diff --git a/lib/bbs/blind/core.js b/lib/bbs/blind/core.js
index 64c6a11..801f111 100644
--- a/lib/bbs/blind/core.js
+++ b/lib/bbs/blind/core.js
@@ -48,9 +48,9 @@ export function CoreBlindSign({
     commitment_with_proof, generators, api_id, ciphersuite
   });
   const {Q_1} = generators;
-  // Identity_G1 == ciphersuite.E1.ONE
+  // Identity_G1 == ciphersuite.Identity_E1
   const Q_2 = commitment_with_proof.length === 0 ?
-    ciphersuite.E1.ONE : generators[1];
+    ciphersuite.Identity_E1 : generators[1];
   const H = generators.slice(M + 1, M + L + 2);
 
   /* Algorithm:
@@ -100,7 +100,7 @@ export function CoreBlindSign({
   const {Fr} = ciphersuite;
   const A = B.multiply(Fr.inv(Fr.add(SK, e)));
   // if A == Identity_G1 throw invalid signature error
-  if(ciphersuite.E1.eql(A, ciphersuite.E1.ONE)) {
+  if(A.equals(ciphersuite.Identity_E1)) {
     throw new Error('Invalid signature.');
   }
   return signature_to_octets({signature: [A, e], ciphersuite});
diff --git a/lib/bbs/blind/util.js b/lib/bbs/blind/util.js
index e84a0f1..ba26ea1 100644
--- a/lib/bbs/blind/util.js
+++ b/lib/bbs/blind/util.js
@@ -156,7 +156,7 @@ export function octets_to_commitment_with_proof({
   const C_octets = commitment_with_proof_octets.subarray(
     0, octet_point_length);
   const C = ciphersuite.octets_to_point_E1(C_octets);
-  if(ciphersuite.E1.eql(C, ciphersuite.E1.ONE)) {
+  if(C.equals(ciphersuite.Identity_E1)) {
     throw new Error('Invalid point in commitment.');
   }
 
diff --git a/lib/bbs/core.js b/lib/bbs/core.js
index e194bfe..c12314f 100644
--- a/lib/bbs/core.js
+++ b/lib/bbs/core.js
@@ -217,7 +217,7 @@ export function CoreSign({
   const {Fr} = ciphersuite;
   const A = B.multiply(Fr.inv(Fr.add(SK, e)));
   // if A == Identity_G1 throw invalid signature error
-  if(ciphersuite.E1.eql(A, ciphersuite.E1.ONE)) {
+  if(A.equals(ciphersuite.Identity_E1)) {
     throw new Error('Invalid signature.');
   }
   return signature_to_octets({signature: [A, e], ciphersuite});
diff --git a/lib/bbs/pseudonym/interface.js b/lib/bbs/pseudonym/interface.js
index f422cb2..4e96452 100644
--- a/lib/bbs/pseudonym/interface.js
+++ b/lib/bbs/pseudonym/interface.js
@@ -29,9 +29,9 @@ export function CalculatePseudonym({verifier_id, pid, ciphersuite} = {}) {
 
   */
   const OP = ciphersuite.hash_to_curve_g1(verifier_id, api_id);
-  // Identity_G1 == ciphersuite.E1.ONE
-  const {BP1, P1, E1} = ciphersuite;
-  if(E1.eql(OP, E1.ONE) || E1.eql(OP, BP1) || E1.eql(OP, P1)) {
+  // Identity_G1 == ciphersuite.Identity_E1
+  const {BP1, Identity_E1, P1} = ciphersuite;
+  if(OP.equals(Identity_E1) || OP.equals(BP1) || OP.equals(OP, P1)) {
     throw new Error('Invalid verifier ID.');
   }
   const messages = [pid];
diff --git a/lib/bbs/util.js b/lib/bbs/util.js
index 4b35969..c539e5a 100644
--- a/lib/bbs/util.js
+++ b/lib/bbs/util.js
@@ -288,7 +288,7 @@ export function octets_to_proof({proof_octets, ciphersuite} = {}) {
   for(let i = 0; i <= 2; ++i) {
     A[i] = ciphersuite.octets_to_point_E1(
       proof_octets.subarray(index, index + octet_point_length));
-    if(ciphersuite.E1.eql(A, ciphersuite.E1.ONE)) {
+    if(A[i].equals(ciphersuite.Identity_E1)) {
       throw new Error('Invalid point in proof.');
     }
     index += octet_point_length;
@@ -339,7 +339,7 @@ export function octets_to_pubkey({PK, ciphersuite} = {}) {
   // conversion handles checking that point is on the curve
   const W = ciphersuite.octets_to_point_E2(PK);
   // if W == Identity_E2 throw invalid public key error
-  if(ciphersuite.E2.eql(W, ciphersuite.E2.ONE)) {
+  if(W.equals(ciphersuite.Identity_E2)) {
     throw new Error('Invalid public key.');
   }
   return W;
@@ -374,7 +374,7 @@ export function octets_to_signature({signature_octets, ciphersuite} = {}) {
   // conversion handles checking that point is on the curve
   const A = ciphersuite.octets_to_point_E1(A_octets);
   // if A == Identity_G1 throw invalid signature error
-  if(ciphersuite.E1.eql(A, ciphersuite.E1.ONE)) {
+  if(A.equals(ciphersuite.Identity_E1)) {
     throw new Error('Invalid signature.');
   }
   const e = os2ip(signature_octets.subarray(octet_point_length));