diff --git a/src/scalar.h b/src/scalar.h
index e5a10ca4..70f49b1c 100644
--- a/src/scalar.h
+++ b/src/scalar.h
@@ -22,10 +22,10 @@
 /** Clear a scalar to prevent the leak of sensitive data. */
 static void secp256k1_scalar_clear(secp256k1_scalar *r);
 
-/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
+/** Access bits (1 < count <= 32) from a scalar. All requested bits must belong to the same 32-bit limb. */
 static uint32_t secp256k1_scalar_get_bits_limb32(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
 
-/** Access bits from a scalar. Not constant time in offset and count. */
+/** Access bits (1 < count <= 32) from a scalar. offset + count must be < 256. Not constant time in offset and count. */
 static uint32_t secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
 
 /** Set a scalar from a big endian byte array. The scalar will be reduced modulo group order `n`.
diff --git a/src/scalar_4x64_impl.h b/src/scalar_4x64_impl.h
index 9fa2ca28..4aaec85b 100644
--- a/src/scalar_4x64_impl.h
+++ b/src/scalar_4x64_impl.h
@@ -47,21 +47,22 @@ SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsig
 
 SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_limb32(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     SECP256K1_SCALAR_VERIFY(a);
+    VERIFY_CHECK(count > 0 && count <= 32);
     VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
 
-    return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
+    return (a->d[offset >> 6] >> (offset & 0x3F)) & (0xFFFFFFFF >> (32 - count));
 }
 
 SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     SECP256K1_SCALAR_VERIFY(a);
-    VERIFY_CHECK(count < 32);
+    VERIFY_CHECK(count > 0 && count <= 32);
     VERIFY_CHECK(offset + count <= 256);
 
     if ((offset + count - 1) >> 6 == offset >> 6) {
         return secp256k1_scalar_get_bits_limb32(a, offset, count);
     } else {
         VERIFY_CHECK((offset >> 6) + 1 < 4);
-        return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1);
+        return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & (0xFFFFFFFF >> (32 - count));
     }
 }
 
diff --git a/src/scalar_8x32_impl.h b/src/scalar_8x32_impl.h
index d49c464b..c7d87b17 100644
--- a/src/scalar_8x32_impl.h
+++ b/src/scalar_8x32_impl.h
@@ -64,21 +64,22 @@ SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsig
 
 SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_limb32(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     SECP256K1_SCALAR_VERIFY(a);
+    VERIFY_CHECK(count > 0 && count <= 32);
     VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
 
-    return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
+    return (a->d[offset >> 5] >> (offset & 0x1F)) & (0xFFFFFFFF >> (32 - count));
 }
 
 SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     SECP256K1_SCALAR_VERIFY(a);
-    VERIFY_CHECK(count < 32);
+    VERIFY_CHECK(count > 0 && count <= 32);
     VERIFY_CHECK(offset + count <= 256);
 
     if ((offset + count - 1) >> 5 == offset >> 5) {
         return secp256k1_scalar_get_bits_limb32(a, offset, count);
     } else {
         VERIFY_CHECK((offset >> 5) + 1 < 8);
-        return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1);
+        return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & (0xFFFFFFFF >> (32 - count));
     }
 }
 
diff --git a/src/scalar_low_impl.h b/src/scalar_low_impl.h
index 2c176e83..45d2f3e4 100644
--- a/src/scalar_low_impl.h
+++ b/src/scalar_low_impl.h
@@ -30,10 +30,12 @@ SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsig
 SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_limb32(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     SECP256K1_SCALAR_VERIFY(a);
 
-    if (offset < 32)
-        return ((*a >> offset) & ((((uint32_t)1) << count) - 1));
-    else
+    VERIFY_CHECK(count > 0 && count <= 32);
+    if (offset < 32) {
+        return (*a >> offset) & (0xFFFFFFFF >> (32 - count));
+    } else {
         return 0;
+    }
 }
 
 SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {