diff --git a/bellman/src/domain.rs b/bellman/src/domain.rs
index be97c2037..bafa59633 100644
--- a/bellman/src/domain.rs
+++ b/bellman/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/bellman/src/groth16/generator.rs b/bellman/src/groth16/generator.rs
index 02efc21bd..264d3ab2a 100644
--- a/bellman/src/groth16/generator.rs
+++ b/bellman/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/bellman/src/groth16/mod.rs b/bellman/src/groth16/mod.rs
index 6f5af85fc..b338b0c62 100644
--- a/bellman/src/groth16/mod.rs
+++ b/bellman/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/bellman/src/groth16/prover.rs b/bellman/src/groth16/prover.rs
index 34abbb4ea..97707fb09 100644
--- a/bellman/src/groth16/prover.rs
+++ b/bellman/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/bellman/src/groth16/tests/dummy_engine.rs b/bellman/src/groth16/tests/dummy_engine.rs
index c1bf51660..c95a7510a 100644
--- a/bellman/src/groth16/tests/dummy_engine.rs
+++ b/bellman/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/bellman/src/multiexp.rs b/bellman/src/multiexp.rs
index deed9fa05..948086b46 100644
--- a/bellman/src/multiexp.rs
+++ b/bellman/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()));
diff --git a/group/src/lib.rs b/group/src/lib.rs
index 05afa6f09..8f40d0a2c 100644
--- a/group/src/lib.rs
+++ b/group/src/lib.rs
@@ -55,13 +55,13 @@ pub trait CurveProjective:
     fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self;
 
     /// Returns the additive identity.
-    fn zero() -> Self;
+    fn identity() -> Self;
 
     /// Returns a fixed generator of unknown exponent.
-    fn one() -> Self;
+    fn generator() -> Self;
 
     /// Determines if this point is the point at infinity.
-    fn is_zero(&self) -> bool;
+    fn is_identity(&self) -> bool;
 
     /// Normalizes a slice of projective elements so that
     /// conversion to affine is cheap.
@@ -112,14 +112,14 @@ pub trait CurveAffine:
     type Compressed: EncodedPoint<Affine = Self>;
 
     /// Returns the additive identity.
-    fn zero() -> Self;
+    fn identity() -> Self;
 
     /// Returns a fixed generator of unknown exponent.
-    fn one() -> Self;
+    fn generator() -> Self;
 
     /// Determines if this point represents the point at infinity; the
     /// additive identity.
-    fn is_zero(&self) -> bool;
+    fn is_identity(&self) -> bool;
 
     /// Performs scalar multiplication of this element with mixed addition.
     fn mul<S: Into<<Self::Scalar as PrimeField>::Repr>>(&self, other: S) -> Self::Projective;
diff --git a/group/src/tests/mod.rs b/group/src/tests/mod.rs
index 75fc46f87..5540cc8c2 100644
--- a/group/src/tests/mod.rs
+++ b/group/src/tests/mod.rs
@@ -11,33 +11,33 @@ pub fn curve_tests<G: CurveProjective>() {
         0xe5,
     ]);
 
-    // Negation edge case with zero.
+    // Negation edge case with identity.
     {
-        let z = G::zero().neg();
-        assert!(z.is_zero());
+        let z = G::identity().neg();
+        assert!(z.is_identity());
     }
 
-    // Doubling edge case with zero.
+    // Doubling edge case with identity.
     {
-        let mut z = G::zero();
+        let mut z = G::identity();
         z.double();
-        assert!(z.is_zero());
+        assert!(z.is_identity());
     }
 
-    // Addition edge cases with zero
+    // Addition edge cases with identity
     {
         let mut r = G::random(&mut rng);
         let rcopy = r;
-        r.add_assign(&G::zero());
+        r.add_assign(&G::identity());
         assert_eq!(r, rcopy);
-        r.add_assign(&G::Affine::zero());
+        r.add_assign(&G::Affine::identity());
         assert_eq!(r, rcopy);
 
-        let mut z = G::zero();
-        z.add_assign(&G::zero());
-        assert!(z.is_zero());
-        z.add_assign(&G::Affine::zero());
-        assert!(z.is_zero());
+        let mut z = G::identity();
+        z.add_assign(&G::identity());
+        assert!(z.is_identity());
+        z.add_assign(&G::Affine::identity());
+        assert!(z.is_identity());
 
         let mut z2 = z;
         z2.add_assign(&r);
@@ -209,11 +209,11 @@ fn random_negation_tests<G: CurveProjective>() {
 
         let mut t3 = t1;
         t3.add_assign(&t2);
-        assert!(t3.is_zero());
+        assert!(t3.is_identity());
 
         let mut t4 = t1;
         t4.add_assign(&t2.into_affine());
-        assert!(t4.is_zero());
+        assert!(t4.is_identity());
 
         assert_eq!(t1.neg(), t2);
     }
@@ -313,7 +313,7 @@ fn random_addition_tests<G: CurveProjective>() {
             assert_eq!(aplusa, aplusamixed);
         }
 
-        let mut tmp = vec![G::zero(); 6];
+        let mut tmp = vec![G::identity(); 6];
 
         // (a + b) + c
         tmp[0] = a;
@@ -390,7 +390,7 @@ fn random_transformation_tests<G: CurveProjective>() {
         let between = Uniform::new(0, 1000);
         // Sprinkle in some normalized points
         for _ in 0..5 {
-            v[between.sample(&mut rng)] = G::zero();
+            v[between.sample(&mut rng)] = G::identity();
         }
         for _ in 0..5 {
             let s = between.sample(&mut rng);
@@ -418,13 +418,19 @@ fn random_encoding_tests<G: CurveProjective>() {
     ]);
 
     assert_eq!(
-        G::Affine::zero().into_uncompressed().into_affine().unwrap(),
-        G::Affine::zero()
+        G::Affine::identity()
+            .into_uncompressed()
+            .into_affine()
+            .unwrap(),
+        G::Affine::identity()
     );
 
     assert_eq!(
-        G::Affine::zero().into_compressed().into_affine().unwrap(),
-        G::Affine::zero()
+        G::Affine::identity()
+            .into_compressed()
+            .into_affine()
+            .unwrap(),
+        G::Affine::identity()
     );
 
     for _ in 0..1000 {
diff --git a/group/src/wnaf.rs b/group/src/wnaf.rs
index 57f780d30..86f77e2ff 100644
--- a/group/src/wnaf.rs
+++ b/group/src/wnaf.rs
@@ -80,7 +80,7 @@ pub(crate) fn wnaf_form<S: AsRef<[u8]>>(wnaf: &mut Vec<i64>, c: S, window: usize
 /// This function must be provided a `table` and `wnaf` that were constructed with
 /// the same window size; otherwise, it may panic or produce invalid results.
 pub(crate) fn wnaf_exp<G: CurveProjective>(table: &[G], wnaf: &[i64]) -> G {
-    let mut result = G::zero();
+    let mut result = G::identity();
 
     let mut found_one = false;
 
diff --git a/pairing/src/bls12_381/ec.rs b/pairing/src/bls12_381/ec.rs
index 071544491..39032ae7d 100644
--- a/pairing/src/bls12_381/ec.rs
+++ b/pairing/src/bls12_381/ec.rs
@@ -42,11 +42,11 @@ macro_rules! curve_impl {
 
         impl PartialEq for $projective {
             fn eq(&self, other: &$projective) -> bool {
-                if self.is_zero() {
-                    return other.is_zero();
+                if self.is_identity() {
+                    return other.is_identity();
                 }
 
-                if other.is_zero() {
+                if other.is_identity() {
                     return false;
                 }
 
@@ -82,7 +82,7 @@ macro_rules! curve_impl {
 
         impl $affine {
             fn mul_bits_u64<S: AsRef<[u64]>>(&self, bits: BitIterator<u64, S>) -> $projective {
-                let mut res = $projective::zero();
+                let mut res = $projective::identity();
                 for i in bits {
                     res.double();
                     if i {
@@ -93,7 +93,7 @@ macro_rules! curve_impl {
             }
 
             fn mul_bits_u8<S: AsRef<[u8]>>(&self, bits: BitIterator<u8, S>) -> $projective {
-                let mut res = $projective::zero();
+                let mut res = $projective::identity();
                 for i in bits {
                     res.double();
                     if i {
@@ -126,7 +126,7 @@ macro_rules! curve_impl {
             }
 
             fn is_on_curve(&self) -> bool {
-                if self.is_zero() {
+                if self.is_identity() {
                     true
                 } else {
                     // Check that the point is on the curve
@@ -141,7 +141,7 @@ macro_rules! curve_impl {
             }
 
             fn is_in_correct_subgroup_assuming_on_curve(&self) -> bool {
-                self.mul($scalarfield::char()).is_zero()
+                self.mul($scalarfield::char()).is_identity()
             }
         }
 
@@ -151,7 +151,7 @@ macro_rules! curve_impl {
             #[inline]
             fn neg(self) -> Self {
                 let mut ret = self;
-                if !ret.is_zero() {
+                if !ret.is_identity() {
                     ret.y = ret.y.neg();
                 }
                 ret
@@ -166,7 +166,7 @@ macro_rules! curve_impl {
             type Uncompressed = $uncompressed;
             type Compressed = $compressed;
 
-            fn zero() -> Self {
+            fn identity() -> Self {
                 $affine {
                     x: $basefield::zero(),
                     y: $basefield::one(),
@@ -174,11 +174,11 @@ macro_rules! curve_impl {
                 }
             }
 
-            fn one() -> Self {
+            fn generator() -> Self {
                 Self::get_generator()
             }
 
-            fn is_zero(&self) -> bool {
+            fn is_identity(&self) -> bool {
                 self.infinity
             }
 
@@ -212,7 +212,7 @@ macro_rules! curve_impl {
             #[inline]
             fn neg(self) -> Self {
                 let mut ret = self;
-                if !ret.is_zero() {
+                if !ret.is_identity() {
                     ret.y = ret.y.neg();
                 }
                 ret
@@ -241,12 +241,12 @@ macro_rules! curve_impl {
 
         impl<'r> ::std::ops::AddAssign<&'r $projective> for $projective {
             fn add_assign(&mut self, other: &Self) {
-                if self.is_zero() {
+                if self.is_identity() {
                     *self = *other;
                     return;
                 }
 
-                if other.is_zero() {
+                if other.is_identity() {
                     return;
                 }
 
@@ -390,11 +390,11 @@ macro_rules! curve_impl {
             for $projective
         {
             fn add_assign(&mut self, other: &<$projective as CurveProjective>::Affine) {
-                if other.is_zero() {
+                if other.is_identity() {
                     return;
                 }
 
-                if self.is_zero() {
+                if self.is_identity() {
                     self.x = other.x;
                     self.y = other.y;
                     self.z = $basefield::one();
@@ -524,7 +524,7 @@ macro_rules! curve_impl {
                     if p.is_some().into() {
                         let p = p.unwrap().scale_by_cofactor();
 
-                        if !p.is_zero() {
+                        if !p.is_identity() {
                             return p;
                         }
                     }
@@ -533,7 +533,7 @@ macro_rules! curve_impl {
 
             // The point at infinity is always represented by
             // Z = 0.
-            fn zero() -> Self {
+            fn identity() -> Self {
                 $projective {
                     x: $basefield::zero(),
                     y: $basefield::one(),
@@ -541,18 +541,18 @@ macro_rules! curve_impl {
                 }
             }
 
-            fn one() -> Self {
-                $affine::one().into()
+            fn generator() -> Self {
+                $affine::generator().into()
             }
 
             // The point at infinity is always represented by
             // Z = 0.
-            fn is_zero(&self) -> bool {
+            fn is_identity(&self) -> bool {
                 self.z.is_zero()
             }
 
             fn is_normalized(&self) -> bool {
-                self.is_zero() || self.z == $basefield::one()
+                self.is_identity() || self.z == $basefield::one()
             }
 
             fn batch_normalization(v: &mut [Self]) {
@@ -609,7 +609,7 @@ macro_rules! curve_impl {
             }
 
             fn double(&mut self) {
-                if self.is_zero() {
+                if self.is_identity() {
                     return;
                 }
 
@@ -662,7 +662,7 @@ macro_rules! curve_impl {
             }
 
             fn mul_assign<S: Into<<Self::Scalar as PrimeField>::Repr>>(&mut self, other: S) {
-                let mut res = Self::zero();
+                let mut res = Self::identity();
 
                 let mut found_one = false;
 
@@ -700,8 +700,8 @@ macro_rules! curve_impl {
         // coordinates with Z = 1.
         impl From<$affine> for $projective {
             fn from(p: $affine) -> $projective {
-                if p.is_zero() {
-                    $projective::zero()
+                if p.is_identity() {
+                    $projective::identity()
                 } else {
                     $projective {
                         x: p.x,
@@ -716,8 +716,8 @@ macro_rules! curve_impl {
         // coordinates as X/Z^2, Y/Z^3.
         impl From<$projective> for $affine {
             fn from(p: $projective) -> $affine {
-                if p.is_zero() {
-                    $affine::zero()
+                if p.is_identity() {
+                    $affine::identity()
                 } else if p.z == $basefield::one() {
                     // If Z is one, the point is already normalized.
                     $affine {
@@ -830,7 +830,7 @@ pub mod g1 {
                 copy[0] &= 0x3f;
 
                 if copy.iter().all(|b| *b == 0) {
-                    Ok(G1Affine::zero())
+                    Ok(G1Affine::identity())
                 } else {
                     Err(GroupDecodingError::UnexpectedInformation)
                 }
@@ -867,7 +867,7 @@ pub mod g1 {
         fn from_affine(affine: G1Affine) -> Self {
             let mut res = Self::empty();
 
-            if affine.is_zero() {
+            if affine.is_identity() {
                 // Set the second-most significant bit to indicate this point
                 // is at infinity.
                 res.0[0] |= 1 << 6;
@@ -937,7 +937,7 @@ pub mod g1 {
                 copy[0] &= 0x3f;
 
                 if copy.iter().all(|b| *b == 0) {
-                    Ok(G1Affine::zero())
+                    Ok(G1Affine::identity())
                 } else {
                     Err(GroupDecodingError::UnexpectedInformation)
                 }
@@ -964,7 +964,7 @@ pub mod g1 {
         fn from_affine(affine: G1Affine) -> Self {
             let mut res = Self::empty();
 
-            if affine.is_zero() {
+            if affine.is_identity() {
                 // Set the second-most significant bit to indicate this point
                 // is at infinity.
                 res.0[0] |= 1 << 6;
@@ -1043,8 +1043,8 @@ pub mod g1 {
     pub struct G1Prepared(pub(crate) G1Affine);
 
     impl G1Prepared {
-        pub fn is_zero(&self) -> bool {
-            self.0.is_zero()
+        pub fn is_identity(&self) -> bool {
+            self.0.is_identity()
         }
 
         pub fn from_affine(p: G1Affine) -> Self {
@@ -1075,13 +1075,13 @@ pub mod g1 {
                 assert!(!p.is_in_correct_subgroup_assuming_on_curve());
 
                 let g1 = p.scale_by_cofactor();
-                if !g1.is_zero() {
+                if !g1.is_identity() {
                     assert_eq!(i, 4);
                     let g1 = G1Affine::from(g1);
 
                     assert!(g1.is_in_correct_subgroup_assuming_on_curve());
 
-                    assert_eq!(g1, G1Affine::one());
+                    assert_eq!(g1, G1Affine::generator());
                     break;
                 }
             }
@@ -1440,7 +1440,7 @@ pub mod g2 {
                 copy[0] &= 0x3f;
 
                 if copy.iter().all(|b| *b == 0) {
-                    Ok(G2Affine::zero())
+                    Ok(G2Affine::identity())
                 } else {
                     Err(GroupDecodingError::UnexpectedInformation)
                 }
@@ -1489,7 +1489,7 @@ pub mod g2 {
         fn from_affine(affine: G2Affine) -> Self {
             let mut res = Self::empty();
 
-            if affine.is_zero() {
+            if affine.is_identity() {
                 // Set the second-most significant bit to indicate this point
                 // is at infinity.
                 res.0[0] |= 1 << 6;
@@ -1561,7 +1561,7 @@ pub mod g2 {
                 copy[0] &= 0x3f;
 
                 if copy.iter().all(|b| *b == 0) {
-                    Ok(G2Affine::zero())
+                    Ok(G2Affine::identity())
                 } else {
                     Err(GroupDecodingError::UnexpectedInformation)
                 }
@@ -1603,7 +1603,7 @@ pub mod g2 {
         fn from_affine(affine: G2Affine) -> Self {
             let mut res = Self::empty();
 
-            if affine.is_zero() {
+            if affine.is_identity() {
                 // Set the second-most significant bit to indicate this point
                 // is at infinity.
                 res.0[0] |= 1 << 6;
@@ -1728,12 +1728,12 @@ pub mod g2 {
                 assert!(!p.is_in_correct_subgroup_assuming_on_curve());
 
                 let g2 = p.scale_by_cofactor();
-                if !g2.is_zero() {
+                if !g2.is_identity() {
                     assert_eq!(i, 2);
                     let g2 = G2Affine::from(g2);
 
                     assert!(g2.is_in_correct_subgroup_assuming_on_curve());
-                    assert_eq!(g2, G2Affine::one());
+                    assert_eq!(g2, G2Affine::generator());
                     break;
                 }
             }
diff --git a/pairing/src/bls12_381/mod.rs b/pairing/src/bls12_381/mod.rs
index afe9c826a..748ba5f31 100644
--- a/pairing/src/bls12_381/mod.rs
+++ b/pairing/src/bls12_381/mod.rs
@@ -59,7 +59,7 @@ impl Engine for Bls12 {
     {
         let mut pairs = vec![];
         for &(p, q) in i {
-            if !p.is_zero() && !q.is_zero() {
+            if !p.is_identity() && !q.is_identity() {
                 pairs.push((p, q.coeffs.iter()));
             }
         }
@@ -168,12 +168,12 @@ impl Engine for Bls12 {
 }
 
 impl G2Prepared {
-    pub fn is_zero(&self) -> bool {
+    pub fn is_identity(&self) -> bool {
         self.infinity
     }
 
     pub fn from_affine(q: G2Affine) -> Self {
-        if q.is_zero() {
+        if q.is_identity() {
             return G2Prepared {
                 coeffs: vec![],
                 infinity: true,
diff --git a/pairing/src/bls12_381/tests/mod.rs b/pairing/src/bls12_381/tests/mod.rs
index e8663199f..734e6f3cc 100644
--- a/pairing/src/bls12_381/tests/mod.rs
+++ b/pairing/src/bls12_381/tests/mod.rs
@@ -23,7 +23,7 @@ fn test_pairing_result_against_relic() {
     0F41E58663BF08CF 068672CBD01A7EC7 3BACA4D72CA93544 DEFF686BFD6DF543 D48EAA24AFE47E1E FDE449383B676631
     */
 
-    assert_eq!(Bls12::pairing(G1::one(), G2::one()), Fq12 {
+    assert_eq!(Bls12::pairing(G1::generator(), G2::generator()), Fq12 {
         c0: Fq6 {
             c0: Fq2 {
                 c0: Fq::from_str("2819105605953691245277803056322684086884703000473961065716485506033588504203831029066448642358042597501014294104502").unwrap(),
@@ -56,7 +56,7 @@ fn test_pairing_result_against_relic() {
 }
 
 fn test_vectors<G: CurveProjective, E: EncodedPoint<Affine = G::Affine>>(expected: &[u8]) {
-    let mut e = G::zero();
+    let mut e = G::identity();
 
     let mut v = vec![];
     {
@@ -72,7 +72,7 @@ fn test_vectors<G: CurveProjective, E: EncodedPoint<Affine = G::Affine>>(expecte
             let decoded = decoded.into_affine().unwrap();
             assert_eq!(e_affine, decoded);
 
-            e.add_assign(&G::one());
+            e.add_assign(&G::generator());
         }
     }
 
@@ -102,7 +102,7 @@ fn test_g2_compressed_valid_vectors() {
 #[test]
 fn test_g1_uncompressed_invalid_vectors() {
     {
-        let z = G1Affine::zero().into_uncompressed();
+        let z = G1Affine::identity().into_uncompressed();
 
         {
             let mut z = z;
@@ -135,7 +135,7 @@ fn test_g1_uncompressed_invalid_vectors() {
         }
     }
 
-    let o = G1Affine::one().into_uncompressed();
+    let o = G1Affine::generator().into_uncompressed();
 
     {
         let mut o = o;
@@ -218,7 +218,7 @@ fn test_g1_uncompressed_invalid_vectors() {
 #[test]
 fn test_g2_uncompressed_invalid_vectors() {
     {
-        let z = G2Affine::zero().into_uncompressed();
+        let z = G2Affine::identity().into_uncompressed();
 
         {
             let mut z = z;
@@ -251,7 +251,7 @@ fn test_g2_uncompressed_invalid_vectors() {
         }
     }
 
-    let o = G2Affine::one().into_uncompressed();
+    let o = G2Affine::generator().into_uncompressed();
 
     {
         let mut o = o;
@@ -362,7 +362,7 @@ fn test_g2_uncompressed_invalid_vectors() {
 #[test]
 fn test_g1_compressed_invalid_vectors() {
     {
-        let z = G1Affine::zero().into_compressed();
+        let z = G1Affine::identity().into_compressed();
 
         {
             let mut z = z;
@@ -395,7 +395,7 @@ fn test_g1_compressed_invalid_vectors() {
         }
     }
 
-    let o = G1Affine::one().into_compressed();
+    let o = G1Affine::generator().into_compressed();
 
     {
         let mut o = o;
@@ -476,7 +476,7 @@ fn test_g1_compressed_invalid_vectors() {
 #[test]
 fn test_g2_compressed_invalid_vectors() {
     {
-        let z = G2Affine::zero().into_compressed();
+        let z = G2Affine::identity().into_compressed();
 
         {
             let mut z = z;
@@ -509,7 +509,7 @@ fn test_g2_compressed_invalid_vectors() {
         }
     }
 
-    let o = G2Affine::one().into_compressed();
+    let o = G2Affine::generator().into_compressed();
 
     {
         let mut o = o;
diff --git a/pairing/src/tests/engine.rs b/pairing/src/tests/engine.rs
index e9f057042..f2277ba02 100644
--- a/pairing/src/tests/engine.rs
+++ b/pairing/src/tests/engine.rs
@@ -21,8 +21,8 @@ pub fn engine_tests<E: Engine>() {
     }
 
     for _ in 0..1000 {
-        let z1 = E::G1Affine::zero().prepare();
-        let z2 = E::G2Affine::zero().prepare();
+        let z1 = E::G1Affine::identity().prepare();
+        let z2 = E::G2Affine::identity().prepare();
 
         let a = E::G1::random(&mut rng).into_affine().prepare();
         let b = E::G2::random(&mut rng).into_affine().prepare();