diff --git a/src/curves/bls12_377.nr b/src/curves/bls12_377.nr
index 835f62e..8910016 100644
--- a/src/curves/bls12_377.nr
+++ b/src/curves/bls12_377.nr
@@ -5,7 +5,7 @@ use bignum::BigNum;
 
 pub use bignum::{BLS12_377_Fq, BLS12_377_Fr};
 
-global BLS12_377_SCALAR_SLICES: u32 = 64;
+pub global BLS12_377_SCALAR_SLICES: u32 = 64;
 pub struct BLS12_377_Params {}
 impl CurveParamsTrait<BLS12_377_Fq> for BLS12_377_Params {
     fn a() -> BLS12_377_Fq {
diff --git a/src/curves/bls12_381.nr b/src/curves/bls12_381.nr
index 9b88301..ae2a9de 100644
--- a/src/curves/bls12_381.nr
+++ b/src/curves/bls12_381.nr
@@ -4,7 +4,7 @@ use crate::scalar_field::ScalarField;
 use bignum::BigNum;
 use bignum::BLS12_381_Fq;
 
-global BLS12_381_SCALAR_SLICES: u32 = 64;
+pub global BLS12_381_SCALAR_SLICES: u32 = 64;
 pub struct BLS12_381_Params {}
 impl CurveParamsTrait<BLS12_381_Fq> for BLS12_381_Params {
     fn a() -> BLS12_381_Fq {
diff --git a/src/curves/bn254.nr b/src/curves/bn254.nr
index 42ee169..fd3190f 100644
--- a/src/curves/bn254.nr
+++ b/src/curves/bn254.nr
@@ -46,7 +46,7 @@ impl CurveParamsTrait<BN254_Fq> for BN254Params {
     }
 }
 
-global BN254_SCALAR_SLICES: u32 = 64;
+pub global BN254_SCALAR_SLICES: u32 = 64;
 pub type BN254 = BigCurve<BN254_Fq, BN254Params>;
 pub type BN254Scalar = ScalarField<BN254_SCALAR_SLICES>;
 // pub type Secp256r1Fr = BigNum<3, Secp256r1_Fr_Params>;
diff --git a/src/curves/mnt4_753.nr b/src/curves/mnt4_753.nr
index b5f282b..c33c92c 100644
--- a/src/curves/mnt4_753.nr
+++ b/src/curves/mnt4_753.nr
@@ -4,7 +4,7 @@ use crate::scalar_field::ScalarField;
 use bignum::BigNum;
 pub use bignum::{MNT4_753_Fq, MNT4_753_Fr};
 
-global MNT4_753_SCALAR_SLICES: u32 = 189;
+pub global MNT4_753_SCALAR_SLICES: u32 = 189;
 pub struct MNT4_753_Params {}
 impl CurveParamsTrait<MNT4_753_Fq> for MNT4_753_Params {
     fn a() -> MNT4_753_Fq {
diff --git a/src/curves/mnt6_753.nr b/src/curves/mnt6_753.nr
index 521336f..a7d999e 100644
--- a/src/curves/mnt6_753.nr
+++ b/src/curves/mnt6_753.nr
@@ -4,7 +4,7 @@ use crate::scalar_field::ScalarField;
 use bignum::BigNum;
 pub use bignum::{MNT6_753_Fq, MNT6_753_Fr};
 
-global MNT6_753_SCALAR_SLICES: u32 = 189;
+pub global MNT6_753_SCALAR_SLICES: u32 = 189;
 pub struct MNT6_753_Params {}
 impl CurveParamsTrait<MNT6_753_Fq> for MNT6_753_Params {
     fn a() -> MNT6_753_Fq {
diff --git a/src/curves/mod.nr b/src/curves/mod.nr
index b190bf8..09593a4 100644
--- a/src/curves/mod.nr
+++ b/src/curves/mod.nr
@@ -1,10 +1,10 @@
-pub(crate) mod pallas;
-pub(crate) mod vesta;
-pub(crate) mod bls12_377;
-pub(crate) mod bls12_381;
-pub(crate) mod secp256k1;
-pub(crate) mod secp256r1;
-pub(crate) mod secp384r1;
-pub(crate) mod mnt4_753;
-pub(crate) mod mnt6_753;
-pub(crate) mod bn254;
+pub mod pallas;
+pub mod vesta;
+pub mod bls12_377;
+pub mod bls12_381;
+pub mod secp256k1;
+pub mod secp256r1;
+pub mod secp384r1;
+pub mod mnt4_753;
+pub mod mnt6_753;
+pub mod bn254;
diff --git a/src/curves/pallas.nr b/src/curves/pallas.nr
index 0c2f175..11d3241 100644
--- a/src/curves/pallas.nr
+++ b/src/curves/pallas.nr
@@ -5,7 +5,7 @@ use bignum::BigNum;
 
 pub use bignum::{Pallas_Fq, Pallas_Fr};
 
-global PALLAS_SCALAR_SLICES: u32 = 64;
+pub global PALLAS_SCALAR_SLICES: u32 = 64;
 
 pub struct Pallas_Params {}
 impl CurveParamsTrait<Pallas_Fq> for Pallas_Params {
diff --git a/src/curves/secp256k1.nr b/src/curves/secp256k1.nr
index b5b20e3..c8ca8fc 100644
--- a/src/curves/secp256k1.nr
+++ b/src/curves/secp256k1.nr
@@ -5,7 +5,7 @@ use bignum::BigNum;
 
 pub use bignum::{Secp256k1_Fq, Secp256k1_Fr};
 
-global SECP256k1_SCALAR_SLICES: u32 = 65;
+pub global SECP256k1_SCALAR_SLICES: u32 = 65;
 pub struct Secp256k1_Params {}
 
 impl CurveParamsTrait<Secp256k1_Fq> for Secp256k1_Params {
diff --git a/src/lib.nr b/src/lib.nr
index d50746f..14630b6 100644
--- a/src/lib.nr
+++ b/src/lib.nr
@@ -1,4 +1,4 @@
-pub(crate) mod scalar_field;
+pub mod scalar_field;
 pub(crate) mod curve_jac;
 mod test_data;
 mod bigcurve_test;
@@ -23,7 +23,7 @@ pub struct BigCurve<B, CurveParams> {
     pub is_infinity: bool,
 }
 
-trait CurveParamsTrait<B: BigNum> {
+pub trait CurveParamsTrait<B: BigNum> {
     fn offset_generator() -> [B; 2];
     fn offset_generator_final() -> [B; 2];
     fn one() -> [B; 2];
@@ -92,7 +92,7 @@ impl<B: BigNum> PointTable<B> {
     }
 }
 
-trait BigCurveTrait {
+pub trait BigCurveTrait {
     fn neg(self) -> Self;
     fn point_at_infinity() -> Self;
     fn offset_generator() -> Self;
@@ -417,6 +417,7 @@ where
             [false],
         );
 
+        // x3 = lambda * lambda - x2 - x1
         bignum::bignum::evaluate_quadratic_expression(
             [[lambda]],
             [[false]],