Optimize bls12 381 pairing

math/benches/criterion_elliptic_curve.rs

@@ -10,6 +10,6 @@ use elliptic_curves::{
 criterion_group!(
     name = elliptic_curve_benches;
     config = Criterion::default().with_profiler(PProfProfiler::new(100, Output::Flamegraph(None)));
-    targets = bn_254_elliptic_curve_benchmarks,bls12_377_elliptic_curve_benchmarks,bls12_381_elliptic_curve_benchmarks
+    targets = bn_254_elliptic_curve_benchmarks,bls12_381_elliptic_curve_benchmarks,bls12_377_elliptic_curve_benchmarks
 );
 criterion_main!(elliptic_curve_benches);

math/benches/elliptic_curves/bls12_381.rs

@@ -4,7 +4,12 @@ use lambdaworks_math::{
     elliptic_curve::{
         short_weierstrass::{
             curves::bls12_381::{
-                curve::BLS12381Curve, pairing::BLS12381AtePairing, twist::BLS12381TwistCurve,
+                curve::BLS12381Curve,
+                pairing::{
+                    final_exponentiation, final_exponentiation_optimized, miller, miller_optimized,
+                    BLS12381AtePairing,
+                },
+                twist::BLS12381TwistCurve,
             },
             traits::Compress,
         },
@@ -24,6 +29,8 @@ pub fn bls12_381_elliptic_curve_benchmarks(c: &mut Criterion) {
     let a_g2 = BLS12381TwistCurve::generator();
     let b_g2 = BLS12381TwistCurve::generator();
 
+    let miller_loop_output = miller_optimized(&a_g2, &a_g1);
+
     let mut group = c.benchmark_group("BLS12-381 Ops");
     group.significance_level(0.1).sample_size(10000);
     group.throughput(criterion::Throughput::Elements(1));
@@ -93,4 +100,28 @@ pub fn bls12_381_elliptic_curve_benchmarks(c: &mut Criterion) {
             ))
         });
     });
+
+    // Miller Naive
+    group.bench_function("Miller Naive", |bencher| {
+        bencher.iter(|| black_box(miller(black_box(&a_g2), black_box(&a_g1))))
+    });
+
+    // Miller Optimized
+    group.bench_function("Miller Optimized", |bencher| {
+        bencher.iter(|| black_box(miller_optimized(black_box(&a_g2), black_box(&a_g1))))
+    });
+
+    // Final Exponentiation Naive
+    group.bench_function("Final Exponentiation Naive", |bencher| {
+        bencher.iter(|| black_box(final_exponentiation(black_box(&miller_loop_output))))
+    });
+
+    // Final Exponentiation Optimized
+    group.bench_function("Final Exponentiation Optimized", |bencher| {
+        bencher.iter(|| {
+            black_box(final_exponentiation_optimized(black_box(
+                &miller_loop_output,
+            )))
+        })
+    });
 }

math/src/elliptic_curve/short_weierstrass/curves/bls12_381/field_extension.rs

@@ -21,6 +21,7 @@ impl IsModulus<U384> for BLS12381FieldModulus {
 }
 
 pub type BLS12381PrimeField = MontgomeryBackendPrimeField<BLS12381FieldModulus, 6>;
+type Fp2E = FieldElement<Degree2ExtensionField>;
 
 //////////////////
 #[derive(Clone, Debug)]
@@ -199,6 +200,16 @@ impl HasCubicNonResidue<Degree2ExtensionField> for LevelTwoResidue {
     }
 }
 
+impl HasQuadraticNonResidue<Degree2ExtensionField> for LevelTwoResidue {
+    fn residue() -> FieldElement<Degree2ExtensionField> {
+        FieldElement::new([
+            FieldElement::new(U384::from("1")),
+            FieldElement::new(U384::from("1")),
+        ])
+    }
+}
+pub type Degree4ExtensionField = QuadraticExtensionField<Degree2ExtensionField, LevelTwoResidue>;
+
 pub type Degree6ExtensionField = CubicExtensionField<Degree2ExtensionField, LevelTwoResidue>;
 
 #[derive(Debug, Clone)]
@@ -284,6 +295,14 @@ impl FieldElement<Degree12ExtensionField> {
     }
 }
 
+/// Computes the multiplication of an element of fp2 by the level two non-residue 9+u.
+pub fn mul_fp2_by_nonresidue(a: &Fp2E) -> Fp2E {
+    // (c0 + c1 * u) * (1 + u) = (c0 - c1) + (c1 + c0) * u
+    let c0 = &a.value()[0] - &a.value()[1]; // c0 - c1
+    let c1 = &a.value()[0] + &a.value()[1]; // c1 + c0
+
+    Fp2E::new([c0, c1])
+}
 #[cfg(test)]
 mod tests {
     use crate::elliptic_curve::{