diff --git a/crypto/dalek-ff-group/src/field.rs b/crypto/dalek-ff-group/src/field.rs
index 6f771ac3..f167c5df 100644
--- a/crypto/dalek-ff-group/src/field.rs
+++ b/crypto/dalek-ff-group/src/field.rs
@@ -117,9 +117,8 @@ impl Field for FieldElement {
   }
 
   fn invert(&self) -> CtOption<Self> {
-    const NEG_2: FieldElement =
-      FieldElement(ResidueType::new(&MODULUS.saturating_sub(&U256::from_u8(2))));
-    CtOption::new(self.pow(NEG_2), !self.is_zero())
+    let res = self.0.invert();
+    CtOption::new(Self(res.0), res.1.into())
   }
 
   // RFC-8032 sqrt8k5
diff --git a/crypto/helioselene/src/backend.rs b/crypto/helioselene/src/backend.rs
index 62d7574d..9ae2547e 100644
--- a/crypto/helioselene/src/backend.rs
+++ b/crypto/helioselene/src/backend.rs
@@ -178,16 +178,15 @@ macro_rules! field {
       }
 
       fn square(&self) -> Self {
-        *self * self
+        Self(self.0.square())
       }
       fn double(&self) -> Self {
         *self + self
       }
 
       fn invert(&self) -> CtOption<Self> {
-        const NEG_2: $FieldName =
-          Self($ResidueType::sub(&$ResidueType::ZERO, &$ResidueType::new(&U256::from_u8(2))));
-        CtOption::new(self.pow(NEG_2), !self.is_zero())
+        let res = self.0.invert();
+        CtOption::new(Self(res.0), res.1.into())
       }
 
       fn sqrt(&self) -> CtOption<Self> {