diff --git a/ec/src/hashing/curve_maps/swu.rs b/ec/src/hashing/curve_maps/swu/mod.rs
similarity index 95%
rename from ec/src/hashing/curve_maps/swu.rs
rename to ec/src/hashing/curve_maps/swu/mod.rs
index c989ece48..47330c52c 100644
--- a/ec/src/hashing/curve_maps/swu.rs
+++ b/ec/src/hashing/curve_maps/swu/mod.rs
@@ -35,8 +35,8 @@ pub fn parity<F: Field>(element: &F) -> bool {
 }
 
 impl<P: SWUConfig> MapToCurve<Projective<P>> for SWUMap<P> {
-    /// Checks if `P` represents a valid map.
-    fn check_parameters() -> Result<(), HashToCurveError> {
+    /// Constructs a new map if `P` represents a valid map.
+    fn new() -> Result<Self, HashToCurveError> {
         // Verifying that ZETA is a non-square
         if P::ZETA.legendre().is_qr() {
             return Err(HashToCurveError::MapToCurveError(
@@ -49,13 +49,13 @@ impl<P: SWUConfig> MapToCurve<Projective<P>> for SWUMap<P> {
             return Err(HashToCurveError::MapToCurveError("Simplified SWU requires a * b != 0 in the short Weierstrass form of y^2 = x^3 + a*x + b ".to_string()));
         }
 
-        Ok(())
+        Ok(SWUMap(PhantomData))
     }
 
     /// Map an arbitrary base field element to a curve point.
     /// Based on
     /// <https://github.com/zcash/pasta_curves/blob/main/src/hashtocurve.rs>.
-    fn map_to_curve(point: P::BaseField) -> Result<Affine<P>, HashToCurveError> {
+    fn map_to_curve(&self, point: P::BaseField) -> Result<Affine<P>, HashToCurveError> {
         // 1. tv1 = inv0(Z^2 * u^4 + Z * u^2)
         // 2. x1 = (-B / A) * (1 + tv1)
         // 3. If tv1 == 0, set x1 = B / (Z * A)
@@ -256,12 +256,15 @@ mod test {
     /// elements should be mapped to curve successfully. everything can be mapped
     #[test]
     fn map_field_to_curve_swu() {
-        SWUMap::<TestSWUMapToCurveConfig>::check_parameters().unwrap();
+        let test_map_to_curve = SWUMap::<TestSWUMapToCurveConfig>::new().unwrap();
 
         let mut map_range: Vec<Affine<TestSWUMapToCurveConfig>> = vec![];
         for current_field_element in 0..127 {
-            let point = F127::from(current_field_element as u64);
-            map_range.push(SWUMap::<TestSWUMapToCurveConfig>::map_to_curve(point).unwrap());
+            map_range.push(
+                test_map_to_curve
+                    .map_to_curve(F127::from(current_field_element as u64))
+                    .unwrap(),
+            );
         }
 
         let mut counts = HashMap::new();
diff --git a/ec/src/hashing/curve_maps/wb.rs b/ec/src/hashing/curve_maps/wb/mod.rs
similarity index 96%
rename from ec/src/hashing/curve_maps/wb.rs
rename to ec/src/hashing/curve_maps/wb/mod.rs
index 46b635b1c..10ddbb0f7 100644
--- a/ec/src/hashing/curve_maps/wb.rs
+++ b/ec/src/hashing/curve_maps/wb/mod.rs
@@ -79,13 +79,13 @@ pub trait WBConfig: SWCurveConfig + Sized {
 }
 
 pub struct WBMap<P: WBConfig> {
-    swu_field_curve_hasher: PhantomData<SWUMap<P::IsogenousCurve>>,
+    swu_field_curve_hasher: SWUMap<P::IsogenousCurve>,
     curve_params: PhantomData<fn() -> P>,
 }
 
 impl<P: WBConfig> MapToCurve<Projective<P>> for WBMap<P> {
-    /// Checks if `P` represents a valid map.
-    fn check_parameters() -> Result<(), HashToCurveError> {
+    /// Constructs a new map if `P` represents a valid map.
+    fn new() -> Result<Self, HashToCurveError> {
         match P::ISOGENY_MAP.apply(P::IsogenousCurve::GENERATOR) {
             Ok(point_on_curve) => {
                 if !point_on_curve.is_on_curve() {
@@ -95,18 +95,21 @@ impl<P: WBConfig> MapToCurve<Projective<P>> for WBMap<P> {
             Err(e) => return Err(e),
         }
 
-        SWUMap::<P::IsogenousCurve>::check_parameters().unwrap(); // Or ?
-        Ok(())
+        Ok(WBMap {
+            swu_field_curve_hasher: SWUMap::<P::IsogenousCurve>::new().unwrap(),
+            curve_params: PhantomData,
+        })
     }
 
     /// Map random field point to a random curve point
     /// inspired from
     /// <https://github.com/zcash/pasta_curves/blob/main/src/hashtocurve.rs>
     fn map_to_curve(
+        &self,
         element: <Affine<P> as AffineRepr>::BaseField,
     ) -> Result<Affine<P>, HashToCurveError> {
         // first we need to map the field point to the isogenous curve
-        let point_on_isogenious_curve = SWUMap::<P::IsogenousCurve>::map_to_curve(element).unwrap();
+        let point_on_isogenious_curve = self.swu_field_curve_hasher.map_to_curve(element).unwrap();
         P::ISOGENY_MAP.apply(point_on_isogenious_curve)
     }
 }
diff --git a/ec/src/hashing/map_to_curve_hasher.rs b/ec/src/hashing/map_to_curve_hasher.rs
index fa50a5e57..bbb005767 100644
--- a/ec/src/hashing/map_to_curve_hasher.rs
+++ b/ec/src/hashing/map_to_curve_hasher.rs
@@ -7,11 +7,11 @@ use ark_std::marker::PhantomData;
 
 /// Trait for mapping a random field element to a random curve point.
 pub trait MapToCurve<T: CurveGroup>: Sized {
-    /// Checks whether supplied parameters represent a valid map.
-    fn check_parameters() -> Result<(), HashToCurveError>;
+    /// Constructs a new mapping.
+    fn new() -> Result<Self, HashToCurveError>;
 
     /// Map an arbitary field element to a corresponding curve point.
-    fn map_to_curve(point: T::BaseField) -> Result<T::Affine, HashToCurveError>;
+    fn map_to_curve(&self, point: T::BaseField) -> Result<T::Affine, HashToCurveError>;
 }
 
 /// Helper struct that can be used to construct elements on the elliptic curve
@@ -24,7 +24,8 @@ where
     M2C: MapToCurve<T>,
 {
     field_hasher: H2F,
-    _phantom: PhantomData<(T, M2C)>,
+    curve_mapper: M2C,
+    _params_t: PhantomData<T>,
 }
 
 impl<T, H2F, M2C> HashToCurve<T> for MapToCurveBasedHasher<T, H2F, M2C>
@@ -34,11 +35,13 @@ where
     M2C: MapToCurve<T>,
 {
     fn new(domain: &[u8]) -> Result<Self, HashToCurveError> {
-        #[cfg(test)]
-        M2C::check_parameters()?;
+        let field_hasher = H2F::new(domain);
+        let curve_mapper = M2C::new()?;
+        let _params_t = PhantomData;
         Ok(MapToCurveBasedHasher {
-            field_hasher: H2F::new(domain),
-            _phantom: PhantomData,
+            field_hasher,
+            curve_mapper,
+            _params_t,
         })
     }
 
@@ -58,8 +61,8 @@ where
 
         let rand_field_elems = self.field_hasher.hash_to_field(msg, 2);
 
-        let rand_curve_elem_0 = M2C::map_to_curve(rand_field_elems[0])?;
-        let rand_curve_elem_1 = M2C::map_to_curve(rand_field_elems[1])?;
+        let rand_curve_elem_0 = self.curve_mapper.map_to_curve(rand_field_elems[0])?;
+        let rand_curve_elem_1 = self.curve_mapper.map_to_curve(rand_field_elems[1])?;
 
         let rand_curve_elem = (rand_curve_elem_0 + rand_curve_elem_1).into();
         let rand_subgroup_elem = rand_curve_elem.clear_cofactor();