diff --git a/include/psa/crypto_values.h b/include/psa/crypto_values.h
index 524cde1a0..a17bfc2bf 100644
--- a/include/psa/crypto_values.h
+++ b/include/psa/crypto_values.h
@@ -868,7 +868,8 @@
 
 /* In the encoding of a MAC algorithm, the bit corresponding to
  * #PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG encodes the fact that the algorithm
- * is a wildcard algorithm, which allows any algorithm corresponding to the
+ * is a wildcard algorithm. A key with such wildcard algorithm as permitted
+ * algorithm policy can be used with any algorithm corresponding to the
  * same base class and having a (potentially truncated) MAC length greater or
  * equal than the one encoded in #PSA_ALG_MAC_TRUNCATION_MASK. */
 #define PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG   ((psa_algorithm_t)0x00008000)
@@ -906,8 +907,9 @@
  *                      MAC algorithm or if \p mac_length is too small or
  *                      too large for the specified MAC algorithm.
  */
-#define PSA_ALG_TRUNCATED_MAC(mac_alg, mac_length)                      \
-    (((mac_alg) & ~(PSA_ALG_MAC_TRUNCATION_MASK | PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG)) | \
+#define PSA_ALG_TRUNCATED_MAC(mac_alg, mac_length)              \
+    (((mac_alg) & ~(PSA_ALG_MAC_TRUNCATION_MASK |               \
+                    PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG)) |   \
      ((mac_length) << PSA_MAC_TRUNCATION_OFFSET & PSA_ALG_MAC_TRUNCATION_MASK))
 
 /** Macro to build the base MAC algorithm corresponding to a truncated
@@ -922,8 +924,9 @@
  * \return              Unspecified if \p alg is not a supported
  *                      MAC algorithm.
  */
-#define PSA_ALG_FULL_LENGTH_MAC(mac_alg)        \
-    ((mac_alg) & ~(PSA_ALG_MAC_TRUNCATION_MASK | PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG))
+#define PSA_ALG_FULL_LENGTH_MAC(mac_alg)                        \
+    ((mac_alg) & ~(PSA_ALG_MAC_TRUNCATION_MASK |                \
+                   PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG))
 
 /** Length to which a MAC algorithm is truncated.
  *
@@ -963,8 +966,9 @@
  *                        algorithm or if \p min_mac_length is less than 1 or
  *                        too large for the specified MAC algorithm.
  */
-#define PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(mac_alg, min_mac_length) \
-    ( PSA_ALG_TRUNCATED_MAC(mac_alg, min_mac_length) | PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG )
+#define PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(mac_alg, min_mac_length)   \
+    ( PSA_ALG_TRUNCATED_MAC(mac_alg, min_mac_length) |              \
+      PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG )
 
 #define PSA_ALG_CIPHER_MAC_BASE                 ((psa_algorithm_t)0x03c00000)
 /** The CBC-MAC construction over a block cipher
@@ -1128,7 +1132,8 @@
 
 /* In the encoding of an AEAD algorithm, the bit corresponding to
  * #PSA_ALG_AEAD_AT_LEAST_THIS_LENGTH_FLAG encodes the fact that the algorithm
- * is a wildcard algorithm, which allows any algorithm corresponding to the
+ * is a wildcard algorithm. A key with such wildcard algorithm as permitted
+ * algorithm policy can be used with any algorithm corresponding to the
  * same base class and having a tag length greater than or equal to the one
  * encoded in #PSA_ALG_AEAD_TAG_LENGTH_MASK. */
 #define PSA_ALG_AEAD_AT_LEAST_THIS_LENGTH_FLAG  ((psa_algorithm_t)0x00008000)
@@ -1152,7 +1157,8 @@
  *                      for the specified AEAD algorithm.
  */
 #define PSA_ALG_AEAD_WITH_SHORTENED_TAG(aead_alg, tag_length)           \
-    (((aead_alg) & ~(PSA_ALG_AEAD_TAG_LENGTH_MASK | PSA_ALG_AEAD_AT_LEAST_THIS_LENGTH_FLAG)) | \
+    (((aead_alg) & ~(PSA_ALG_AEAD_TAG_LENGTH_MASK |                     \
+                     PSA_ALG_AEAD_AT_LEAST_THIS_LENGTH_FLAG)) |         \
      ((tag_length) << PSA_AEAD_TAG_LENGTH_OFFSET &                      \
       PSA_ALG_AEAD_TAG_LENGTH_MASK))
 
@@ -1215,7 +1221,8 @@
  *                        or too large for the specified AEAD algorithm.
  */
 #define PSA_ALG_AEAD_WITH_AT_LEAST_THIS_LENGTH_TAG(aead_alg, min_tag_length) \
-    ( PSA_ALG_AEAD_WITH_SHORTENED_TAG(aead_alg, min_tag_length) | PSA_ALG_AEAD_AT_LEAST_THIS_LENGTH_FLAG )
+    ( PSA_ALG_AEAD_WITH_SHORTENED_TAG(aead_alg, min_tag_length) |            \
+      PSA_ALG_AEAD_AT_LEAST_THIS_LENGTH_FLAG )
 
 #define PSA_ALG_RSA_PKCS1V15_SIGN_BASE          ((psa_algorithm_t)0x06000200)
 /** RSA PKCS#1 v1.5 signature with hashing.
diff --git a/library/psa_crypto.c b/library/psa_crypto.c
index eff86bcf0..4f67ddf9c 100644
--- a/library/psa_crypto.c
+++ b/library/psa_crypto.c
@@ -890,9 +890,11 @@ static psa_status_t psa_get_and_lock_key_slot_with_policy(
     if( PSA_KEY_TYPE_IS_PUBLIC_KEY( slot->attr.type ) )
         usage &= ~PSA_KEY_USAGE_EXPORT;
 
-    status = PSA_ERROR_NOT_PERMITTED;
     if( ( slot->attr.policy.usage & usage ) != usage )
+    {
+        status = PSA_ERROR_NOT_PERMITTED;
         goto error;
+    }
 
     /* Enforce that the usage policy permits the requested algortihm. */
     if( alg != 0 )
@@ -2938,21 +2940,29 @@ static psa_status_t psa_mac_setup( psa_mac_operation_t *operation,
          * a corner case due to the default MAC length being unknown
          * at key loading time. */
         if( PSA_ALG_IS_MAC( slot->attr.policy.alg ) &&
-            ( PSA_ALG_FULL_LENGTH_MAC( slot->attr.policy.alg ) == full_length_alg ) &&
+            ( PSA_ALG_FULL_LENGTH_MAC( slot->attr.policy.alg ) ==
+                full_length_alg ) &&
             ( slot->attr.policy.alg & PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG ) )
         {
             /* validate policy length */
-            if( PSA_MAC_TRUNCATED_LENGTH( slot->attr.policy.alg ) > operation->mac_size )
+            if( PSA_MAC_TRUNCATED_LENGTH( slot->attr.policy.alg ) >
+                    operation->mac_size )
+            {
                 status = PSA_ERROR_NOT_PERMITTED;
+            }
         }
 
         if( PSA_ALG_IS_MAC( slot->attr.policy.alg2 ) &&
-            ( PSA_ALG_FULL_LENGTH_MAC( slot->attr.policy.alg2 ) == full_length_alg ) &&
+            ( PSA_ALG_FULL_LENGTH_MAC( slot->attr.policy.alg2 ) ==
+                full_length_alg ) &&
             ( slot->attr.policy.alg2 & PSA_ALG_MAC_AT_LEAST_THIS_LENGTH_FLAG ) )
         {
             /* validate policy length */
-            if( PSA_MAC_TRUNCATED_LENGTH( slot->attr.policy.alg2 ) > operation->mac_size )
+            if( PSA_MAC_TRUNCATED_LENGTH( slot->attr.policy.alg2 ) >
+                    operation->mac_size )
+            {
                 status = PSA_ERROR_NOT_PERMITTED;
+            }
         }
     }
     else if( truncated < 4 )
diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index 6e379a217..b542938ac 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -428,43 +428,43 @@ PSA key policy: CMAC, sign-verify, tag length < min-length policy
 depends_on:MBEDTLS_AES_C:MBEDTLS_CMAC_C
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_CMAC, 10):PSA_KEY_TYPE_AES:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_TRUNCATED_MAC(PSA_ALG_CMAC, 8):PSA_ERROR_NOT_PERMITTED
 
-PSA key policy: MAC, sign-verify, default tag length > min-length policy
+PSA key policy: HMAC, sign-verify, default tag length > min-length policy
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 31):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_HMAC(PSA_ALG_SHA_256):PSA_SUCCESS
 
-PSA key policy: MAC, sign-verify, default tag length = min-length policy
+PSA key policy: HMAC, sign-verify, default tag length = min-length policy
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 32):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_HMAC(PSA_ALG_SHA_256):PSA_SUCCESS
 
-PSA key policy: MAC, sign-verify, default tag length < min-length policy
+PSA key policy: HMAC, sign-verify, default tag length < min-length policy
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 33):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_HMAC(PSA_ALG_SHA_256):PSA_ERROR_NOT_PERMITTED
 
-PSA key policy: MAC, sign-verify, min-length policy, unmatched base alg
+PSA key policy: HMAC, sign-verify, min-length policy, unmatched base alg
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC:MBEDTLS_CMAC_C
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 20):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_TRUNCATED_MAC(PSA_ALG_CMAC, 20):PSA_ERROR_NOT_PERMITTED
 
-PSA key policy: MAC, sign-verify, min-length policy, unmatched base alg (different hash base)
+PSA key policy: HMAC, sign-verify, min-length policy, unmatched base alg (different hash base)
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_ALG_SHA_224:PSA_WANT_KEY_TYPE_HMAC
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 20):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_TRUNCATED_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_224), 20):PSA_ERROR_NOT_PERMITTED
 
-PSA key policy: MAC, sign-verify, min-length policy, unmatched base alg (different algorithm)
+PSA key policy: HMAC, sign-verify, min-length policy, unmatched base alg (different algorithm)
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC:MBEDTLS_CMAC_C
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 10):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_CMAC:PSA_ERROR_NOT_PERMITTED
 
-PSA key policy: MAC, sign-verify, min-length policy used as algorithm
+PSA key policy: HMAC, sign-verify, min-length policy used as algorithm
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 20):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_AT_LEAST_THIS_LENGTH_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 20):PSA_ERROR_INVALID_ARGUMENT
 
-PSA key policy: MAC, sign-verify, tag length > exact-length policy
+PSA key policy: HMAC, sign-verify, tag length > exact-length policy
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_TRUNCATED_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 10):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_TRUNCATED_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 20):PSA_ERROR_NOT_PERMITTED
 
-PSA key policy: MAC, sign-verify, tag length = exact-length policy
+PSA key policy: HMAC, sign-verify, tag length = exact-length policy
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_TRUNCATED_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 20):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_TRUNCATED_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 20):PSA_SUCCESS
 
-PSA key policy: MAC, sign-verify, tag length < exact-length policy
+PSA key policy: HMAC, sign-verify, tag length < exact-length policy
 depends_on:PSA_WANT_ALG_HMAC:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_HMAC
 mac_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_TRUNCATED_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 20):PSA_KEY_TYPE_HMAC:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_ALG_TRUNCATED_MAC(PSA_ALG_HMAC(PSA_ALG_SHA_256), 10):PSA_ERROR_NOT_PERMITTED