diff --git a/src/field.h b/src/field.h
index ee222ee5d7167..cf3bf10bb9e32 100644
--- a/src/field.h
+++ b/src/field.h
@@ -43,13 +43,12 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
 /** Normalize a field element, without constant-time guarantee. */
 static void secp256k1_fe_normalize_var(secp256k1_fe *r);
 
-/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
- *  implementation may optionally normalize the input, but this should not be relied upon. */
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r);
+/** Verify whether a field element represents zero i.e. would normalize to a zero value. */
+static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r);
 
-/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
- *  implementation may optionally normalize the input, but this should not be relied upon. */
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
+/** Verify whether a field element represents zero i.e. would normalize to a zero value,
+ *  without constant-time guarantee. */
+static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r);
 
 /** Set a field element equal to a small integer. Resulting field element is normalized. */
 static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h
index 62bffdc21bd44..17de9a68d9e4e 100644
--- a/src/field_10x26_impl.h
+++ b/src/field_10x26_impl.h
@@ -181,7 +181,7 @@ static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
 #endif
 }
 
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
+static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -210,7 +210,7 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
     return (z0 == 0) | (z1 == 0x3FFFFFFUL);
 }
 
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
+static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
     uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
     uint32_t z0, z1;
     uint32_t x;
diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h
index 3465ea3247b42..dc6edcca97b20 100644
--- a/src/field_5x52_impl.h
+++ b/src/field_5x52_impl.h
@@ -161,7 +161,7 @@ static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
 #endif
 }
 
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
+static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
@@ -184,7 +184,7 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 }
 
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
+static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
     uint64_t t0, t1, t2, t3, t4;
     uint64_t z0, z1;
     uint64_t x;