diff --git a/src/domain.rs b/src/domain.rs
index e1dc229..098b0ed 100644
--- a/src/domain.rs
+++ b/src/domain.rs
@@ -12,7 +12,7 @@
 //! [Groth16]: https://eprint.iacr.org/2016/260
 
 use ff::PrimeField;
-use group::CofactorCurve;
+use group::cofactor::CofactorCurve;
 
 use super::SynthesisError;
 
diff --git a/src/groth16/generator.rs b/src/groth16/generator.rs
index e84fc12..084e7a3 100644
--- a/src/groth16/generator.rs
+++ b/src/groth16/generator.rs
@@ -3,7 +3,7 @@ use std::ops::{AddAssign, MulAssign};
 use std::sync::Arc;
 
 use ff::{Field, PrimeField};
-use group::{CurveAffine, CofactorCurve, Group, Wnaf};
+use group::{cofactor::CofactorCurveAffine, Curve, Group, Wnaf};
 use pairing::Engine;
 
 use super::{Parameters, VerifyingKey};
diff --git a/src/groth16/mod.rs b/src/groth16/mod.rs
index 2602bc7..7c97197 100644
--- a/src/groth16/mod.rs
+++ b/src/groth16/mod.rs
@@ -2,7 +2,7 @@
 //!
 //! [Groth16]: https://eprint.iacr.org/2016/260
 
-use group::{CurveAffine, GroupEncoding, UncompressedEncoding};
+use group::{cofactor::CofactorCurveAffine, GroupEncoding, UncompressedEncoding};
 use pairing::{Engine, MultiMillerLoop};
 
 use crate::SynthesisError;
diff --git a/src/groth16/prover.rs b/src/groth16/prover.rs
index 293cad2..cbe883a 100644
--- a/src/groth16/prover.rs
+++ b/src/groth16/prover.rs
@@ -5,7 +5,7 @@ use std::sync::Arc;
 use futures::Future;
 
 use ff::{Field, PrimeField};
-use group::{CurveAffine, CofactorCurve};
+use group::{cofactor::CofactorCurveAffine, Curve};
 use pairing::Engine;
 
 use super::{ParameterSource, Proof};
diff --git a/src/groth16/tests/dummy_engine.rs b/src/groth16/tests/dummy_engine.rs
index 01e8b82..17e0043 100644
--- a/src/groth16/tests/dummy_engine.rs
+++ b/src/groth16/tests/dummy_engine.rs
@@ -1,5 +1,9 @@
 use ff::{Field, PrimeField};
-use group::{CurveAffine, CofactorCurve, Group, GroupEncoding, PrimeGroup, UncompressedEncoding};
+use group::{
+    cofactor::{CofactorCurve, CofactorCurveAffine, CofactorGroup},
+    prime::PrimeGroup,
+    Curve, Group, GroupEncoding, UncompressedEncoding,
+};
 use pairing::{Engine, MillerLoopResult, MultiMillerLoop, PairingCurveAffine};
 
 use rand_core::RngCore;
@@ -367,7 +371,6 @@ impl MillerLoopResult for Fr {
 }
 
 impl Group for Fr {
-    type Subgroup = Fr;
     type Scalar = Fr;
 
     fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self {
@@ -393,8 +396,20 @@ impl Group for Fr {
 
 impl PrimeGroup for Fr {}
 
-impl CofactorCurve for Fr {
-    type Affine = Fr;
+impl CofactorGroup for Fr {
+    type Subgroup = Fr;
+
+    fn mul_by_cofactor(&self) -> Self::Subgroup {
+        *self
+    }
+
+    fn into_subgroup(self) -> CtOption<Self::Subgroup> {
+        CtOption::new(self, Choice::from(1))
+    }
+}
+
+impl Curve for Fr {
+    type AffineRepr = Fr;
 
     fn to_affine(&self) -> Fr {
         *self
@@ -409,6 +424,10 @@ impl CofactorCurve for Fr {
     }
 }
 
+impl CofactorCurve for Fr {
+    type Affine = Fr;
+}
+
 #[derive(Copy, Clone, Default)]
 pub struct FakePoint;
 
@@ -424,7 +443,7 @@ impl AsRef<[u8]> for FakePoint {
     }
 }
 
-impl CurveAffine for Fr {
+impl CofactorCurveAffine for Fr {
     type Curve = Fr;
     type Scalar = Fr;
 
diff --git a/src/groth16/verifier.rs b/src/groth16/verifier.rs
index 5758d5d..0fe8c94 100644
--- a/src/groth16/verifier.rs
+++ b/src/groth16/verifier.rs
@@ -1,4 +1,4 @@
-use group::{CurveAffine, CofactorCurve};
+use group::{cofactor::CofactorCurveAffine, Curve};
 use pairing::{MillerLoopResult, MultiMillerLoop};
 use std::ops::{AddAssign, Neg};
 
diff --git a/src/multiexp.rs b/src/multiexp.rs
index fea10c6..8fdbc70 100644
--- a/src/multiexp.rs
+++ b/src/multiexp.rs
@@ -2,7 +2,7 @@ use super::multicore::Worker;
 use bit_vec::{self, BitVec};
 use ff::{Endianness, Field, PrimeField};
 use futures::Future;
-use group::{CofactorCurve, CurveAffine};
+use group::cofactor::{CofactorCurve, CofactorCurveAffine};
 use std::io;
 use std::iter;
 use std::ops::AddAssign;
@@ -11,14 +11,14 @@ use std::sync::Arc;
 use super::SynthesisError;
 
 /// An object that builds a source of bases.
-pub trait SourceBuilder<G: CurveAffine>: Send + Sync + 'static + Clone {
+pub trait SourceBuilder<G: CofactorCurveAffine>: Send + Sync + 'static + Clone {
     type Source: Source<G>;
 
     fn new(self) -> Self::Source;
 }
 
 /// A source of bases, like an iterator.
-pub trait Source<G: CurveAffine> {
+pub trait Source<G: CofactorCurveAffine> {
     fn next(&mut self) -> Result<&G, SynthesisError>;
 
     /// Skips `amt` elements from the source, avoiding deserialization.
@@ -37,7 +37,7 @@ pub trait AddAssignFromSource: CofactorCurve {
 }
 impl<G> AddAssignFromSource for G where G: CofactorCurve {}
 
-impl<G: CurveAffine> SourceBuilder<G> for (Arc<Vec<G>>, usize) {
+impl<G: CofactorCurveAffine> SourceBuilder<G> for (Arc<Vec<G>>, usize) {
     type Source = (Arc<Vec<G>>, usize);
 
     fn new(self) -> (Arc<Vec<G>>, usize) {
@@ -45,7 +45,7 @@ impl<G: CurveAffine> SourceBuilder<G> for (Arc<Vec<G>>, usize) {
     }
 }
 
-impl<G: CurveAffine> Source<G> for (Arc<Vec<G>>, usize) {
+impl<G: CofactorCurveAffine> Source<G> for (Arc<Vec<G>>, usize) {
     fn next(&mut self) -> Result<&G, SynthesisError> {
         if self.0.len() <= self.1 {
             return Err(io::Error::new(
@@ -311,7 +311,7 @@ fn test_with_bls12() {
         acc
     }
 
-    use group::Group;
+    use group::{Curve, Group};
     use pairing::{
         bls12_381::{Bls12, Fr},
         Engine,