use num_traits::One;
 
@@ -31,7 +31,7 @@ pub trait BnParameters: 'static {
     const TWIST_TYPE: TwistType;
     const TWIST_MUL_BY_Q_X: Fp2<Self::Fp2Params>;
     const TWIST_MUL_BY_Q_Y: Fp2<Self::Fp2Params>;
-    type Fp: PrimeField + SquareRootField + Into<<Self::Fp as PrimeField>::BigInt>;
+    type Fp: PrimeField + Into<<Self::Fp as PrimeField>::BigInt>;
     type Fp2Params: Fp2Config<Fp = Self::Fp>;
     type Fp6Params: Fp6Config<Fp2Params = Self::Fp2Params>;
     type Fp12Params: Fp12Parameters<Fp6Params = Self::Fp6Params>;

ec/src/models/bw6/mod.rs

@@ -5,7 +5,7 @@ use crate::{
 use ark_ff::fields::{
     fp3::Fp3Config,
     fp6_2over3::{Fp6, Fp6Config},
-    BitIteratorBE, Field, PrimeField, SquareRootField,
+    BitIteratorBE, Field, PrimeField,
 };
 use num_traits::One;
 
@@ -24,7 +24,7 @@ pub trait BW6Parameters: 'static + Eq + PartialEq {
     const ATE_LOOP_COUNT_2: &'static [i8];
     const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool;
     const TWIST_TYPE: TwistType;
-    type Fp: PrimeField + SquareRootField + Into<<Self::Fp as PrimeField>::BigInt>;
+    type Fp: PrimeField + Into<<Self::Fp as PrimeField>::BigInt>;
     type Fp3Params: Fp3Config<Fp = Self::Fp>;
     type Fp6Params: Fp6Config<Fp3Params = Self::Fp3Params>;
     type G1Parameters: SWModelParameters<BaseField = Self::Fp>;

ec/src/models/mnt4/mod.rs

@@ -5,7 +5,7 @@ use crate::{
 use ark_ff::{
     fp2::{Fp2, Fp2Config},
     fp4::{Fp4, Fp4Config},
-    BitIteratorBE, Field, PrimeField, SquareRootField,
+    BitIteratorBE, Field, PrimeField,
 };
 use num_traits::{One, Zero};
 
@@ -30,8 +30,8 @@ pub trait MNT4Parameters: 'static {
     const FINAL_EXPONENT_LAST_CHUNK_1: <Self::Fp as PrimeField>::BigInt;
     const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool;
     const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: <Self::Fp as PrimeField>::BigInt;
-    type Fp: PrimeField + SquareRootField + Into<<Self::Fp as PrimeField>::BigInt>;
-    type Fr: PrimeField + SquareRootField + Into<<Self::Fr as PrimeField>::BigInt>;
+    type Fp: PrimeField + Into<<Self::Fp as PrimeField>::BigInt>;
+    type Fr: PrimeField + Into<<Self::Fr as PrimeField>::BigInt>;
     type Fp2Params: Fp2Config<Fp = Self::Fp>;
     type Fp4Params: Fp4Config<Fp2Params = Self::Fp2Params>;
     type G1Parameters: SWModelParameters<BaseField = Self::Fp, ScalarField = Self::Fr>;

ec/src/models/mnt6/mod.rs

@@ -5,7 +5,7 @@ use crate::{
 use ark_ff::{
     fp3::{Fp3, Fp3Config},
     fp6_2over3::{Fp6, Fp6Config},
-    BitIteratorBE, Field, PrimeField, SquareRootField,
+    BitIteratorBE, Field, PrimeField,
 };
 use num_traits::{One, Zero};
 
@@ -30,8 +30,8 @@ pub trait MNT6Parameters: 'static {
     const FINAL_EXPONENT_LAST_CHUNK_1: <Self::Fp as PrimeField>::BigInt;
     const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool;
     const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: <Self::Fp as PrimeField>::BigInt;
-    type Fp: PrimeField + SquareRootField + Into<<Self::Fp as PrimeField>::BigInt>;
-    type Fr: PrimeField + SquareRootField + Into<<Self::Fr as PrimeField>::BigInt>;
+    type Fp: PrimeField + Into<<Self::Fp as PrimeField>::BigInt>;
+    type Fr: PrimeField + Into<<Self::Fr as PrimeField>::BigInt>;
     type Fp3Params: Fp3Config<Fp = Self::Fp>;
     type Fp6Params: Fp6Config<Fp3Params = Self::Fp3Params>;
     type G1Parameters: SWModelParameters<BaseField = Self::Fp, ScalarField = Self::Fr>;

ec/src/models/mod.rs

@@ -1,5 +1,5 @@
 use crate::AffineCurve;
-use ark_ff::{fields::BitIteratorBE, Field, PrimeField, SquareRootField, Zero};
+use ark_ff::{fields::BitIteratorBE, Field, PrimeField, Zero};
 
 pub mod bls12;
 pub mod bn;
@@ -11,8 +11,8 @@ pub mod twisted_edwards_extended;
 
 /// Model parameters for an elliptic curve.
 pub trait ModelParameters: Send + Sync + Sized + 'static {
-    type BaseField: Field + SquareRootField;
-    type ScalarField: PrimeField + SquareRootField + Into<<Self::ScalarField as PrimeField>::BigInt>;
+    type BaseField: Field;
+    type ScalarField: PrimeField + Into<<Self::ScalarField as PrimeField>::BigInt>;
 
     const COFACTOR: &'static [u64];
     const COFACTOR_INV: Self::ScalarField;

ec/src/models/short_weierstrass_jacobian.rs

@@ -12,7 +12,7 @@ use ark_std::{
 
 use ark_ff::{
     bytes::{FromBytes, ToBytes},
-    fields::{Field, PrimeField, SquareRootField},
+    fields::{Field, PrimeField},
     ToConstraintField, UniformRand,
 };
 

ec/src/models/twisted_edwards_extended.rs

@@ -22,7 +22,7 @@ use zeroize::Zeroize;
 
 use ark_ff::{
     bytes::{FromBytes, ToBytes},
-    fields::{Field, PrimeField, SquareRootField},
+    fields::{Field, PrimeField},
     ToConstraintField, UniformRand,
 };
 

ff/src/fields/mod.rs

@@ -84,7 +84,7 @@ pub trait Field:
     + From<bool>
 {
     type BasePrimeField: PrimeField;
-
+    const SqrtPrecomp: SqrtPrecomputation<Self>;
     /// Returns the characteristic of the field,
     /// in little-endian representation.
     fn characteristic() -> &'static [u64] {
@@ -119,6 +119,19 @@ pub trait Field:
     /// random field elements from a hash-function or RNG output.
     fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)>;
 
+    /// Returns a `LegendreSymbol`, which indicates whether this field element
+    /// is  1 : a quadratic residue
+    ///  0 : equal to 0
+    /// -1 : a quadratic non-residue
+    fn legendre(&self) -> LegendreSymbol;
+
+    /// Returns the square root of self, if it exists.
+    #[must_use]
+    fn sqrt(&self) -> Option<Self>;
+
+    /// Sets `self` to be the square root of `self`, if it exists.
+    fn sqrt_in_place(&mut self) -> Option<&mut Self>;
+
     /// Returns `self * self`.
     #[must_use]
     fn square(&self) -> Self;
@@ -329,30 +342,13 @@ pub trait PrimeField:
     }
 }
 
-/// The interface for a field that supports an efficient square-root operation.
-pub trait SquareRootField: Field {
-    /// Returns a `LegendreSymbol`, which indicates whether this field element
-    /// is  
-    /// - 1: a quadratic residue
-    /// - 0: equal to 0
-    /// - -1: a quadratic non-residue
-    fn legendre(&self) -> LegendreSymbol;
-
-    /// Returns the square root of self, if it exists.
-    #[must_use]
-    fn sqrt(&self) -> Option<Self>;
-
-    /// Sets `self` to be the square root of `self`, if it exists.
-    fn sqrt_in_place(&mut self) -> Option<&mut Self>;
-}
-
 /// Indication of the field element's quadratic residuosity
 ///
 /// # Examples
 /// ```
 /// # use ark_std::test_rng;
 /// # use ark_std::UniformRand;
-/// # use ark_test_curves::{LegendreSymbol, Field, SquareRootField, bls12_381::Fq as Fp};
+/// # use ark_test_curves::{LegendreSymbol, Field, bls12_381::Fq as Fp};
 /// let a: Fp = Fp::rand(&mut test_rng());
 /// let b = a.square();
 /// assert_eq!(b.legendre(), LegendreSymbol::QuadraticResidue);
@@ -371,7 +367,7 @@ impl LegendreSymbol {
     /// ```
     /// # use ark_std::test_rng;
     /// # use ark_std::UniformRand;
-    /// # use ark_test_curves::{LegendreSymbol, Field, SquareRootField, bls12_381::Fq as Fp};
+    /// # use ark_test_curves::{LegendreSymbol, Field, bls12_381::Fq as Fp};
     /// let a: Fp = Fp::rand(&mut test_rng());
     /// let b: Fp = a.square();
     /// assert!(!b.legendre().is_zero());
@@ -384,7 +380,7 @@ impl LegendreSymbol {
     ///
     /// # Examples
     /// ```
-    /// # use ark_test_curves::{Fp2Config, LegendreSymbol, SquareRootField, bls12_381::{Fq, Fq2Config}};
+    /// # use ark_test_curves::{Fp2Config, LegendreSymbol, bls12_381::{Fq, Fq2Config}};
     /// let a: Fq = Fq2Config::NONRESIDUE;
     /// assert!(a.legendre().is_qnr());
     /// ```
@@ -398,7 +394,7 @@ impl LegendreSymbol {
     /// # use ark_std::test_rng;
     /// # use ark_test_curves::bls12_381::Fq as Fp;
     /// # use ark_std::UniformRand;
-    /// # use ark_ff::{LegendreSymbol, Field, SquareRootField};
+    /// # use ark_ff::{LegendreSymbol, Field};
     /// let a: Fp = Fp::rand(&mut test_rng());
     /// let b: Fp = a.square();
     /// assert!(b.legendre().is_qr());