diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h
index 2172222..5a9df33 100644
--- a/src/field_10x26_impl.h
+++ b/src/field_10x26_impl.h
@@ -110,13 +110,13 @@ void static inline secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-// TODO: not constant time!
 int static inline secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
     secp256k1_fe_verify(a);
 #endif
-    return (a->n[0] == 0 && a->n[1] == 0 && a->n[2] == 0 && a->n[3] == 0 && a->n[4] == 0 && a->n[5] == 0 && a->n[6] == 0 && a->n[7] == 0 && a->n[8] == 0 && a->n[9] == 0);
+    const uint32_t *t = a->n;
+    return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
 }
 
 int static inline secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
@@ -137,7 +137,6 @@ void static inline secp256k1_fe_clear(secp256k1_fe_t *a) {
     }
 }
 
-// TODO: not constant time!
 int static inline secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -145,8 +144,9 @@ int static inline secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe
     secp256k1_fe_verify(a);
     secp256k1_fe_verify(b);
 #endif
-    return (a->n[0] == b->n[0] && a->n[1] == b->n[1] && a->n[2] == b->n[2] && a->n[3] == b->n[3] && a->n[4] == b->n[4] &&
-            a->n[5] == b->n[5] && a->n[6] == b->n[6] && a->n[7] == b->n[7] && a->n[8] == b->n[8] && a->n[9] == b->n[9]);
+    const uint32_t *t = a->n, *u = b->n;
+    return ((t[0]^u[0]) | (t[1]^u[1]) | (t[2]^u[2]) | (t[3]^u[3]) | (t[4]^u[4])
+          | (t[5]^u[5]) | (t[6]^u[6]) | (t[7]^u[7]) | (t[8]^u[8]) | (t[9]^u[9])) == 0;
 }
 
 void static secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
@@ -166,7 +166,7 @@ void static secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
 #endif
 }
 
-/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+/** Convert a field element to a 32-bote big endian value. Requires the input to be normalized */
 void static secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h
index dce16d4..5afabae 100644
--- a/src/field_5x52_impl.h
+++ b/src/field_5x52_impl.h
@@ -109,13 +109,13 @@ void static inline secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-// TODO: not constant time!
 int static inline secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
     secp256k1_fe_verify(a);
 #endif
-    return (a->n[0] == 0 && a->n[1] == 0 && a->n[2] == 0 && a->n[3] == 0 && a->n[4] == 0);
+    const uint64_t *t = a->n;
+    return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
 }
 
 int static inline secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
@@ -136,7 +136,6 @@ void static inline secp256k1_fe_clear(secp256k1_fe_t *a) {
     }
 }
 
-// TODO: not constant time!
 int static inline secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -144,7 +143,8 @@ int static inline secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe
     secp256k1_fe_verify(a);
     secp256k1_fe_verify(b);
 #endif
-    return (a->n[0] == b->n[0] && a->n[1] == b->n[1] && a->n[2] == b->n[2] && a->n[3] == b->n[3] && a->n[4] == b->n[4]);
+    const uint64_t *t = a->n, *u = b->n;
+    return ((t[0]^u[0]) | (t[1]^u[1]) | (t[2]^u[2]) | (t[3]^u[3]) | (t[4]^u[4])) == 0;
 }
 
 void static secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {