Remove SquareRootField, and move functionality to Field

CHANGELOG.md

@@ -34,6 +34,7 @@
 - [\#408](https://github.com/arkworks-rs/algebra/pull/408) (`ark-ff`) Change the output of `Display` formatting for BigInt & Fp from hex to decimal.
 - [\#412](https://github.com/arkworks-rs/algebra/pull/412) (`ark-poly`) Rename UV/MVPolynomial to DenseUV/MVPolynomial.
 - [\#417](https://github.com/arkworks-rs/algebra/pull/417) (`ark-ff`) Remove `ToBytes` and `FromBytes`.
+- [\#422](https://github.com/arkworks-rs/algebra/pull/422) (`ark-ff`) Remove `SquareRootField`, and move functionality to `Field`
 - [\#425](https://github.com/arkworks-rs/algebra/pull/425) (`ark-ec`) Refactor `VariableBase` struct to `VariableBaseMSM` trait and implement it for `GroupProjective`.
 - [\#438](https://github.com/arkworks-rs/algebra/pull/438) (`ark-ec`) Rename modules, structs, and traits related to `ec`.
     - `short_weierstrass_jacobian` → `short_weierstrass`

ec/src/hashing/curve_maps/swu/mod.rs

@@ -1,5 +1,5 @@
 use crate::models::short_weierstrass::SWCurveConfig;
-use ark_ff::{BigInteger, Field, One, PrimeField, SquareRootField, Zero};
+use ark_ff::{BigInteger, Field, One, PrimeField, Zero};
 use ark_std::string::ToString;
 use core::marker::PhantomData;
 

ec/src/hashing/tests/mod.rs

@@ -12,11 +12,10 @@ use crate::{
     CurveConfig,
 };
 use ark_ff::{
-    biginteger::BigInteger64, field_hashers::DefaultFieldHasher, fields::Fp64, BigInt, MontBackend,
-    MontFp,
+    biginteger::BigInteger64, field_hashers::DefaultFieldHasher, fields::Fp64, BigInt, Field,
+    MontBackend, MontFp,
 };
 
-use ark_ff::SquareRootField;
 use ark_std::vec::Vec;
 use ark_test_curves::bls12_381::{Fq, Fq2, Fq6};
 use hashbrown::HashMap;
@@ -119,7 +118,7 @@ fn test_field_division() {
 /// Check that the hashing parameters are sane: zeta should be a non-square
 #[test]
 fn checking_the_hashing_parameters() {
-    assert!(!SquareRootField::legendre(&TestSWUMapToCurveParams::ZETA).is_qr());
+    assert!(!Field::legendre(&TestSWUMapToCurveParams::ZETA).is_qr());
 }
 
 /// The point of the test is to get a simple SWU compatible curve and make

ec/src/lib.rs

@@ -20,7 +20,7 @@ extern crate derivative;
 extern crate ark_std;
 
 use ark_ff::{
-    fields::{Field, PrimeField, SquareRootField},
+    fields::{Field, PrimeField},
     UniformRand,
 };
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
@@ -50,7 +50,7 @@ pub mod wnaf;
 /// how to compute a pairing over a pairing-friendly curve.
 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>
@@ -87,10 +87,10 @@ pub trait PairingEngine: Sized + 'static + Copy + Debug + Sync + Send + Eq + Par
     type G2Prepared: 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;
@@ -161,7 +161,7 @@ pub trait ProjectiveCurve:
     + From<<Self as ProjectiveCurve>::Affine>
 {
     type Config: CurveConfig<ScalarField = Self::ScalarField, BaseField = Self::BaseField>;
-    type ScalarField: PrimeField + SquareRootField;
+    type ScalarField: PrimeField;
     type BaseField: Field;
     type Affine: AffineCurve<
             Config = Self::Config,
@@ -251,7 +251,7 @@ pub trait AffineCurve:
 
     /// The group defined by this curve has order `h * r` where `r` is a large
     /// prime. `Self::ScalarField` is the prime field defined by `r`
-    type ScalarField: PrimeField + SquareRootField + Into<<Self::ScalarField as PrimeField>::BigInt>;
+    type ScalarField: PrimeField + Into<<Self::ScalarField as PrimeField>::BigInt>;
 
     /// The finite field over which this curve is defined.
     type BaseField: Field;

ec/src/models/bls12/mod.rs

@@ -6,7 +6,7 @@ use ark_ff::fields::{
     fp12_2over3over2::{Fp12, Fp12Config},
     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 Fp2Config: Fp2Config<Fp = Self::Fp>;
     type Fp6Config: Fp6Config<Fp2Config = Self::Fp2Config>;
     type Fp12Config: Fp12Config<Fp6Config = Self::Fp6Config>;

ec/src/models/bn/mod.rs

@@ -6,7 +6,7 @@ use ark_ff::fields::{
     fp12_2over3over2::{Fp12, Fp12Config},
     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::Fp2Config>;
     const TWIST_MUL_BY_Q_Y: Fp2<Self::Fp2Config>;
-    type Fp: PrimeField + SquareRootField + Into<<Self::Fp as PrimeField>::BigInt>;
+    type Fp: PrimeField + Into<<Self::Fp as PrimeField>::BigInt>;
     type Fp2Config: Fp2Config<Fp = Self::Fp>;
     type Fp6Config: Fp6Config<Fp2Config = Self::Fp2Config>;
     type Fp12Config: Fp12Config<Fp6Config = Self::Fp6Config>;

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 Fp3Config: Fp3Config<Fp = Self::Fp>;
     type Fp6Config: Fp6Config<Fp3Config = Self::Fp3Config>;
     type G1Parameters: SWCurveConfig<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 Fp2Config: Fp2Config<Fp = Self::Fp>;
     type Fp4Config: Fp4Config<Fp2Config = Self::Fp2Config>;
     type G1Parameters: SWCurveConfig<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 Fp3Config: Fp3Config<Fp = Self::Fp>;
     type Fp6Config: Fp6Config<Fp3Config = Self::Fp3Config>;
     type G1Parameters: SWCurveConfig<BaseField = Self::Fp, ScalarField = Self::Fr>;

ec/src/models/mod.rs

@@ -1,4 +1,4 @@
-use ark_ff::{Field, PrimeField, SquareRootField};
+use ark_ff::{Field, PrimeField};
 
 pub mod bls12;
 pub mod bn;
@@ -16,10 +16,10 @@ pub mod twisted_edwards;
 /// prime-order subgroup of the curve.
 pub trait CurveConfig: Send + Sync + Sized + 'static {
     /// Base field that the curve is defined over.
-    type BaseField: Field + SquareRootField;
+    type BaseField: Field;
     /// Finite prime field corresponding to an appropriate prime-order subgroup
     /// of the curve group.
-    type ScalarField: PrimeField + SquareRootField + Into<<Self::ScalarField as PrimeField>::BigInt>;
+    type ScalarField: PrimeField + Into<<Self::ScalarField as PrimeField>::BigInt>;
 
     const COFACTOR: &'static [u64];
     const COFACTOR_INV: Self::ScalarField;

ec/src/models/short_weierstrass.rs

@@ -11,7 +11,7 @@ use ark_std::{
 };
 
 use ark_ff::{
-    fields::{Field, PrimeField, SquareRootField},
+    fields::{Field, PrimeField},
     ToConstraintField, UniformRand,
 };
 

ec/src/models/twisted_edwards.rs

@@ -18,7 +18,7 @@ use num_traits::{One, Zero};
 use zeroize::Zeroize;
 
 use ark_ff::{
-    fields::{Field, PrimeField, SquareRootField},
+    fields::{Field, PrimeField},
     ToConstraintField, UniformRand,
 };
 

ff/src/fields/arithmetic.rs

@@ -1,66 +1,3 @@
-macro_rules! sqrt_impl {
-    ($Self:ident, $P:tt, $self:expr) => {{
-        // https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
-        // Actually this is just normal Tonelli-Shanks; since `P::Generator`
-        // is a quadratic non-residue, `P::ROOT_OF_UNITY = P::GENERATOR ^ t`
-        // is also a quadratic non-residue (since `t` is odd).
-        if $self.is_zero() {
-            return Some($Self::zero());
-        }
-        // Try computing the square root (x at the end of the algorithm)
-        // Check at the end of the algorithm if x was a square root
-        // Begin Tonelli-Shanks
-        let mut z = $Self::qnr_to_t();
-        let mut w = $self.pow($P::TRACE_MINUS_ONE_DIV_TWO);
-        let mut x = w * $self;
-        let mut b = x * &w;
-
-        let mut v = $P::TWO_ADICITY as usize;
-
-        while !b.is_one() {
-            let mut k = 0usize;
-
-            let mut b2k = b;
-            while !b2k.is_one() {
-                // invariant: b2k = b^(2^k) after entering this loop
-                b2k.square_in_place();
-                k += 1;
-            }
-
-            if k == ($P::TWO_ADICITY as usize) {
-                // We are in the case where self^(T * 2^k) = x^(P::MODULUS - 1) = 1,
-                // which means that no square root exists.
-                return None;
-            }
-            let j = v - k;
-            w = z;
-            for _ in 1..j {
-                w.square_in_place();
-            }
-
-            z = w.square();
-            b *= &z;
-            x *= &w;
-            v = k;
-        }
-        // Is x the square root? If so, return it.
-        if (x.square() == *$self) {
-            return Some(x);
-        } else {
-            // Consistency check that if no square root is found,
-            // it is because none exists.
-            #[cfg(debug_assertions)]
-            {
-                use crate::fields::LegendreSymbol::*;
-                if ($self.legendre() != QuadraticNonResidue) {
-                    panic!("Input has a square root per its legendre symbol, but it was not found")
-                }
-            }
-            None
-        }
-    }};
-}
-
 // Implements AddAssign on Self by deferring to an implementation on &Self
 #[macro_export]
 macro_rules! impl_additive_ops_from_ref {