Improve ergonomics of scalar field multiplication. (#443)

Co-authored-by: Michele Orrù <[email protected]> Co-authored-by: George Kadianakis <[email protected]> Co-authored-by: Pratyush Mishra <[email protected]> Co-authored-by: Weikeng Chen <[email protected]>
arkworks-rs · Aug 1, 2022 · dd5b9d6 · dd5b9d6
1 parent ffea2b8
commit dd5b9d6
Show file tree

Hide file tree

Showing 7 changed files with 80 additions and 54 deletions.
diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -46,6 +46,13 @@
     - `TEModelParameters` → `TECurveConfig`
     - `MontgomeryModelParameters` → `MontCurveConfig`
 - [\#440](https://github.com/arkworks-rs/algebra/pull/440) (`ark-ff`) Add a method to construct a field element from an element of the underlying base prime field.
+- [\#443](https://github.com/arkworks-rs/algebra/pull/443) (`ark-ec`) Improve ergonomics of scalar multiplication.
+    - Rename `ProjectiveCurve::mul(AsRef[u64])` to `ProjectiveCurve::mul_bigint(AsRef[u64])`.
+    - Bound `ProjectiveCurve` by
+        - `Mul<ScalarField>`,
+        - `for<'a> Mul<&'a ScalarField>`
+        - `MulAssign<ScalarField>`,
+        - `for<'a> MulAssign<&'a ScalarField>`
 
 ### Features
 

diff --git a/ec/src/lib.rs b/ec/src/lib.rs
@@ -27,7 +27,7 @@ use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::{
     fmt::{Debug, Display},
     hash::Hash,
-    ops::{Add, AddAssign, MulAssign, Neg, Sub, SubAssign},
+    ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign},
     vec::Vec,
 };
 use msm::VariableBaseMSM;
@@ -149,13 +149,16 @@ pub trait ProjectiveCurve:
     + Neg<Output = Self>
     + Add<Self, Output = Self>
     + Sub<Self, Output = Self>
+    + Mul<<Self as ProjectiveCurve>::ScalarField, Output = Self>
     + AddAssign<Self>
     + SubAssign<Self>
     + MulAssign<<Self as ProjectiveCurve>::ScalarField>
     + for<'a> Add<&'a Self, Output = Self>
     + for<'a> Sub<&'a Self, Output = Self>
+    + for<'a> Mul<&'a <Self as ProjectiveCurve>::ScalarField, Output = Self>
     + for<'a> AddAssign<&'a Self>
     + for<'a> SubAssign<&'a Self>
+    + for<'a> MulAssign<&'a <Self as ProjectiveCurve>::ScalarField>
     + core::iter::Sum<Self>
     + for<'a> core::iter::Sum<&'a Self>
     + From<<Self as ProjectiveCurve>::Affine>
@@ -220,7 +223,7 @@ pub trait ProjectiveCurve:
     fn add_assign_mixed(&mut self, other: &Self::Affine);
 
     /// Performs scalar multiplication of this element.
-    fn mul<S: AsRef<[u64]>>(self, other: S) -> Self;
+    fn mul_bigint<S: AsRef<[u64]>>(self, other: S) -> Self;
 }
 
 /// Affine representation of an elliptic curve point guaranteed to be
@@ -285,7 +288,7 @@ pub trait AffineCurve:
 
     /// Performs scalar multiplication of this element with mixed addition.
     #[must_use]
-    fn mul<S: Into<<Self::ScalarField as PrimeField>::BigInt>>(&self, by: S) -> Self::Projective;
+    fn mul_bigint<S: AsRef<[u64]>>(&self, by: S) -> Self::Projective;
 
     /// Performs cofactor clearing.
     /// The default method is simply to multiply by the cofactor.
@@ -308,7 +311,8 @@ pub trait AffineCurve:
     /// `Self::ScalarField`.
     #[must_use]
     fn mul_by_cofactor_inv(&self) -> Self {
-        self.mul(Self::Config::COFACTOR_INV).into()
+        self.mul_bigint(&Self::Config::COFACTOR_INV.into_bigint())
+            .into()
     }
 }
 

diff --git a/ec/src/models/short_weierstrass.rs b/ec/src/models/short_weierstrass.rs
@@ -3,17 +3,15 @@ use ark_serialize::{
     CanonicalSerializeWithFlags, SWFlags, SerializationError,
 };
 use ark_std::{
+    borrow::Borrow,
     fmt::{Display, Formatter, Result as FmtResult},
     hash::{Hash, Hasher},
     io::{Read, Write},
-    ops::{Add, AddAssign, MulAssign, Neg, Sub, SubAssign},
+    ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign},
     vec::Vec,
 };
 
-use ark_ff::{
-    fields::{Field, PrimeField},
-    ToConstraintField, UniformRand,
-};
+use ark_ff::{fields::Field, PrimeField, ToConstraintField, UniformRand};
 
 use crate::{msm::VariableBaseMSM, AffineCurve, ProjectiveCurve};
 
@@ -326,8 +324,8 @@ impl<P: SWCurveConfig> AffineCurve for Affine<P> {
         })
     }
 
-    fn mul<S: Into<<Self::ScalarField as PrimeField>::BigInt>>(&self, by: S) -> Self::Projective {
-        P::mul_affine(self, by.into().as_ref())
+    fn mul_bigint<S: AsRef<[u64]>>(&self, by: S) -> Self::Projective {
+        P::mul_affine(self, by.as_ref())
     }
 
     /// Multiplies this element by the cofactor and output the
@@ -688,7 +686,7 @@ impl<P: SWCurveConfig> ProjectiveCurve for Projective<P> {
     }
 
     #[inline]
-    fn mul<S: AsRef<[u64]>>(self, other: S) -> Self {
+    fn mul_bigint<S: AsRef<[u64]>>(self, other: S) -> Self {
         P::mul_projective(&self, other.as_ref())
     }
 }
@@ -796,9 +794,19 @@ impl<'a, P: SWCurveConfig> SubAssign<&'a Self> for Projective<P> {
     }
 }
 
-impl<P: SWCurveConfig> MulAssign<P::ScalarField> for Projective<P> {
-    fn mul_assign(&mut self, other: P::ScalarField) {
-        *self = self.mul(other.into_bigint())
+impl<P: SWCurveConfig, T: Borrow<P::ScalarField>> MulAssign<T> for Projective<P> {
+    fn mul_assign(&mut self, other: T) {
+        *self = self.mul_bigint(other.borrow().into_bigint())
+    }
+}
+
+impl<'a, P: SWCurveConfig, T: Borrow<P::ScalarField>> Mul<T> for Projective<P> {
+    type Output = Self;
+
+    #[inline]
+    fn mul(mut self, other: T) -> Self {
+        self *= other;
+        self
     }
 }
 

diff --git a/ec/src/models/twisted_edwards.rs b/ec/src/models/twisted_edwards.rs
@@ -4,10 +4,11 @@ use ark_serialize::{
     CanonicalSerializeWithFlags, EdwardsFlags, SerializationError,
 };
 use ark_std::{
+    borrow::Borrow,
     fmt::{Display, Formatter, Result as FmtResult},
     hash::{Hash, Hasher},
     io::{Read, Write},
-    ops::{Add, AddAssign, MulAssign, Neg, Sub, SubAssign},
+    ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign},
     rand::{
         distributions::{Distribution, Standard},
         Rng,
@@ -17,10 +18,7 @@ use ark_std::{
 use num_traits::{One, Zero};
 use zeroize::Zeroize;
 
-use ark_ff::{
-    fields::{Field, PrimeField},
-    ToConstraintField, UniformRand,
-};
+use ark_ff::{fields::Field, PrimeField, ToConstraintField, UniformRand};
 
 #[cfg(feature = "parallel")]
 use rayon::prelude::*;
@@ -234,8 +232,8 @@ impl<P: TECurveConfig> AffineCurve for Affine<P> {
         })
     }
 
-    fn mul<S: Into<<Self::ScalarField as PrimeField>::BigInt>>(&self, by: S) -> Self::Projective {
-        P::mul_affine(self, by.into().as_ref())
+    fn mul_bigint<S: AsRef<[u64]>>(&self, by: S) -> Self::Projective {
+        P::mul_affine(self, by.as_ref())
     }
 
     /// Multiplies this element by the cofactor and output the
@@ -315,7 +313,7 @@ impl<'a, P: TECurveConfig> SubAssign<&'a Self> for Affine<P> {
 
 impl<P: TECurveConfig> MulAssign<P::ScalarField> for Affine<P> {
     fn mul_assign(&mut self, other: P::ScalarField) {
-        *self = self.mul(other.into_bigint()).into()
+        *self = self.mul_bigint(&other.into_bigint()).into()
     }
 }
 
@@ -573,7 +571,7 @@ impl<P: TECurveConfig> ProjectiveCurve for Projective<P> {
     }
 
     #[inline]
-    fn mul<S: AsRef<[u64]>>(self, other: S) -> Self {
+    fn mul_bigint<S: AsRef<[u64]>>(self, other: S) -> Self {
         P::mul_projective(&self, other.as_ref())
     }
 }
@@ -655,9 +653,19 @@ impl<'a, P: TECurveConfig> SubAssign<&'a Self> for Projective<P> {
     }
 }
 
-impl<P: TECurveConfig> MulAssign<P::ScalarField> for Projective<P> {
-    fn mul_assign(&mut self, other: P::ScalarField) {
-        *self = self.mul(other.into_bigint())
+impl<P: TECurveConfig, T: Borrow<P::ScalarField>> MulAssign<T> for Projective<P> {
+    fn mul_assign(&mut self, other: T) {
+        *self = self.mul_bigint(other.borrow().into_bigint())
+    }
+}
+
+impl<P: TECurveConfig, T: Borrow<P::ScalarField>> Mul<T> for Projective<P> {
+    type Output = Self;
+
+    #[inline]
+    fn mul(mut self, other: T) -> Self {
+        self *= other;
+        self
     }
 }
 

diff --git a/test-curves/src/bls12_381/g2.rs b/test-curves/src/bls12_381/g2.rs
@@ -64,7 +64,7 @@ impl short_weierstrass::SWCurveConfig for Parameters {
         // Checks that [p]P = [X]P
 
         let mut x_times_point =
-            point.mul(BigInt::new([crate::bls12_381::Parameters::X[0], 0, 0, 0]));
+            point.mul_bigint(BigInt::new([crate::bls12_381::Parameters::X[0], 0, 0, 0]));
         if crate::bls12_381::Parameters::X_IS_NEGATIVE {
             x_times_point = -x_times_point;
         }
@@ -99,7 +99,7 @@ impl short_weierstrass::SWCurveConfig for Parameters {
 
         // tmp2 = [x^2]P + [x]ψ(P)
         let mut tmp2: Projective<Parameters> = tmp;
-        tmp2 = tmp2.mul(x).neg();
+        tmp2 = tmp2.mul_bigint(x).neg();
 
         // add up all the terms
         psi2_p2 += tmp2;

diff --git a/test-templates/src/curves.rs b/test-templates/src/curves.rs
@@ -127,11 +127,14 @@ fn random_multiplication_test<G: ProjectiveCurve>() {
         tmp2.add_assign(&b);
 
         // Affine multiplication
-        let mut tmp3 = a_affine.mul(s.into_bigint());
-        tmp3.add_assign(&b_affine.mul(s.into_bigint()));
-
+        let mut tmp3 = a_affine.mul_bigint(&s.into_bigint());
+        tmp3.add_assign(&b_affine.mul_bigint(&s.into_bigint()));
         assert_eq!(tmp1, tmp2);
         assert_eq!(tmp1, tmp3);
+
+        let expected = a_affine.mul_bigint(s.into_bigint());
+        let got = a_affine.mul_bigint(&s.into_bigint());
+        assert_eq!(expected, got);
     }
 }
 
@@ -304,12 +307,12 @@ pub fn curve_tests<G: ProjectiveCurve>() {
 
         assert_eq!(zero, zero);
         assert_eq!(zero.is_zero(), true);
-        assert_eq!(a.mul(&fr_one.into_bigint()), a);
-        assert_eq!(a.mul(&fr_two.into_bigint()), a + &a);
-        assert_eq!(a.mul(&fr_zero.into_bigint()), zero);
-        assert_eq!(a.mul(&fr_zero.into_bigint()) - &a, -a);
-        assert_eq!(a.mul(&fr_one.into_bigint()) - &a, zero);
-        assert_eq!(a.mul(&fr_two.into_bigint()) - &a, a);
+        assert_eq!(a.mul(&fr_one), a);
+        assert_eq!(a.mul(&fr_two), a + &a);
+        assert_eq!(a.mul(&fr_zero), zero);
+        assert_eq!(a.mul(&fr_zero) - &a, -a);
+        assert_eq!(a.mul(&fr_one) - &a, zero);
+        assert_eq!(a.mul(&fr_two) - &a, a);
 
         // a == a
         assert_eq!(a, a);
@@ -341,31 +344,27 @@ pub fn curve_tests<G: ProjectiveCurve>() {
 
         let fr_rand1 = G::ScalarField::rand(&mut rng);
         let fr_rand2 = G::ScalarField::rand(&mut rng);
-        let a_rand1 = a.mul(&fr_rand1.into_bigint());
-        let a_rand2 = a.mul(&fr_rand2.into_bigint());
+        let a_rand1 = a.mul(&fr_rand1);
+        let a_rand2 = a.mul(&fr_rand2);
         let fr_three = fr_two + &fr_rand1;
-        let a_two = a.mul(&fr_two.into_bigint());
+        let a_two = a.mul(&fr_two);
         assert_eq!(a_two, a.double(), "(a * 2)  != a.double()");
-        let a_six = a.mul(&(fr_three * &fr_two).into_bigint());
-        assert_eq!(
-            a_two.mul(&fr_three.into_bigint()),
-            a_six,
-            "(a * 2) * 3 != a * (2 * 3)"
-        );
+        let a_six = a.mul(&(fr_three * &fr_two));
+        assert_eq!(a_two.mul(&fr_three), a_six, "(a * 2) * 3 != a * (2 * 3)");
 
         assert_eq!(
-            a_rand1.mul(&fr_rand2.into_bigint()),
-            a_rand2.mul(&fr_rand1.into_bigint()),
+            a_rand1.mul(&fr_rand2),
+            a_rand2.mul(&fr_rand1),
             "(a * r1) * r2 != (a * r2) * r1"
         );
         assert_eq!(
-            a_rand2.mul(&fr_rand1.into_bigint()),
-            a.mul(&(fr_rand1 * &fr_rand2).into_bigint()),
+            a_rand2.mul(&fr_rand1),
+            a.mul(&(fr_rand1 * &fr_rand2)),
             "(a * r2) * r1 != a * (r1 * r2)"
         );
         assert_eq!(
-            a_rand1.mul(&fr_rand2.into_bigint()),
-            a.mul(&(fr_rand1 * &fr_rand2).into_bigint()),
+            a_rand1.mul(&fr_rand2),
+            a.mul(&(fr_rand1 * &fr_rand2)),
             "(a * r1) * r2 != a * (r1 * r2)"
         );
     }

diff --git a/test-templates/src/msm.rs b/test-templates/src/msm.rs
@@ -8,7 +8,7 @@ fn naive_var_base_msm<G: AffineCurve>(bases: &[G], scalars: &[G::ScalarField]) -
     let mut acc = G::Projective::zero();
 
     for (base, scalar) in bases.iter().zip(scalars.iter()) {
-        acc += &base.mul(scalar.into_bigint());
+        acc += base.mul_bigint(&scalar.into_bigint());
     }
     acc
 }