Add AdditiveGroup trait + Field: AdditiveGroup. (#507)

bench-templates/src/macros/ec.rs

@@ -3,10 +3,10 @@ macro_rules! ec_bench {
     ($curve_name:expr, $Group:ident) => {
         $crate::paste! {
             mod [<$Group:lower>] {
-                use ark_ec::Group;
+                use ark_ec::PrimeGroup;
                 use super::*;
 
-                type Scalar = <$Group as Group>::ScalarField;
+                type Scalar = <$Group::ScalarField;
                 fn rand(c: &mut $crate::criterion::Criterion) {
                     let name = format!("{}::{}", $curve_name, stringify!($Group));
                     use ark_std::UniformRand;
@@ -18,11 +18,11 @@ macro_rules! ec_bench {
                 }
 
                 fn arithmetic(c: &mut $crate::criterion::Criterion) {
-                    use ark_ec::{CurveGroup, Group};
+                    use ark_ec::{CurveGroup, PrimeGroup};
                     use ark_std::UniformRand;
                     let name = format!("{}::{}", $curve_name, stringify!($Group));
 
-                    type Scalar = <$Group as Group>::ScalarField;
+                    type Scalar = $Group::ScalarField;
                     const SAMPLES: usize = 1000;
                     let mut rng = ark_std::test_rng();
                     let mut arithmetic =

ec/README.md

@@ -13,10 +13,10 @@ Implementations of particular curves using these curve models can be found in [`
 
 ### The `Group` trait
 
-Many cryptographic protocols use as core building-blocks prime-order groups. The [`Group`](https://github.com/arkworks-rs/algebra/blob/master/ec/src/lib.rs) trait is an abstraction that represents elements of such abelian prime-order groups. It provides methods for performing common operations on group elements:
+Many cryptographic protocols use as core building-blocks prime-order groups. The [`PrimeGroup`](https://github.com/arkworks-rs/algebra/blob/master/ec/src/lib.rs) trait is an abstraction that represents elements of such abelian prime-order groups. It provides methods for performing common operations on group elements:
 
 ```rust
-use ark_ec::Group;
+use ark_ec::PrimeGroup;
 use ark_ff::{PrimeField, Field};
 // We'll use the BLS12-381 G1 curve for this example.
 // This group has a prime order `r`, and is associated with a prime field `Fr`.
@@ -49,12 +49,12 @@ assert_eq!(f, c);
 
 ## Scalar multiplication
 
-While the `Group` trait already produces scalar multiplication routines, in many cases one can take advantage of
+While the `PrimeGroup` trait already produces scalar multiplication routines, in many cases one can take advantage of
 the group structure to perform scalar multiplication more efficiently. To allow such specialization, `ark-ec` provides
 the `ScalarMul` and `VariableBaseMSM` traits. The latter trait computes an "inner product" between a vector of scalars `s` and a vector of group elements `g`. That is, it computes `s.iter().zip(g).map(|(s, g)| g * s).sum()`.
 
 ```rust
-use ark_ec::{Group, VariableBaseMSM};
+use ark_ec::{PrimeGroup, VariableBaseMSM};
 use ark_ff::{PrimeField, Field};
 // We'll use the BLS12-381 G1 curve for this example.
 // This group has a prime order `r`, and is associated with a prime field `Fr`.
@@ -72,7 +72,7 @@ let s2 = ScalarField::rand(&mut rng);
 // Note that we're using the `GAffine` type here, as opposed to `G`.
 // This is because MSMs are more efficient when the group elements are in affine form. (See below for why.)
 //
-// The `VariableBaseMSM` trait allows specializing the input group element representation to allow 
+// The `VariableBaseMSM` trait allows specializing the input group element representation to allow
 // for more efficient implementations.
 let r = G::msm(&[a, b], &[s1, s2]).unwrap();
 assert_eq!(r, a * s1 + b * s2);
@@ -90,7 +90,7 @@ but is slower for most arithmetic operations. Let's explore how and when to use
 these:
 
 ```rust
-use ark_ec::{AffineRepr, Group, CurveGroup, VariableBaseMSM};
+use ark_ec::{AffineRepr, PrimeGroup, CurveGroup, VariableBaseMSM};
 use ark_ff::{PrimeField, Field};
 use ark_test_curves::bls12_381::{G1Projective as G, G1Affine as GAffine, Fr as ScalarField};
 use ark_std::{Zero, UniformRand};
@@ -105,9 +105,9 @@ assert_eq!(a_aff, a);
 // We can also convert back to the `CurveGroup` representation:
 assert_eq!(a, a_aff.into_group());
 
-// As a general rule, most group operations are slower when elements 
-// are represented as `AffineRepr`. However, adding an `AffineRepr` 
-// point to a `CurveGroup` one is usually slightly more efficient than 
+// As a general rule, most group operations are slower when elements
+// are represented as `AffineRepr`. However, adding an `AffineRepr`
+// point to a `CurveGroup` one is usually slightly more efficient than
 // adding two `CurveGroup` points.
 let d = a + a_aff;
 assert_eq!(d, a.double());

ec/src/lib.rs

@@ -22,16 +22,15 @@ extern crate ark_std;
 
 use ark_ff::{
     fields::{Field, PrimeField},
-    UniformRand,
+    UniformRand, AdditiveGroup,
 };
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::{
     fmt::{Debug, Display},
     hash::Hash,
-    ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign},
+    ops::{Add, AddAssign, Mul, MulAssign},
     vec::Vec,
 };
-use num_traits::Zero;
 pub use scalar_mul::{variable_base::VariableBaseMSM, ScalarMul};
 use zeroize::Zeroize;
 
@@ -47,38 +46,7 @@ pub mod hashing;
 pub mod pairing;
 
 /// Represents (elements of) a group of prime order `r`.
-pub trait Group:
-    Eq
-    + 'static
-    + Sized
-    + CanonicalSerialize
-    + CanonicalDeserialize
-    + Copy
-    + Clone
-    + Default
-    + Send
-    + Sync
-    + Hash
-    + Debug
-    + Display
-    + UniformRand
-    + Zeroize
-    + Zero
-    + Neg<Output = Self>
-    + Add<Self, Output = Self>
-    + Sub<Self, Output = Self>
-    + Mul<<Self as Group>::ScalarField, Output = Self>
-    + AddAssign<Self>
-    + SubAssign<Self>
-    + MulAssign<<Self as Group>::ScalarField>
-    + for<'a> Add<&'a Self, Output = Self>
-    + for<'a> Sub<&'a Self, Output = Self>
-    + for<'a> Mul<&'a <Self as Group>::ScalarField, Output = Self>
-    + for<'a> AddAssign<&'a Self>
-    + for<'a> SubAssign<&'a Self>
-    + for<'a> MulAssign<&'a <Self as Group>::ScalarField>
-    + core::iter::Sum<Self>
-    + for<'a> core::iter::Sum<&'a Self>
+pub trait PrimeGroup: AdditiveGroup<Scalar = Self::ScalarField>
 {
     /// The scalar field `F_r`, where `r` is the order of this group.
     type ScalarField: PrimeField;
@@ -116,12 +84,13 @@ pub trait Group:
     }
 }
 
+
 /// An opaque representation of an elliptic curve group element that is suitable
 /// for efficient group arithmetic.
 ///
 /// The point is guaranteed to be in the correct prime order subgroup.
 pub trait CurveGroup:
-    Group
+    PrimeGroup<ScalarField = <Self as CurveGroup>::ScalarField>
     + Add<Self::Affine, Output = Self>
     + AddAssign<Self::Affine>
     // + for<'a> Add<&'a Self::Affine, Output = Self>
@@ -133,14 +102,15 @@ pub trait CurveGroup:
     + core::iter::Sum<Self::Affine>
     + for<'a> core::iter::Sum<&'a Self::Affine>
 {
-    type Config: CurveConfig<ScalarField = Self::ScalarField, BaseField = Self::BaseField>;
+    type Config: CurveConfig<ScalarField = <Self as PrimeGroup>::ScalarField, BaseField = Self::BaseField>;
+    type ScalarField: PrimeField;
     /// The field over which this curve is defined.
     type BaseField: Field;
     /// The affine representation of this element.
     type Affine: AffineRepr<
             Config = Self::Config,
             Group = Self,
-            ScalarField = Self::ScalarField,
+            ScalarField = <Self as PrimeGroup>::ScalarField,
             BaseField = Self::BaseField,
         > + From<Self>
         + Into<Self>;
@@ -278,7 +248,7 @@ where
     Self::E2: MulAssign<<Self::E1 as CurveGroup>::BaseField>,
 {
     type E1: CurveGroup<
-        BaseField = <Self::E2 as Group>::ScalarField,
+        BaseField = <Self::E2 as PrimeGroup>::ScalarField,
         ScalarField = <Self::E2 as CurveGroup>::BaseField,
     >;
     type E2: CurveGroup;
@@ -289,12 +259,12 @@ pub trait PairingFriendlyCycle: CurveCycle {
     type Engine1: pairing::Pairing<
         G1 = Self::E1,
         G1Affine = <Self::E1 as CurveGroup>::Affine,
-        ScalarField = <Self::E1 as Group>::ScalarField,
+        ScalarField = <Self::E1 as PrimeGroup>::ScalarField,
     >;
 
     type Engine2: pairing::Pairing<
         G1 = Self::E2,
         G1Affine = <Self::E2 as CurveGroup>::Affine,
-        ScalarField = <Self::E2 as Group>::ScalarField,
+        ScalarField = <Self::E2 as PrimeGroup>::ScalarField,
     >;
 }

ec/src/models/short_weierstrass/group.rs

@@ -15,7 +15,7 @@ use ark_std::{
     One, Zero,
 };
 
-use ark_ff::{fields::Field, PrimeField, ToConstraintField, UniformRand};
+use ark_ff::{AdditiveGroup, fields::Field, PrimeField, ToConstraintField, UniformRand};
 
 use zeroize::Zeroize;
 
@@ -25,7 +25,7 @@ use rayon::prelude::*;
 use super::{Affine, SWCurveConfig};
 use crate::{
     scalar_mul::{variable_base::VariableBaseMSM, ScalarMul},
-    AffineRepr, CurveGroup, Group,
+    AffineRepr, CurveGroup, PrimeGroup,
 };
 
 /// Jacobian coordinates for a point on an elliptic curve in short Weierstrass
@@ -160,7 +160,11 @@ impl<P: SWCurveConfig> Zero for Projective<P> {
     }
 }
 
-impl<P: SWCurveConfig> Group for Projective<P> {
+impl<P: SWCurveConfig> AdditiveGroup for Projective<P> {
+    type Scalar = P::ScalarField;
+}
+
+impl<P: SWCurveConfig> PrimeGroup for Projective<P> {
     type ScalarField = P::ScalarField;
 
     #[inline]
@@ -283,6 +287,7 @@ impl<P: SWCurveConfig> Group for Projective<P> {
 impl<P: SWCurveConfig> CurveGroup for Projective<P> {
     type Config = P;
     type BaseField = P::BaseField;
+    type ScalarField = P::ScalarField;
     type Affine = Affine<P>;
     type FullGroup = Affine<P>;
 

ec/src/models/short_weierstrass/mod.rs

@@ -6,7 +6,7 @@ use ark_std::io::{Read, Write};
 
 use ark_ff::fields::Field;
 
-use crate::{scalar_mul::variable_base::VariableBaseMSM, AffineRepr, Group};
+use crate::{scalar_mul::variable_base::VariableBaseMSM, AffineRepr, PrimeGroup};
 
 use num_traits::Zero;
 

ec/src/models/twisted_edwards/group.rs

@@ -15,7 +15,7 @@ use ark_std::{
     One, Zero,
 };
 
-use ark_ff::{fields::Field, PrimeField, ToConstraintField, UniformRand};
+use ark_ff::{AdditiveGroup, fields::Field, PrimeField, ToConstraintField, UniformRand};
 
 use zeroize::Zeroize;
 
@@ -25,7 +25,7 @@ use rayon::prelude::*;
 use super::{Affine, MontCurveConfig, TECurveConfig};
 use crate::{
     scalar_mul::{variable_base::VariableBaseMSM, ScalarMul},
-    AffineRepr, CurveGroup, Group,
+    AffineRepr, CurveGroup, PrimeGroup,
 };
 
 /// `Projective` implements Extended Twisted Edwards Coordinates
@@ -150,7 +150,11 @@ impl<P: TECurveConfig> Zero for Projective<P> {
     }
 }
 
-impl<P: TECurveConfig> Group for Projective<P> {
+impl<P: TECurveConfig> AdditiveGroup for Projective<P> {
+    type Scalar = P::ScalarField;
+}
+
+impl<P: TECurveConfig> PrimeGroup for Projective<P> {
     type ScalarField = P::ScalarField;
 
     fn generator() -> Self {
@@ -201,6 +205,7 @@ impl<P: TECurveConfig> CurveGroup for Projective<P> {
     type Config = P;
     type BaseField = P::BaseField;
     type Affine = Affine<P>;
+    type ScalarField = P::ScalarField;
     type FullGroup = Affine<P>;
 
     fn normalize_batch(v: &[Self]) -> Vec<Self::Affine> {
@@ -226,6 +231,7 @@ impl<P: TECurveConfig> CurveGroup for Projective<P> {
             })
             .collect()
     }
+
 }
 
 impl<P: TECurveConfig> Neg for Projective<P> {

ec/src/models/twisted_edwards/mod.rs

@@ -4,7 +4,7 @@ use ark_serialize::{
 };
 use ark_std::io::{Read, Write};
 
-use crate::{scalar_mul::variable_base::VariableBaseMSM, AffineRepr, Group};
+use crate::{scalar_mul::variable_base::VariableBaseMSM, AffineRepr, PrimeGroup};
 use num_traits::Zero;
 
 use ark_ff::fields::Field;

ec/src/pairing.rs

@@ -1,4 +1,4 @@
-use ark_ff::{CyclotomicMultSubgroup, Field, One, PrimeField};
+use ark_ff::{CyclotomicMultSubgroup, Field, One, PrimeField, AdditiveGroup};
 use ark_serialize::{
     CanonicalDeserialize, CanonicalSerialize, Compress, SerializationError, Valid, Validate,
 };
@@ -16,7 +16,7 @@ use ark_std::{
 };
 use zeroize::Zeroize;
 
-use crate::{AffineRepr, CurveGroup, Group, VariableBaseMSM};
+use crate::{AffineRepr, CurveGroup, PrimeGroup, VariableBaseMSM};
 
 /// Collection of types (mainly fields and curves) that together describe
 /// how to compute a pairing over a pairing-friendly curve.
@@ -265,7 +265,11 @@ impl<P: Pairing> Distribution<PairingOutput<P>> for Standard {
     }
 }
 
-impl<P: Pairing> Group for PairingOutput<P> {
+impl<P: Pairing> AdditiveGroup for PairingOutput<P> {
+    type Scalar = P::ScalarField;
+}
+
+impl<P: Pairing> PrimeGroup for PairingOutput<P> {
     type ScalarField = P::ScalarField;
 
     fn generator() -> Self {

ec/src/scalar_mul/fixed_base.rs

@@ -4,6 +4,8 @@ use ark_std::{cfg_iter, cfg_iter_mut, vec::Vec};
 #[cfg(feature = "parallel")]
 use rayon::prelude::*;
 
+use crate::PrimeGroup;
+
 use super::ScalarMul;
 
 pub struct FixedBase;

ec/src/scalar_mul/mod.rs

@@ -4,7 +4,7 @@ pub mod wnaf;
 pub mod fixed_base;
 pub mod variable_base;
 
-use crate::Group;
+use crate::PrimeGroup;
 use ark_std::{
     ops::{Add, AddAssign, Mul, Neg, Sub, SubAssign},
     vec::Vec,
@@ -20,7 +20,7 @@ fn ln_without_floats(a: usize) -> usize {
 }
 
 pub trait ScalarMul:
-    Group
+    PrimeGroup
     + Add<Self::MulBase, Output = Self>
     + AddAssign<Self::MulBase>
     + for<'a> Add<&'a Self::MulBase, Output = Self>