diff --git a/field/src/extension/quadratic.rs b/field/src/extension/quadratic.rs
index c0c9758b..281369d2 100644
--- a/field/src/extension/quadratic.rs
+++ b/field/src/extension/quadratic.rs
@@ -109,6 +109,14 @@ impl<F: Extendable<2>> Field for QuadraticExtension<F> {
     fn from_noncanonical_u128(n: u128) -> Self {
         F::from_noncanonical_u128(n).into()
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        F::from_noncanonical_i64(n).into()
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        F::from_noncanonical_u64(n).into()
+    }
 }
 
 impl<F: Extendable<2>> Display for QuadraticExtension<F> {
diff --git a/field/src/extension/quartic.rs b/field/src/extension/quartic.rs
index e7aba63b..8c8a9e7e 100644
--- a/field/src/extension/quartic.rs
+++ b/field/src/extension/quartic.rs
@@ -119,6 +119,14 @@ impl<F: Extendable<4>> Field for QuarticExtension<F> {
     fn from_noncanonical_u128(n: u128) -> Self {
         F::from_noncanonical_u128(n).into()
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        F::from_noncanonical_i64(n).into()
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        F::from_noncanonical_u64(n).into()
+    }
 }
 
 impl<F: Extendable<4>> Display for QuarticExtension<F> {
diff --git a/field/src/extension/quintic.rs b/field/src/extension/quintic.rs
index d4b605eb..28ec9226 100644
--- a/field/src/extension/quintic.rs
+++ b/field/src/extension/quintic.rs
@@ -126,6 +126,14 @@ impl<F: Extendable<5>> Field for QuinticExtension<F> {
     fn from_noncanonical_u128(n: u128) -> Self {
         F::from_noncanonical_u128(n).into()
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        F::from_noncanonical_i64(n).into()
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        F::from_noncanonical_u64(n).into()
+    }
 }
 
 impl<F: Extendable<5>> Display for QuinticExtension<F> {
diff --git a/field/src/goldilocks_field.rs b/field/src/goldilocks_field.rs
index e10d0c74..4432d9c4 100644
--- a/field/src/goldilocks_field.rs
+++ b/field/src/goldilocks_field.rs
@@ -118,22 +118,6 @@ impl Field for GoldilocksField {
         reduce128(n)
     }
 
-    #[inline]
-    fn multiply_accumulate(&self, x: Self, y: Self) -> Self {
-        // u64 + u64 * u64 cannot overflow.
-        reduce128((self.0 as u128) + (x.0 as u128) * (y.0 as u128))
-    }
-}
-
-impl PrimeField for GoldilocksField {
-    fn to_canonical_biguint(&self) -> BigUint {
-        self.to_canonical_u64().into()
-    }
-}
-
-impl Field64 for GoldilocksField {
-    const ORDER: u64 = 0xFFFFFFFF00000001;
-
     #[inline]
     fn from_noncanonical_u64(n: u64) -> Self {
         Self(n)
@@ -151,6 +135,22 @@ impl Field64 for GoldilocksField {
         })
     }
 
+    #[inline]
+    fn multiply_accumulate(&self, x: Self, y: Self) -> Self {
+        // u64 + u64 * u64 cannot overflow.
+        reduce128((self.0 as u128) + (x.0 as u128) * (y.0 as u128))
+    }
+}
+
+impl PrimeField for GoldilocksField {
+    fn to_canonical_biguint(&self) -> BigUint {
+        self.to_canonical_u64().into()
+    }
+}
+
+impl Field64 for GoldilocksField {
+    const ORDER: u64 = 0xFFFFFFFF00000001;
+
     #[inline]
     unsafe fn add_canonical_u64(&self, rhs: u64) -> Self {
         let (res_wrapped, carry) = self.0.overflowing_add(rhs);
diff --git a/field/src/secp256k1_base.rs b/field/src/secp256k1_base.rs
index eaa964f8..6632a7f8 100644
--- a/field/src/secp256k1_base.rs
+++ b/field/src/secp256k1_base.rs
@@ -142,6 +142,19 @@ impl Field for Secp256K1Base {
     fn from_noncanonical_u96(n: (u64, u32)) -> Self {
         Self([n.0, n.1 as u64, 0, 0])
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        let f = Self::from_canonical_u64(n.unsigned_abs());
+        if n < 0 {
+            -f
+        } else {
+            f
+        }
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        Self::from_canonical_u64(n)
+    }
 }
 
 impl PrimeField for Secp256K1Base {
diff --git a/field/src/secp256k1_scalar.rs b/field/src/secp256k1_scalar.rs
index 1f1de697..3ca5b6ba 100644
--- a/field/src/secp256k1_scalar.rs
+++ b/field/src/secp256k1_scalar.rs
@@ -150,6 +150,19 @@ impl Field for Secp256K1Scalar {
     fn from_noncanonical_u96(n: (u64, u32)) -> Self {
         Self([n.0, n.1 as u64, 0, 0])
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        let f = Self::from_canonical_u64(n.unsigned_abs());
+        if n < 0 {
+            -f
+        } else {
+            f
+        }
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        Self::from_canonical_u64(n)
+    }
 }
 
 impl PrimeField for Secp256K1Scalar {
diff --git a/field/src/types.rs b/field/src/types.rs
index 0ae31847..646dff73 100644
--- a/field/src/types.rs
+++ b/field/src/types.rs
@@ -341,6 +341,12 @@ pub trait Field:
     /// Returns `n % Self::characteristic()`.
     fn from_noncanonical_u128(n: u128) -> Self;
 
+    /// Returns `x % Self::CHARACTERISTIC`.
+    fn from_noncanonical_u64(n: u64) -> Self;
+
+    /// Returns `n` as an element of this field.
+    fn from_noncanonical_i64(n: i64) -> Self;
+
     /// Returns `n % Self::characteristic()`. May be cheaper than from_noncanonical_u128 when we know
     /// that `n < 2 ** 96`.
     #[inline]
@@ -501,14 +507,6 @@ pub trait PrimeField: Field {
 pub trait Field64: Field {
     const ORDER: u64;
 
-    /// Returns `x % Self::CHARACTERISTIC`.
-    // TODO: Move to `Field`.
-    fn from_noncanonical_u64(n: u64) -> Self;
-
-    /// Returns `n` as an element of this field.
-    // TODO: Move to `Field`.
-    fn from_noncanonical_i64(n: i64) -> Self;
-
     /// Returns `n` as an element of this field. Assumes that `0 <= n < Self::ORDER`.
     // TODO: Move to `Field`.
     // TODO: Should probably be unsafe.