diff --git a/ipa-core/src/ff/boolean.rs b/ipa-core/src/ff/boolean.rs
index ec6d9f6ad..1afcdbdf2 100644
--- a/ipa-core/src/ff/boolean.rs
+++ b/ipa-core/src/ff/boolean.rs
@@ -16,6 +16,16 @@ impl Block for bool {
 #[derive(Clone, Copy, PartialEq, Debug, Eq)]
 pub struct Boolean(bool);
 
+impl Boolean {
+    pub const TRUE: Boolean = Self(true);
+    pub const FALSE: Boolean = Self(false);
+
+    #[must_use]
+    pub fn as_u128(&self) -> u128 {
+        bool::from(*self).into()
+    }
+}
+
 impl ExtendableField for Boolean {
     type ExtendedField = Gf32Bit;
 
@@ -134,7 +144,7 @@ impl Field for Boolean {
     const ONE: Boolean = Boolean(true);
 
     fn as_u128(&self) -> u128 {
-        bool::from(*self).into()
+        Boolean::as_u128(self)
     }
 
     fn truncate_from<T: Into<u128>>(v: T) -> Self {
diff --git a/ipa-core/src/protocol/boolean/generate_random_bits.rs b/ipa-core/src/protocol/boolean/generate_random_bits.rs
index d97cd4cb9..952002c3e 100644
--- a/ipa-core/src/protocol/boolean/generate_random_bits.rs
+++ b/ipa-core/src/protocol/boolean/generate_random_bits.rs
@@ -4,7 +4,7 @@ use futures::stream::{iter as stream_iter, StreamExt};
 
 use crate::{
     error::Error,
-    ff::{ArrayAccessReplicated, PrimeField},
+    ff::{boolean::Boolean, ArrayAccessReplicated, PrimeField},
     helpers::Role,
     protocol::{
         basics::SecureMul,
@@ -47,21 +47,21 @@ impl ArrayAccessReplicated for RawRandomBits {
 }
 
 impl<'a> BorrowReplicated for RawRandomBitsIndex<'a> {
-    type Output = bool;
+    type Output = Boolean;
 
-    fn borrow_left(&self) -> &bool {
+    fn borrow_left(&self) -> &Self::Output {
         if ((self.bits.left >> self.index) & 1) == 1 {
-            &true
+            &Boolean::TRUE
         } else {
-            &false
+            &Boolean::FALSE
         }
     }
 
-    fn borrow_right(&self) -> &bool {
+    fn borrow_right(&self) -> &Self::Output {
         if ((self.bits.right >> self.index) & 1) == 1 {
-            &true
+            &Boolean::TRUE
         } else {
-            &false
+            &Boolean::FALSE
         }
     }
 }
diff --git a/ipa-core/src/protocol/modulus_conversion/convert_shares.rs b/ipa-core/src/protocol/modulus_conversion/convert_shares.rs
index 93bd94242..78e68f045 100644
--- a/ipa-core/src/protocol/modulus_conversion/convert_shares.rs
+++ b/ipa-core/src/protocol/modulus_conversion/convert_shares.rs
@@ -34,7 +34,7 @@ use pin_project::pin_project;
 use crate::{
     error::Error,
     exact::ExactSizeStream,
-    ff::{ArrayAccessReplicated, Field, Gf2, PrimeField},
+    ff::{boolean::Boolean, ArrayAccessReplicated, Field, Gf2, PrimeField},
     helpers::Role,
     protocol::{
         basics::{SecureMul, ZeroPositions},
@@ -73,14 +73,14 @@ impl<F: PrimeField> BitConversionTriple<Replicated<F>> {
     ///
     /// # Panics
     /// If any bits in the bitwise shared input cannot be converted into the given field `F`
-    /// without truncation or if the bit index is out of range for `B`.
+    /// without truncation.
     #[must_use]
-    pub fn new<G: Copy + Into<bool>, T: BorrowReplicated<Output = G>>(
-        helper_role: Role,
-        src: &T,
-    ) -> Self {
-        let left = F::try_from(u128::from((*src.borrow_left()).into())).unwrap();
-        let right = F::try_from(u128::from((*src.borrow_right()).into())).unwrap();
+    pub fn new<B>(helper_role: Role, src: &B) -> Self
+    where
+        B: BorrowReplicated<Output = Boolean>,
+    {
+        let left = F::try_from(src.borrow_left().as_u128()).unwrap();
+        let right = F::try_from(src.borrow_right().as_u128()).unwrap();
         Self(match helper_role {
             Role::H1 => [
                 Replicated::new(left, F::ZERO),
@@ -143,12 +143,11 @@ pub trait ToBitConversionTriples: Sized {
     }
 }
 
-impl<B, G> ToBitConversionTriples for Replicated<B>
+impl<B> ToBitConversionTriples for Replicated<B>
 where
     Self: ArrayAccessReplicated,
-    for<'a> <Self as ArrayAccessReplicated>::Ref<'a>: BorrowReplicated<Output = G>,
+    for<'a> <Self as ArrayAccessReplicated>::Ref<'a>: BorrowReplicated<Output = Boolean>,
     B: SharedValue,
-    G: Copy + Into<bool>,
 {
     type Residual = ();
 
diff --git a/ipa-core/src/secret_sharing/replicated/semi_honest/additive_share.rs b/ipa-core/src/secret_sharing/replicated/semi_honest/additive_share.rs
index e6d258578..d0cd19fe2 100644
--- a/ipa-core/src/secret_sharing/replicated/semi_honest/additive_share.rs
+++ b/ipa-core/src/secret_sharing/replicated/semi_honest/additive_share.rs
@@ -7,7 +7,7 @@ use generic_array::{ArrayLength, GenericArray};
 use typenum::Unsigned;
 
 use crate::{
-    ff::{ArrayAccess, ArrayAccessReplicated, Expand, Field, Gf2, Serializable},
+    ff::{boolean::Boolean, ArrayAccess, ArrayAccessReplicated, Expand, Field, Serializable},
     secret_sharing::{
         replicated::ReplicatedSecretSharing, Linear as LinearSecretSharing, SecretSharing,
         SharedValue,
@@ -71,25 +71,27 @@ pub trait BorrowReplicatedMut: BorrowReplicated {
     fn borrow_right_mut(&mut self) -> &mut Self::Output;
 }
 
+// This exists as a special case so we can provide an impl of `BorrowReplicated` that
+// returns `bool` rather than `Gf2`.
 #[derive(Clone, Copy)]
-pub struct AdditiveShareGf2(Gf2, Gf2);
+pub struct BooleanAdditiveShare(Boolean, Boolean);
 
-impl BorrowReplicated for AdditiveShareGf2 {
-    type Output = bool;
+impl BorrowReplicated for BooleanAdditiveShare {
+    type Output = Boolean;
 
-    fn borrow_left(&self) -> &bool {
+    fn borrow_left(&self) -> &Self::Output {
         if self.0.into() {
-            &true
+            &Boolean::TRUE
         } else {
-            &false
+            &Boolean::FALSE
         }
     }
 
-    fn borrow_right(&self) -> &bool {
+    fn borrow_right(&self) -> &Self::Output {
         if self.1.into() {
-            &true
+            &Boolean::TRUE
         } else {
-            &false
+            &Boolean::FALSE
         }
     }
 }
@@ -97,21 +99,21 @@ impl BorrowReplicated for AdditiveShareGf2 {
 impl<V: SharedValue> BorrowReplicated for AdditiveShare<V> {
     type Output = V;
 
-    fn borrow_left(&self) -> &V {
+    fn borrow_left(&self) -> &Self::Output {
         &self.0
     }
 
-    fn borrow_right(&self) -> &V {
+    fn borrow_right(&self) -> &Self::Output {
         &self.1
     }
 }
 
 impl<V: SharedValue> BorrowReplicatedMut for AdditiveShare<V> {
-    fn borrow_left_mut(&mut self) -> &mut V {
+    fn borrow_left_mut(&mut self) -> &mut Self::Output {
         &mut self.0
     }
 
-    fn borrow_right_mut(&mut self) -> &mut V {
+    fn borrow_right_mut(&mut self) -> &mut Self::Output {
         &mut self.1
     }
 }
@@ -339,18 +341,18 @@ where
     // This would ideally be an `AdditiveShareRef` type that holds two references,
     // but due to Galois fields not being indexable for `Gf2` values currently,
     // it is not done that way.
-    type Ref<'a> = AdditiveShareGf2;
+    type Ref<'a> = BooleanAdditiveShare;
 
     fn get(&self, index: usize) -> Option<Self::Ref<'_>> {
         self.0
             .get(index)
             .zip(self.1.get(index))
-            .map(|v| AdditiveShareGf2(bool::from(v.0).into(), bool::from(v.1).into()))
+            .map(|v| BooleanAdditiveShare(bool::from(v.0).into(), bool::from(v.1).into()))
     }
 
     fn set(&mut self, index: usize, e: Self::Ref<'_>) {
-        self.0.set(index, <bool as From<Gf2>>::from(e.0).into());
-        self.1.set(index, <bool as From<Gf2>>::from(e.1).into());
+        self.0.set(index, <bool as From<Boolean>>::from(e.0).into());
+        self.1.set(index, <bool as From<Boolean>>::from(e.1).into());
     }
 }