diff --git a/src/bls12_381/ec.rs b/src/bls12_381/ec.rs
index 5cd5091..37fcbba 100644
--- a/src/bls12_381/ec.rs
+++ b/src/bls12_381/ec.rs
@@ -623,12 +623,10 @@ macro_rules! curve_impl {
 pub mod g1 {
     use super::super::{Bls12, Fq, Fq12, FqRepr, Fr, FrRepr};
     use super::g2::G2Affine;
+    use ff::{BitIterator, Field, PrimeField, PrimeFieldRepr, SqrtField};
     use rand::{Rand, Rng};
     use std::fmt;
-    use {
-        BitIterator, CurveAffine, CurveProjective, EncodedPoint, Engine, Field, GroupDecodingError,
-        PrimeField, PrimeFieldRepr, SqrtField,
-    };
+    use {CurveAffine, CurveProjective, EncodedPoint, Engine, GroupDecodingError};
 
     curve_impl!(
         "G1",
@@ -1270,12 +1268,10 @@ pub mod g1 {
 pub mod g2 {
     use super::super::{Bls12, Fq, Fq12, Fq2, FqRepr, Fr, FrRepr};
     use super::g1::G1Affine;
+    use ff::{BitIterator, Field, PrimeField, PrimeFieldRepr, SqrtField};
     use rand::{Rand, Rng};
     use std::fmt;
-    use {
-        BitIterator, CurveAffine, CurveProjective, EncodedPoint, Engine, Field, GroupDecodingError,
-        PrimeField, PrimeFieldRepr, SqrtField,
-    };
+    use {CurveAffine, CurveProjective, EncodedPoint, Engine, GroupDecodingError};
 
     curve_impl!(
         "G2",
diff --git a/src/bls12_381/fq.rs b/src/bls12_381/fq.rs
index 738da38..e109294 100644
--- a/src/bls12_381/fq.rs
+++ b/src/bls12_381/fq.rs
@@ -682,7 +682,7 @@ impl PrimeFieldRepr for FqRepr {
         let mut carry = 0;
 
         for (a, b) in self.0.iter_mut().zip(other.0.iter()) {
-            *a = ::adc(*a, *b, &mut carry);
+            *a = ::ff::adc(*a, *b, &mut carry);
         }
     }
 
@@ -691,7 +691,7 @@ impl PrimeFieldRepr for FqRepr {
         let mut borrow = 0;
 
         for (a, b) in self.0.iter_mut().zip(other.0.iter()) {
-            *a = ::sbb(*a, *b, &mut borrow);
+            *a = ::ff::sbb(*a, *b, &mut borrow);
         }
     }
 }
@@ -909,52 +909,52 @@ impl Field for Fq {
     #[inline]
     fn mul_assign(&mut self, other: &Fq) {
         let mut carry = 0;
-        let r0 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[0], &mut carry);
-        let r1 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[1], &mut carry);
-        let r2 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[2], &mut carry);
-        let r3 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[3], &mut carry);
-        let r4 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[4], &mut carry);
-        let r5 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[5], &mut carry);
+        let r0 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[0], &mut carry);
+        let r1 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[1], &mut carry);
+        let r2 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[2], &mut carry);
+        let r3 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[3], &mut carry);
+        let r4 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[4], &mut carry);
+        let r5 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[5], &mut carry);
         let r6 = carry;
         let mut carry = 0;
-        let r1 = ::mac_with_carry(r1, (self.0).0[1], (other.0).0[0], &mut carry);
-        let r2 = ::mac_with_carry(r2, (self.0).0[1], (other.0).0[1], &mut carry);
-        let r3 = ::mac_with_carry(r3, (self.0).0[1], (other.0).0[2], &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[1], (other.0).0[3], &mut carry);
-        let r5 = ::mac_with_carry(r5, (self.0).0[1], (other.0).0[4], &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[1], (other.0).0[5], &mut carry);
+        let r1 = ::ff::mac_with_carry(r1, (self.0).0[1], (other.0).0[0], &mut carry);
+        let r2 = ::ff::mac_with_carry(r2, (self.0).0[1], (other.0).0[1], &mut carry);
+        let r3 = ::ff::mac_with_carry(r3, (self.0).0[1], (other.0).0[2], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[1], (other.0).0[3], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[1], (other.0).0[4], &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[1], (other.0).0[5], &mut carry);
         let r7 = carry;
         let mut carry = 0;
-        let r2 = ::mac_with_carry(r2, (self.0).0[2], (other.0).0[0], &mut carry);
-        let r3 = ::mac_with_carry(r3, (self.0).0[2], (other.0).0[1], &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[2], (other.0).0[2], &mut carry);
-        let r5 = ::mac_with_carry(r5, (self.0).0[2], (other.0).0[3], &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[2], (other.0).0[4], &mut carry);
-        let r7 = ::mac_with_carry(r7, (self.0).0[2], (other.0).0[5], &mut carry);
+        let r2 = ::ff::mac_with_carry(r2, (self.0).0[2], (other.0).0[0], &mut carry);
+        let r3 = ::ff::mac_with_carry(r3, (self.0).0[2], (other.0).0[1], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[2], (other.0).0[2], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[2], (other.0).0[3], &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[2], (other.0).0[4], &mut carry);
+        let r7 = ::ff::mac_with_carry(r7, (self.0).0[2], (other.0).0[5], &mut carry);
         let r8 = carry;
         let mut carry = 0;
-        let r3 = ::mac_with_carry(r3, (self.0).0[3], (other.0).0[0], &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[3], (other.0).0[1], &mut carry);
-        let r5 = ::mac_with_carry(r5, (self.0).0[3], (other.0).0[2], &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[3], (other.0).0[3], &mut carry);
-        let r7 = ::mac_with_carry(r7, (self.0).0[3], (other.0).0[4], &mut carry);
-        let r8 = ::mac_with_carry(r8, (self.0).0[3], (other.0).0[5], &mut carry);
+        let r3 = ::ff::mac_with_carry(r3, (self.0).0[3], (other.0).0[0], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[3], (other.0).0[1], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[3], (other.0).0[2], &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[3], (other.0).0[3], &mut carry);
+        let r7 = ::ff::mac_with_carry(r7, (self.0).0[3], (other.0).0[4], &mut carry);
+        let r8 = ::ff::mac_with_carry(r8, (self.0).0[3], (other.0).0[5], &mut carry);
         let r9 = carry;
         let mut carry = 0;
-        let r4 = ::mac_with_carry(r4, (self.0).0[4], (other.0).0[0], &mut carry);
-        let r5 = ::mac_with_carry(r5, (self.0).0[4], (other.0).0[1], &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[4], (other.0).0[2], &mut carry);
-        let r7 = ::mac_with_carry(r7, (self.0).0[4], (other.0).0[3], &mut carry);
-        let r8 = ::mac_with_carry(r8, (self.0).0[4], (other.0).0[4], &mut carry);
-        let r9 = ::mac_with_carry(r9, (self.0).0[4], (other.0).0[5], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[4], (other.0).0[0], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[4], (other.0).0[1], &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[4], (other.0).0[2], &mut carry);
+        let r7 = ::ff::mac_with_carry(r7, (self.0).0[4], (other.0).0[3], &mut carry);
+        let r8 = ::ff::mac_with_carry(r8, (self.0).0[4], (other.0).0[4], &mut carry);
+        let r9 = ::ff::mac_with_carry(r9, (self.0).0[4], (other.0).0[5], &mut carry);
         let r10 = carry;
         let mut carry = 0;
-        let r5 = ::mac_with_carry(r5, (self.0).0[5], (other.0).0[0], &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[5], (other.0).0[1], &mut carry);
-        let r7 = ::mac_with_carry(r7, (self.0).0[5], (other.0).0[2], &mut carry);
-        let r8 = ::mac_with_carry(r8, (self.0).0[5], (other.0).0[3], &mut carry);
-        let r9 = ::mac_with_carry(r9, (self.0).0[5], (other.0).0[4], &mut carry);
-        let r10 = ::mac_with_carry(r10, (self.0).0[5], (other.0).0[5], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[5], (other.0).0[0], &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[5], (other.0).0[1], &mut carry);
+        let r7 = ::ff::mac_with_carry(r7, (self.0).0[5], (other.0).0[2], &mut carry);
+        let r8 = ::ff::mac_with_carry(r8, (self.0).0[5], (other.0).0[3], &mut carry);
+        let r9 = ::ff::mac_with_carry(r9, (self.0).0[5], (other.0).0[4], &mut carry);
+        let r10 = ::ff::mac_with_carry(r10, (self.0).0[5], (other.0).0[5], &mut carry);
         let r11 = carry;
         self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11);
     }
@@ -962,29 +962,29 @@ impl Field for Fq {
     #[inline]
     fn square(&mut self) {
         let mut carry = 0;
-        let r1 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[1], &mut carry);
-        let r2 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[2], &mut carry);
-        let r3 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[3], &mut carry);
-        let r4 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[4], &mut carry);
-        let r5 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[5], &mut carry);
+        let r1 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[1], &mut carry);
+        let r2 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[2], &mut carry);
+        let r3 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[3], &mut carry);
+        let r4 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[4], &mut carry);
+        let r5 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[5], &mut carry);
         let r6 = carry;
         let mut carry = 0;
-        let r3 = ::mac_with_carry(r3, (self.0).0[1], (self.0).0[2], &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[1], (self.0).0[3], &mut carry);
-        let r5 = ::mac_with_carry(r5, (self.0).0[1], (self.0).0[4], &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[1], (self.0).0[5], &mut carry);
+        let r3 = ::ff::mac_with_carry(r3, (self.0).0[1], (self.0).0[2], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[1], (self.0).0[3], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[1], (self.0).0[4], &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[1], (self.0).0[5], &mut carry);
         let r7 = carry;
         let mut carry = 0;
-        let r5 = ::mac_with_carry(r5, (self.0).0[2], (self.0).0[3], &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[2], (self.0).0[4], &mut carry);
-        let r7 = ::mac_with_carry(r7, (self.0).0[2], (self.0).0[5], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[2], (self.0).0[3], &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[2], (self.0).0[4], &mut carry);
+        let r7 = ::ff::mac_with_carry(r7, (self.0).0[2], (self.0).0[5], &mut carry);
         let r8 = carry;
         let mut carry = 0;
-        let r7 = ::mac_with_carry(r7, (self.0).0[3], (self.0).0[4], &mut carry);
-        let r8 = ::mac_with_carry(r8, (self.0).0[3], (self.0).0[5], &mut carry);
+        let r7 = ::ff::mac_with_carry(r7, (self.0).0[3], (self.0).0[4], &mut carry);
+        let r8 = ::ff::mac_with_carry(r8, (self.0).0[3], (self.0).0[5], &mut carry);
         let r9 = carry;
         let mut carry = 0;
-        let r9 = ::mac_with_carry(r9, (self.0).0[4], (self.0).0[5], &mut carry);
+        let r9 = ::ff::mac_with_carry(r9, (self.0).0[4], (self.0).0[5], &mut carry);
         let r10 = carry;
 
         let r11 = r10 >> 63;
@@ -1000,18 +1000,18 @@ impl Field for Fq {
         let r1 = r1 << 1;
 
         let mut carry = 0;
-        let r0 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[0], &mut carry);
-        let r1 = ::adc(r1, 0, &mut carry);
-        let r2 = ::mac_with_carry(r2, (self.0).0[1], (self.0).0[1], &mut carry);
-        let r3 = ::adc(r3, 0, &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[2], (self.0).0[2], &mut carry);
-        let r5 = ::adc(r5, 0, &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[3], (self.0).0[3], &mut carry);
-        let r7 = ::adc(r7, 0, &mut carry);
-        let r8 = ::mac_with_carry(r8, (self.0).0[4], (self.0).0[4], &mut carry);
-        let r9 = ::adc(r9, 0, &mut carry);
-        let r10 = ::mac_with_carry(r10, (self.0).0[5], (self.0).0[5], &mut carry);
-        let r11 = ::adc(r11, 0, &mut carry);
+        let r0 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[0], &mut carry);
+        let r1 = ::ff::adc(r1, 0, &mut carry);
+        let r2 = ::ff::mac_with_carry(r2, (self.0).0[1], (self.0).0[1], &mut carry);
+        let r3 = ::ff::adc(r3, 0, &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[2], (self.0).0[2], &mut carry);
+        let r5 = ::ff::adc(r5, 0, &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[3], (self.0).0[3], &mut carry);
+        let r7 = ::ff::adc(r7, 0, &mut carry);
+        let r8 = ::ff::mac_with_carry(r8, (self.0).0[4], (self.0).0[4], &mut carry);
+        let r9 = ::ff::adc(r9, 0, &mut carry);
+        let r10 = ::ff::mac_with_carry(r10, (self.0).0[5], (self.0).0[5], &mut carry);
+        let r11 = ::ff::adc(r11, 0, &mut carry);
         self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11);
     }
 }
@@ -1055,63 +1055,63 @@ impl Fq {
 
         let k = r0.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r0, k, MODULUS.0[0], &mut carry);
-        r1 = ::mac_with_carry(r1, k, MODULUS.0[1], &mut carry);
-        r2 = ::mac_with_carry(r2, k, MODULUS.0[2], &mut carry);
-        r3 = ::mac_with_carry(r3, k, MODULUS.0[3], &mut carry);
-        r4 = ::mac_with_carry(r4, k, MODULUS.0[4], &mut carry);
-        r5 = ::mac_with_carry(r5, k, MODULUS.0[5], &mut carry);
-        r6 = ::adc(r6, 0, &mut carry);
+        ::ff::mac_with_carry(r0, k, MODULUS.0[0], &mut carry);
+        r1 = ::ff::mac_with_carry(r1, k, MODULUS.0[1], &mut carry);
+        r2 = ::ff::mac_with_carry(r2, k, MODULUS.0[2], &mut carry);
+        r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[3], &mut carry);
+        r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[4], &mut carry);
+        r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[5], &mut carry);
+        r6 = ::ff::adc(r6, 0, &mut carry);
         let carry2 = carry;
         let k = r1.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r1, k, MODULUS.0[0], &mut carry);
-        r2 = ::mac_with_carry(r2, k, MODULUS.0[1], &mut carry);
-        r3 = ::mac_with_carry(r3, k, MODULUS.0[2], &mut carry);
-        r4 = ::mac_with_carry(r4, k, MODULUS.0[3], &mut carry);
-        r5 = ::mac_with_carry(r5, k, MODULUS.0[4], &mut carry);
-        r6 = ::mac_with_carry(r6, k, MODULUS.0[5], &mut carry);
-        r7 = ::adc(r7, carry2, &mut carry);
+        ::ff::mac_with_carry(r1, k, MODULUS.0[0], &mut carry);
+        r2 = ::ff::mac_with_carry(r2, k, MODULUS.0[1], &mut carry);
+        r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[2], &mut carry);
+        r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[3], &mut carry);
+        r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[4], &mut carry);
+        r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[5], &mut carry);
+        r7 = ::ff::adc(r7, carry2, &mut carry);
         let carry2 = carry;
         let k = r2.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r2, k, MODULUS.0[0], &mut carry);
-        r3 = ::mac_with_carry(r3, k, MODULUS.0[1], &mut carry);
-        r4 = ::mac_with_carry(r4, k, MODULUS.0[2], &mut carry);
-        r5 = ::mac_with_carry(r5, k, MODULUS.0[3], &mut carry);
-        r6 = ::mac_with_carry(r6, k, MODULUS.0[4], &mut carry);
-        r7 = ::mac_with_carry(r7, k, MODULUS.0[5], &mut carry);
-        r8 = ::adc(r8, carry2, &mut carry);
+        ::ff::mac_with_carry(r2, k, MODULUS.0[0], &mut carry);
+        r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[1], &mut carry);
+        r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[2], &mut carry);
+        r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[3], &mut carry);
+        r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[4], &mut carry);
+        r7 = ::ff::mac_with_carry(r7, k, MODULUS.0[5], &mut carry);
+        r8 = ::ff::adc(r8, carry2, &mut carry);
         let carry2 = carry;
         let k = r3.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r3, k, MODULUS.0[0], &mut carry);
-        r4 = ::mac_with_carry(r4, k, MODULUS.0[1], &mut carry);
-        r5 = ::mac_with_carry(r5, k, MODULUS.0[2], &mut carry);
-        r6 = ::mac_with_carry(r6, k, MODULUS.0[3], &mut carry);
-        r7 = ::mac_with_carry(r7, k, MODULUS.0[4], &mut carry);
-        r8 = ::mac_with_carry(r8, k, MODULUS.0[5], &mut carry);
-        r9 = ::adc(r9, carry2, &mut carry);
+        ::ff::mac_with_carry(r3, k, MODULUS.0[0], &mut carry);
+        r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[1], &mut carry);
+        r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[2], &mut carry);
+        r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[3], &mut carry);
+        r7 = ::ff::mac_with_carry(r7, k, MODULUS.0[4], &mut carry);
+        r8 = ::ff::mac_with_carry(r8, k, MODULUS.0[5], &mut carry);
+        r9 = ::ff::adc(r9, carry2, &mut carry);
         let carry2 = carry;
         let k = r4.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r4, k, MODULUS.0[0], &mut carry);
-        r5 = ::mac_with_carry(r5, k, MODULUS.0[1], &mut carry);
-        r6 = ::mac_with_carry(r6, k, MODULUS.0[2], &mut carry);
-        r7 = ::mac_with_carry(r7, k, MODULUS.0[3], &mut carry);
-        r8 = ::mac_with_carry(r8, k, MODULUS.0[4], &mut carry);
-        r9 = ::mac_with_carry(r9, k, MODULUS.0[5], &mut carry);
-        r10 = ::adc(r10, carry2, &mut carry);
+        ::ff::mac_with_carry(r4, k, MODULUS.0[0], &mut carry);
+        r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[1], &mut carry);
+        r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[2], &mut carry);
+        r7 = ::ff::mac_with_carry(r7, k, MODULUS.0[3], &mut carry);
+        r8 = ::ff::mac_with_carry(r8, k, MODULUS.0[4], &mut carry);
+        r9 = ::ff::mac_with_carry(r9, k, MODULUS.0[5], &mut carry);
+        r10 = ::ff::adc(r10, carry2, &mut carry);
         let carry2 = carry;
         let k = r5.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r5, k, MODULUS.0[0], &mut carry);
-        r6 = ::mac_with_carry(r6, k, MODULUS.0[1], &mut carry);
-        r7 = ::mac_with_carry(r7, k, MODULUS.0[2], &mut carry);
-        r8 = ::mac_with_carry(r8, k, MODULUS.0[3], &mut carry);
-        r9 = ::mac_with_carry(r9, k, MODULUS.0[4], &mut carry);
-        r10 = ::mac_with_carry(r10, k, MODULUS.0[5], &mut carry);
-        r11 = ::adc(r11, carry2, &mut carry);
+        ::ff::mac_with_carry(r5, k, MODULUS.0[0], &mut carry);
+        r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[1], &mut carry);
+        r7 = ::ff::mac_with_carry(r7, k, MODULUS.0[2], &mut carry);
+        r8 = ::ff::mac_with_carry(r8, k, MODULUS.0[3], &mut carry);
+        r9 = ::ff::mac_with_carry(r9, k, MODULUS.0[4], &mut carry);
+        r10 = ::ff::mac_with_carry(r10, k, MODULUS.0[5], &mut carry);
+        r11 = ::ff::adc(r11, carry2, &mut carry);
         (self.0).0[0] = r6;
         (self.0).0[1] = r7;
         (self.0).0[2] = r8;
@@ -1123,9 +1123,7 @@ impl Fq {
 }
 
 impl SqrtField for Fq {
-    fn legendre(&self) -> ::LegendreSymbol {
-        use LegendreSymbol::*;
-
+    fn legendre(&self) -> ::ff::LegendreSymbol {
         // s = self^((q - 1) // 2)
         let s = self.pow([
             0xdcff7fffffffd555,
@@ -1136,11 +1134,11 @@ impl SqrtField for Fq {
             0xd0088f51cbff34d,
         ]);
         if s == Fq::zero() {
-            Zero
+            ::ff::LegendreSymbol::Zero
         } else if s == Fq::one() {
-            QuadraticResidue
+            ::ff::LegendreSymbol::QuadraticResidue
         } else {
-            QuadraticNonResidue
+            ::ff::LegendreSymbol::QuadraticNonResidue
         }
     }
 
@@ -2924,7 +2922,7 @@ fn fq_repr_tests() {
 
 #[test]
 fn test_fq_legendre() {
-    use LegendreSymbol::*;
+    use ff::LegendreSymbol::*;
 
     assert_eq!(QuadraticResidue, Fq::one().legendre());
     assert_eq!(Zero, Fq::zero().legendre());
diff --git a/src/bls12_381/fq2.rs b/src/bls12_381/fq2.rs
index 18cd580..1f3cd6f 100644
--- a/src/bls12_381/fq2.rs
+++ b/src/bls12_381/fq2.rs
@@ -160,7 +160,7 @@ impl Field for Fq2 {
 }
 
 impl SqrtField for Fq2 {
-    fn legendre(&self) -> ::LegendreSymbol {
+    fn legendre(&self) -> ::ff::LegendreSymbol {
         self.norm().legendre()
     }
 
@@ -865,7 +865,7 @@ fn test_fq2_sqrt() {
 
 #[test]
 fn test_fq2_legendre() {
-    use LegendreSymbol::*;
+    use ff::LegendreSymbol::*;
 
     assert_eq!(Zero, Fq2::zero().legendre());
     // i^2 = -1
diff --git a/src/bls12_381/fr.rs b/src/bls12_381/fr.rs
index 4e9d6ab..e9eee24 100644
--- a/src/bls12_381/fr.rs
+++ b/src/bls12_381/fr.rs
@@ -1,5 +1,4 @@
-use LegendreSymbol::*;
-use {Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr, SqrtField};
+use ff::{Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr, SqrtField};
 
 // r = 52435875175126190479447740508185965837690552500527637822603658699938581184513
 const MODULUS: FrRepr = FrRepr([
@@ -229,7 +228,7 @@ impl PrimeFieldRepr for FrRepr {
         let mut carry = 0;
 
         for (a, b) in self.0.iter_mut().zip(other.0.iter()) {
-            *a = ::adc(*a, *b, &mut carry);
+            *a = ::ff::adc(*a, *b, &mut carry);
         }
     }
 
@@ -238,7 +237,7 @@ impl PrimeFieldRepr for FrRepr {
         let mut borrow = 0;
 
         for (a, b) in self.0.iter_mut().zip(other.0.iter()) {
-            *a = ::sbb(*a, *b, &mut borrow);
+            *a = ::ff::sbb(*a, *b, &mut borrow);
         }
     }
 }
@@ -437,28 +436,28 @@ impl Field for Fr {
     #[inline]
     fn mul_assign(&mut self, other: &Fr) {
         let mut carry = 0;
-        let r0 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[0], &mut carry);
-        let r1 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[1], &mut carry);
-        let r2 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[2], &mut carry);
-        let r3 = ::mac_with_carry(0, (self.0).0[0], (other.0).0[3], &mut carry);
+        let r0 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[0], &mut carry);
+        let r1 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[1], &mut carry);
+        let r2 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[2], &mut carry);
+        let r3 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[3], &mut carry);
         let r4 = carry;
         let mut carry = 0;
-        let r1 = ::mac_with_carry(r1, (self.0).0[1], (other.0).0[0], &mut carry);
-        let r2 = ::mac_with_carry(r2, (self.0).0[1], (other.0).0[1], &mut carry);
-        let r3 = ::mac_with_carry(r3, (self.0).0[1], (other.0).0[2], &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[1], (other.0).0[3], &mut carry);
+        let r1 = ::ff::mac_with_carry(r1, (self.0).0[1], (other.0).0[0], &mut carry);
+        let r2 = ::ff::mac_with_carry(r2, (self.0).0[1], (other.0).0[1], &mut carry);
+        let r3 = ::ff::mac_with_carry(r3, (self.0).0[1], (other.0).0[2], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[1], (other.0).0[3], &mut carry);
         let r5 = carry;
         let mut carry = 0;
-        let r2 = ::mac_with_carry(r2, (self.0).0[2], (other.0).0[0], &mut carry);
-        let r3 = ::mac_with_carry(r3, (self.0).0[2], (other.0).0[1], &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[2], (other.0).0[2], &mut carry);
-        let r5 = ::mac_with_carry(r5, (self.0).0[2], (other.0).0[3], &mut carry);
+        let r2 = ::ff::mac_with_carry(r2, (self.0).0[2], (other.0).0[0], &mut carry);
+        let r3 = ::ff::mac_with_carry(r3, (self.0).0[2], (other.0).0[1], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[2], (other.0).0[2], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[2], (other.0).0[3], &mut carry);
         let r6 = carry;
         let mut carry = 0;
-        let r3 = ::mac_with_carry(r3, (self.0).0[3], (other.0).0[0], &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[3], (other.0).0[1], &mut carry);
-        let r5 = ::mac_with_carry(r5, (self.0).0[3], (other.0).0[2], &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[3], (other.0).0[3], &mut carry);
+        let r3 = ::ff::mac_with_carry(r3, (self.0).0[3], (other.0).0[0], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[3], (other.0).0[1], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[3], (other.0).0[2], &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[3], (other.0).0[3], &mut carry);
         let r7 = carry;
         self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7);
     }
@@ -466,16 +465,16 @@ impl Field for Fr {
     #[inline]
     fn square(&mut self) {
         let mut carry = 0;
-        let r1 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[1], &mut carry);
-        let r2 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[2], &mut carry);
-        let r3 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[3], &mut carry);
+        let r1 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[1], &mut carry);
+        let r2 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[2], &mut carry);
+        let r3 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[3], &mut carry);
         let r4 = carry;
         let mut carry = 0;
-        let r3 = ::mac_with_carry(r3, (self.0).0[1], (self.0).0[2], &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[1], (self.0).0[3], &mut carry);
+        let r3 = ::ff::mac_with_carry(r3, (self.0).0[1], (self.0).0[2], &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[1], (self.0).0[3], &mut carry);
         let r5 = carry;
         let mut carry = 0;
-        let r5 = ::mac_with_carry(r5, (self.0).0[2], (self.0).0[3], &mut carry);
+        let r5 = ::ff::mac_with_carry(r5, (self.0).0[2], (self.0).0[3], &mut carry);
         let r6 = carry;
 
         let r7 = r6 >> 63;
@@ -487,14 +486,14 @@ impl Field for Fr {
         let r1 = r1 << 1;
 
         let mut carry = 0;
-        let r0 = ::mac_with_carry(0, (self.0).0[0], (self.0).0[0], &mut carry);
-        let r1 = ::adc(r1, 0, &mut carry);
-        let r2 = ::mac_with_carry(r2, (self.0).0[1], (self.0).0[1], &mut carry);
-        let r3 = ::adc(r3, 0, &mut carry);
-        let r4 = ::mac_with_carry(r4, (self.0).0[2], (self.0).0[2], &mut carry);
-        let r5 = ::adc(r5, 0, &mut carry);
-        let r6 = ::mac_with_carry(r6, (self.0).0[3], (self.0).0[3], &mut carry);
-        let r7 = ::adc(r7, 0, &mut carry);
+        let r0 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[0], &mut carry);
+        let r1 = ::ff::adc(r1, 0, &mut carry);
+        let r2 = ::ff::mac_with_carry(r2, (self.0).0[1], (self.0).0[1], &mut carry);
+        let r3 = ::ff::adc(r3, 0, &mut carry);
+        let r4 = ::ff::mac_with_carry(r4, (self.0).0[2], (self.0).0[2], &mut carry);
+        let r5 = ::ff::adc(r5, 0, &mut carry);
+        let r6 = ::ff::mac_with_carry(r6, (self.0).0[3], (self.0).0[3], &mut carry);
+        let r7 = ::ff::adc(r7, 0, &mut carry);
         self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7);
     }
 }
@@ -534,35 +533,35 @@ impl Fr {
 
         let k = r0.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r0, k, MODULUS.0[0], &mut carry);
-        r1 = ::mac_with_carry(r1, k, MODULUS.0[1], &mut carry);
-        r2 = ::mac_with_carry(r2, k, MODULUS.0[2], &mut carry);
-        r3 = ::mac_with_carry(r3, k, MODULUS.0[3], &mut carry);
-        r4 = ::adc(r4, 0, &mut carry);
+        ::ff::mac_with_carry(r0, k, MODULUS.0[0], &mut carry);
+        r1 = ::ff::mac_with_carry(r1, k, MODULUS.0[1], &mut carry);
+        r2 = ::ff::mac_with_carry(r2, k, MODULUS.0[2], &mut carry);
+        r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[3], &mut carry);
+        r4 = ::ff::adc(r4, 0, &mut carry);
         let carry2 = carry;
         let k = r1.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r1, k, MODULUS.0[0], &mut carry);
-        r2 = ::mac_with_carry(r2, k, MODULUS.0[1], &mut carry);
-        r3 = ::mac_with_carry(r3, k, MODULUS.0[2], &mut carry);
-        r4 = ::mac_with_carry(r4, k, MODULUS.0[3], &mut carry);
-        r5 = ::adc(r5, carry2, &mut carry);
+        ::ff::mac_with_carry(r1, k, MODULUS.0[0], &mut carry);
+        r2 = ::ff::mac_with_carry(r2, k, MODULUS.0[1], &mut carry);
+        r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[2], &mut carry);
+        r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[3], &mut carry);
+        r5 = ::ff::adc(r5, carry2, &mut carry);
         let carry2 = carry;
         let k = r2.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r2, k, MODULUS.0[0], &mut carry);
-        r3 = ::mac_with_carry(r3, k, MODULUS.0[1], &mut carry);
-        r4 = ::mac_with_carry(r4, k, MODULUS.0[2], &mut carry);
-        r5 = ::mac_with_carry(r5, k, MODULUS.0[3], &mut carry);
-        r6 = ::adc(r6, carry2, &mut carry);
+        ::ff::mac_with_carry(r2, k, MODULUS.0[0], &mut carry);
+        r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[1], &mut carry);
+        r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[2], &mut carry);
+        r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[3], &mut carry);
+        r6 = ::ff::adc(r6, carry2, &mut carry);
         let carry2 = carry;
         let k = r3.wrapping_mul(INV);
         let mut carry = 0;
-        ::mac_with_carry(r3, k, MODULUS.0[0], &mut carry);
-        r4 = ::mac_with_carry(r4, k, MODULUS.0[1], &mut carry);
-        r5 = ::mac_with_carry(r5, k, MODULUS.0[2], &mut carry);
-        r6 = ::mac_with_carry(r6, k, MODULUS.0[3], &mut carry);
-        r7 = ::adc(r7, carry2, &mut carry);
+        ::ff::mac_with_carry(r3, k, MODULUS.0[0], &mut carry);
+        r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[1], &mut carry);
+        r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[2], &mut carry);
+        r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[3], &mut carry);
+        r7 = ::ff::adc(r7, carry2, &mut carry);
         (self.0).0[0] = r4;
         (self.0).0[1] = r5;
         (self.0).0[2] = r6;
@@ -572,7 +571,7 @@ impl Fr {
 }
 
 impl SqrtField for Fr {
-    fn legendre(&self) -> ::LegendreSymbol {
+    fn legendre(&self) -> ::ff::LegendreSymbol {
         // s = self^((r - 1) // 2)
         let s = self.pow([
             0x7fffffff80000000,
@@ -581,11 +580,11 @@ impl SqrtField for Fr {
             0x39f6d3a994cebea4,
         ]);
         if s == Self::zero() {
-            Zero
+            ::ff::LegendreSymbol::Zero
         } else if s == Self::one() {
-            QuadraticResidue
+            ::ff::LegendreSymbol::QuadraticResidue
         } else {
-            QuadraticNonResidue
+            ::ff::LegendreSymbol::QuadraticNonResidue
         }
     }
 
@@ -593,9 +592,9 @@ impl SqrtField for Fr {
         // Tonelli-Shank's algorithm for q mod 16 = 1
         // https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
         match self.legendre() {
-            Zero => Some(*self),
-            QuadraticNonResidue => None,
-            QuadraticResidue => {
+            ::ff::LegendreSymbol::Zero => Some(*self),
+            ::ff::LegendreSymbol::QuadraticNonResidue => None,
+            ::ff::LegendreSymbol::QuadraticResidue => {
                 let mut c = Fr(ROOT_OF_UNITY);
                 // r = self^((t + 1) // 2)
                 let mut r = self.pow([
@@ -909,6 +908,8 @@ fn test_fr_repr_sub_noborrow() {
 
 #[test]
 fn test_fr_legendre() {
+    use ff::LegendreSymbol::*;
+
     assert_eq!(QuadraticResidue, Fr::one().legendre());
     assert_eq!(Zero, Fr::zero().legendre());
 
diff --git a/src/bls12_381/mod.rs b/src/bls12_381/mod.rs
index a5db4b5..c6c13c5 100644
--- a/src/bls12_381/mod.rs
+++ b/src/bls12_381/mod.rs
@@ -18,7 +18,9 @@ pub use self::fq2::Fq2;
 pub use self::fq6::Fq6;
 pub use self::fr::{Fr, FrRepr};
 
-use super::{BitIterator, CurveAffine, Engine, Field};
+use super::{CurveAffine, Engine};
+
+use ff::{BitIterator, Field};
 
 // The BLS parameter x for BLS12-381 is -0xd201000000010000
 const BLS_X: u64 = 0xd201000000010000;
diff --git a/src/lib.rs b/src/lib.rs
index effc050..0c336ed 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -25,7 +25,7 @@ pub mod bls12_381;
 mod wnaf;
 pub use self::wnaf::Wnaf;
 
-use ff::*;
+use ff::{Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr, SqrtField};
 use std::error::Error;
 use std::fmt;
 
diff --git a/src/tests/field.rs b/src/tests/field.rs
index 74422fd..55396a7 100644
--- a/src/tests/field.rs
+++ b/src/tests/field.rs
@@ -1,5 +1,5 @@
+use ff::{Field, LegendreSymbol, PrimeField, SqrtField};
 use rand::{Rng, SeedableRng, XorShiftRng};
-use {Field, LegendreSymbol, PrimeField, SqrtField};
 
 pub fn random_frobenius_tests<F: Field, C: AsRef<[u64]>>(characteristic: C, maxpower: usize) {
     let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);