feat(elliptic curve): add fuzzer for BLS12-381 (#664)

* add diff fuzz w/o pairing

* remove unused imports

* remove diff fuzzer

* fix cmts

---------

Co-authored-by: Mauro Toscano <12560266+MauroToscano@users.noreply.github.com>

fuzz/no_gpu_fuzz/Cargo.toml

@@ -16,7 +16,6 @@ num-traits = "0.2"
 ibig = "0.3.6"
 p3-goldilocks = { git = "https://github.com/Plonky3/Plonky3", rev = "41cd843" }
 p3-field = { git = "https://github.com/Plonky3/Plonky3", rev = "41cd843" }
-
 p3-mersenne-31 = { git = "https://github.com/Plonky3/Plonky3", rev = "41cd843" }
 p3-field = { git = "https://github.com/Plonky3/Plonky3", rev = "41cd843" }
 
@@ -26,6 +25,12 @@ path = "fuzz_targets/field_fuzzer.rs"
 test = false
 doc = false
 
+[[bin]]
+name = "curve_bls12_381"
+path = "fuzz_targets/curve_bls12_381.rs"
+test = false
+doc = false
+
 [[bin]]
 name = "field_fuzz_mersenne31"
 path = "fuzz_targets/field_mersenne31.rs"

fuzz/no_gpu_fuzz/fuzz_targets/curve_bls12_381.rs

@@ -0,0 +1,101 @@
+#![no_main]
+
+use libfuzzer_sys::fuzz_target;
+use lambdaworks_math::{
+    field::element::FieldElement,
+    cyclic_group::IsGroup,
+    elliptic_curve::{
+        traits::{IsEllipticCurve, IsPairing},
+        short_weierstrass::{
+            curves::bls12_381::{
+                curve::BLS12381Curve, 
+                twist::BLS12381TwistCurve,
+                pairing::BLS12381AtePairing,
+                field_extension::Degree12ExtensionField,
+            },
+            point::ShortWeierstrassProjectivePoint,
+        }
+    },
+    unsigned_integer::element::U384,
+};
+
+type LambdaG1 = ShortWeierstrassProjectivePoint<BLS12381Curve>;
+type LambdaG2 = ShortWeierstrassProjectivePoint<BLS12381TwistCurve>;
+
+//TODO: Derive arbitrary for Affine and Projective or change this to use &[u8] as input to cover more cases.
+//TODO: Use more advanced options to generate values over curve specifically given most inputs will fail curve check.
+//TODO: Investigate normalization of projective coordinates in arkworks to allow for differential fuzzing.
+fuzz_target!(|values: (u64, u64)| {
+    let (a_val, b_val) = values;
+
+    let a_g1 = BLS12381Curve::generator().operate_with_self(a_val);
+    let b_g1 = BLS12381Curve::generator().operate_with_self(b_val);
+
+    let a_g2 = BLS12381TwistCurve::generator().operate_with_self(a_val);
+    let b_g2 = BLS12381TwistCurve::generator().operate_with_self(b_val);
+
+    // ***AXIOM SOUNDNESS***
+    let g1_zero = LambdaG1::neutral_element();
+
+    let g2_zero = LambdaG2::neutral_element();
+
+    // G1
+    // -O = O
+    assert_eq!(g1_zero.neg(), g1_zero, "Neutral mul element a failed");
+
+    // P + O = O
+    assert_eq!(a_g1.operate_with(&g1_zero), a_g1, "Neutral operate_with element a failed");
+    assert_eq!(b_g1.operate_with(&g1_zero), b_g1, "Neutral operate_with element b failed");
+
+    // P + Q = Q + P
+    assert_eq!(a_g1.operate_with(&b_g1), b_g1.operate_with(&a_g1), "Commutative add property failed");
+
+    // (P + Q) + R = Q + (P + R)
+    let c_g1 = a_g1.operate_with(&b_g1);
+    assert_eq!((a_g1.operate_with(&b_g1)).operate_with(&c_g1), a_g1.operate_with(&b_g1.operate_with(&c_g1)), "Associative operate_with property failed");
+
+    // P + -P = O
+    assert_eq!(a_g1.operate_with(&a_g1.neg()), g1_zero, "Inverse add a failed");
+    assert_eq!(b_g1.operate_with(&b_g1.neg()), g1_zero, "Inverse add b failed");
+
+    // G2
+    // -O = O
+    assert_eq!(g2_zero.neg(), g2_zero, "Neutral mul element a failed");
+
+    // P + O = O
+    assert_eq!(a_g2.operate_with(&g2_zero), a_g2, "Neutral operate_with element a failed");
+    assert_eq!(b_g2.operate_with(&g2_zero), b_g2, "Neutral operate_with element b failed");
+
+    // P + Q = Q + P
+    assert_eq!(a_g2.operate_with(&b_g2), b_g2.operate_with(&a_g2), "Commutative add property failed");
+
+    // (P + Q) + R = Q + (P + R)
+    let c_g2 = a_g2.operate_with(&b_g2);
+    assert_eq!((a_g2.operate_with(&b_g2)).operate_with(&c_g2), a_g2.operate_with(&b_g2.operate_with(&c_g2)), "Associative operate_with property failed");
+
+    // P + -P = O
+    assert_eq!(a_g2.operate_with(&a_g2.neg()), g2_zero, "Inverse add a failed");
+    assert_eq!(b_g2.operate_with(&b_g2.neg()), g2_zero, "Inverse add b failed");
+
+    // Pairing Bilinearity
+    let a = U384::from_u64(a_val);
+    let b = U384::from_u64(b_val);
+    let result = BLS12381AtePairing::compute_batch(&[
+        (
+            &a_g1.operate_with_self(a).to_affine(),
+            &a_g2.operate_with_self(b).to_affine(),
+        ),
+        (
+            &a_g1.operate_with_self(a * b).to_affine(),
+            &a_g2.neg().to_affine(),
+        ),
+    ]);
+    assert_eq!(result, FieldElement::<Degree12ExtensionField>::one());
+
+    // Ate Pairing returns one with one element is neutral element
+    let result = BLS12381AtePairing::compute_batch(&[(&a_g1.to_affine(), &LambdaG2::neutral_element())]);
+    assert_eq!(result, FieldElement::<Degree12ExtensionField>::one());
+
+    let result = BLS12381AtePairing::compute_batch(&[(&LambdaG1::neutral_element(), &a_g2.to_affine())]);
+    assert_eq!(result, FieldElement::<Degree12ExtensionField>::one());
+});