diff --git a/src/domain.rs b/src/domain.rs
index be97c20..bafa596 100644
--- a/src/domain.rs
+++ b/src/domain.rs
@@ -218,7 +218,7 @@ impl<G: CurveProjective> Clone for Point<G> {
 
 impl<G: CurveProjective> Group<G::Engine> for Point<G> {
     fn group_zero() -> Self {
-        Point(G::zero())
+        Point(G::identity())
     }
     fn group_mul_assign(&mut self, by: &G::Scalar) {
         self.0.mul_assign(by.to_repr());
diff --git a/src/groth16/generator.rs b/src/groth16/generator.rs
index 02efc21..264d3ab 100644
--- a/src/groth16/generator.rs
+++ b/src/groth16/generator.rs
@@ -234,7 +234,7 @@ where
 
     let worker = Worker::new();
 
-    let mut h = vec![E::G1::zero(); powers_of_tau.as_ref().len() - 1];
+    let mut h = vec![E::G1::identity(); powers_of_tau.as_ref().len() - 1];
     {
         // Compute powers of tau
         {
@@ -287,11 +287,11 @@ where
     powers_of_tau.ifft(&worker);
     let powers_of_tau = powers_of_tau.into_coeffs();
 
-    let mut a = vec![E::G1::zero(); assembly.num_inputs + assembly.num_aux];
-    let mut b_g1 = vec![E::G1::zero(); assembly.num_inputs + assembly.num_aux];
-    let mut b_g2 = vec![E::G2::zero(); assembly.num_inputs + assembly.num_aux];
-    let mut ic = vec![E::G1::zero(); assembly.num_inputs];
-    let mut l = vec![E::G1::zero(); assembly.num_aux];
+    let mut a = vec![E::G1::identity(); assembly.num_inputs + assembly.num_aux];
+    let mut b_g1 = vec![E::G1::identity(); assembly.num_inputs + assembly.num_aux];
+    let mut b_g2 = vec![E::G2::identity(); assembly.num_inputs + assembly.num_aux];
+    let mut ic = vec![E::G1::identity(); assembly.num_inputs];
+    let mut l = vec![E::G1::identity(); assembly.num_aux];
 
     fn eval<E: Engine>(
         // wNAF window tables
@@ -446,7 +446,7 @@ where
     // Don't allow any elements be unconstrained, so that
     // the L query is always fully dense.
     for e in l.iter() {
-        if e.is_zero() {
+        if e.is_identity() {
             return Err(SynthesisError::UnconstrainedVariable);
         }
     }
@@ -472,19 +472,19 @@ where
         // Filter points at infinity away from A/B queries
         a: Arc::new(
             a.into_iter()
-                .filter(|e| !e.is_zero())
+                .filter(|e| !e.is_identity())
                 .map(|e| e.into_affine())
                 .collect(),
         ),
         b_g1: Arc::new(
             b_g1.into_iter()
-                .filter(|e| !e.is_zero())
+                .filter(|e| !e.is_identity())
                 .map(|e| e.into_affine())
                 .collect(),
         ),
         b_g2: Arc::new(
             b_g2.into_iter()
-                .filter(|e| !e.is_zero())
+                .filter(|e| !e.is_identity())
                 .map(|e| e.into_affine())
                 .collect(),
         ),
diff --git a/src/groth16/mod.rs b/src/groth16/mod.rs
index 6f5af85..b338b0c 100644
--- a/src/groth16/mod.rs
+++ b/src/groth16/mod.rs
@@ -54,7 +54,7 @@ impl<E: Engine> Proof<E> {
             .into_affine()
             .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
             .and_then(|e| {
-                if e.is_zero() {
+                if e.is_identity() {
                     Err(io::Error::new(
                         io::ErrorKind::InvalidData,
                         "point at infinity",
@@ -69,7 +69,7 @@ impl<E: Engine> Proof<E> {
             .into_affine()
             .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
             .and_then(|e| {
-                if e.is_zero() {
+                if e.is_identity() {
                     Err(io::Error::new(
                         io::ErrorKind::InvalidData,
                         "point at infinity",
@@ -84,7 +84,7 @@ impl<E: Engine> Proof<E> {
             .into_affine()
             .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
             .and_then(|e| {
-                if e.is_zero() {
+                if e.is_identity() {
                     Err(io::Error::new(
                         io::ErrorKind::InvalidData,
                         "point at infinity",
@@ -198,7 +198,7 @@ impl<E: Engine> VerifyingKey<E> {
                 .into_affine()
                 .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
                 .and_then(|e| {
-                    if e.is_zero() {
+                    if e.is_identity() {
                         Err(io::Error::new(
                             io::ErrorKind::InvalidData,
                             "point at infinity",
@@ -303,7 +303,7 @@ impl<E: Engine> Parameters<E> {
             }
             .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
             .and_then(|e| {
-                if e.is_zero() {
+                if e.is_identity() {
                     Err(io::Error::new(
                         io::ErrorKind::InvalidData,
                         "point at infinity",
@@ -325,7 +325,7 @@ impl<E: Engine> Parameters<E> {
             }
             .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))
             .and_then(|e| {
-                if e.is_zero() {
+                if e.is_identity() {
                     Err(io::Error::new(
                         io::ErrorKind::InvalidData,
                         "point at infinity",
diff --git a/src/groth16/prover.rs b/src/groth16/prover.rs
index 34abbb4..97707fb 100644
--- a/src/groth16/prover.rs
+++ b/src/groth16/prover.rs
@@ -295,7 +295,7 @@ where
     );
     let b_g2_aux = multiexp(&worker, b_g2_aux_source, b_aux_density, aux_assignment);
 
-    if vk.delta_g1.is_zero() || vk.delta_g2.is_zero() {
+    if vk.delta_g1.is_identity() || vk.delta_g2.is_identity() {
         // If this element is zero, someone is trying to perform a
         // subversion-CRS attack.
         return Err(SynthesisError::UnexpectedIdentity);
diff --git a/src/groth16/tests/dummy_engine.rs b/src/groth16/tests/dummy_engine.rs
index c1bf516..c95a751 100644
--- a/src/groth16/tests/dummy_engine.rs
+++ b/src/groth16/tests/dummy_engine.rs
@@ -362,15 +362,15 @@ impl CurveProjective for Fr {
         <Fr as Field>::random(rng)
     }
 
-    fn zero() -> Self {
+    fn identity() -> Self {
         <Fr as Field>::zero()
     }
 
-    fn one() -> Self {
+    fn generator() -> Self {
         <Fr as Field>::one()
     }
 
-    fn is_zero(&self) -> bool {
+    fn is_identity(&self) -> bool {
         <Fr as Field>::is_zero(self)
     }
 
@@ -450,15 +450,15 @@ impl CurveAffine for Fr {
     type Scalar = Fr;
     type Engine = DummyEngine;
 
-    fn zero() -> Self {
+    fn identity() -> Self {
         <Fr as Field>::zero()
     }
 
-    fn one() -> Self {
+    fn generator() -> Self {
         <Fr as Field>::one()
     }
 
-    fn is_zero(&self) -> bool {
+    fn is_identity(&self) -> bool {
         <Fr as Field>::is_zero(self)
     }
 
diff --git a/src/multiexp.rs b/src/multiexp.rs
index deed9fa..948086b 100644
--- a/src/multiexp.rs
+++ b/src/multiexp.rs
@@ -55,7 +55,7 @@ impl<G: CurveAffine> Source<G> for (Arc<Vec<G>>, usize) {
             .into());
         }
 
-        if self.0[self.1].is_zero() {
+        if self.0[self.1].is_identity() {
             return Err(SynthesisError::UnexpectedIdentity);
         }
 
@@ -173,13 +173,13 @@ where
 
         pool.compute(move || {
             // Accumulate the result
-            let mut acc = G::zero();
+            let mut acc = G::identity();
 
             // Build a source for the bases
             let mut bases = bases.new();
 
             // Create space for the buckets
-            let mut buckets = vec![G::zero(); (1 << c) - 1];
+            let mut buckets = vec![G::identity(); (1 << c) - 1];
 
             let one = <G::Engine as ScalarEngine>::Fr::one();
 
@@ -222,7 +222,7 @@ where
             // e.g. 3a + 2b + 1c = a +
             //                    (a) + b +
             //                    ((a) + b) + c
-            let mut running_sum = G::zero();
+            let mut running_sum = G::identity();
             for exp in buckets.into_iter().rev() {
                 running_sum.add_assign(&exp);
                 acc.add_assign(&running_sum);
@@ -302,7 +302,7 @@ fn test_with_bls12() {
     ) -> G {
         assert_eq!(bases.len(), exponents.len());
 
-        let mut acc = G::zero();
+        let mut acc = G::identity();
 
         for (base, exp) in bases.iter().zip(exponents.iter()) {
             AddAssign::<&G>::add_assign(&mut acc, &base.mul(exp.to_repr()));