Adding wNAF multiplication functionality

CHANGELOG.md

@@ -51,6 +51,7 @@ The main features of this release are:
 - #140 (ark-poly) Add support for multilinear extensions in dense and sparse evaluation form.
 - #164 (ark-ff) Add methods `from_{be, le}_bytes_mod_order` to the `PrimeField` trait.
 - #197 (ark-test-curves) Add a BN384 curve with low two-arity for mixed-radix testing.
+- #230 (ark-ec) Add `wnaf_mul` implementation for `ProjectiveCurve`.
 
 ### Improvements
 - #22 (ark-ec) Speedup fixed-base MSMs

ec/src/lib.rs

@@ -36,6 +36,8 @@ pub mod group;
 
 pub mod msm;
 
+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;

ec/src/wnaf.rs

@@ -0,0 +1,42 @@
+extern crate alloc;
+use crate::ProjectiveCurve;
+use alloc::vec::Vec;
+
+// Computes scalar multiplication of a preprocessed group element by a scalar in windowed non-adjacent form (wNAF).
+// `scalar_wnaf` is expected in its NAF form which can be obtained by using `find_wnaf` on the underlying BigInt.
+// `table` holds pre-computed multiples of the group element; it can be calculated using `wnaf_table`.
+pub fn wnaf_mul<G: ProjectiveCurve>(table: &[G], scalar_wnaf: &[i64]) -> G {
+    let mut result = G::zero();
+
+    let mut found_non_zero = false;
+
+    for n in scalar_wnaf.iter().rev() {
+        if found_one {
+            result.double_in_place();
+        }
+
+        if *n != 0 {
+            found_non_zero = true;
+
+            if *n > 0 {
+                result += &table[(n / 2) as usize];
+            } else {
+                result -= &table[((-n) / 2) as usize];
+            }
+        }
+    }
+
+    result
+}
+
+pub fn wnaf_table<G: ProjectiveCurve>(mut base: G, window: usize) -> Vec<G> {
+    let mut table = Vec::with_capacity(1 << (window - 1));
+
+    let dbl = base.double();
+
+    for _ in 0..(1 << (window - 1)) {
+        table.push(base);
+        base += &dbl;
+    }
+    table
+}

test-templates/src/curves.rs

@@ -3,8 +3,10 @@ use ark_ec::{
     AffineCurve, MontgomeryModelParameters, ProjectiveCurve, SWModelParameters, TEModelParameters,
 };
 use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
+use ark_ff::BigInteger;
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, SWFlags, SerializationError};
 use ark_std::{io::Cursor, vec::Vec};
+use ark_ec::wnaf::{wnaf_mul, wnaf_table};
 
 pub const ITERATIONS: usize = 10;
 
@@ -103,6 +105,17 @@ fn random_multiplication_test<G: ProjectiveCurve>() {
         tmp1.add_assign(&b);
         tmp1.mul_assign(s);
 
+        // s ( a + b) using wNAF for several window values in [2,5]
+        for w in 2..=5 {
+            let mut tmp4 = a;
+            tmp4.add_assign(&b);
+
+            let scalar_wnaf = s.into_repr().find_wnaf();
+            let wnaf_lut = wnaf_table(tmp4, w);
+
+            assert_eq!(tmp1, wnaf_mul(&wnaf_lut, &scalar_wnaf));
+        }
+
         // sa + sb
         a.mul_assign(s);
         b.mul_assign(s);

test-templates/src/groups.rs

@@ -1,5 +1,6 @@
 #![allow(unused)]
 use ark_ec::group::Group;
+use ark_ff::fields::PrimeField;
 use ark_ff::{One, UniformRand, Zero};
 
 pub fn group_test<G: Group>(a: G, mut b: G) {
@@ -8,6 +9,7 @@ pub fn group_test<G: Group>(a: G, mut b: G) {
     let fr_zero = G::ScalarField::zero();
     let fr_one = G::ScalarField::one();
     let fr_two = fr_one + &fr_one;
+
     assert_eq!(zero, zero);
     assert_eq!(zero.is_zero(), true);
     assert_eq!(a.mul(&fr_one), a);