diff --git a/library/psa_crypto.c b/library/psa_crypto.c
index c90119f..d61e118 100644
--- a/library/psa_crypto.c
+++ b/library/psa_crypto.c
@@ -1378,9 +1378,9 @@
     defined(MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_PUBLIC_KEY)
         case PSA_KEY_TYPE_RSA_KEY_PAIR:
         case PSA_KEY_TYPE_RSA_PUBLIC_KEY:
-            /* TODO: reporting the public exponent for opaque keys
-             * is not yet implemented.
-             * https://github.com/ARMmbed/mbed-crypto/issues/216
+            /* TODO: This is a temporary situation where domain parameters are deprecated,
+             * but we need it for namely generating an RSA key with a non-default exponent.
+             * This would be improved after https://github.com/Mbed-TLS/mbedtls/issues/6494.
              */
             if (!psa_key_lifetime_is_external(slot->attr.lifetime)) {
                 mbedtls_rsa_context *rsa = NULL;
@@ -1400,6 +1400,12 @@
                 mbedtls_free(rsa);
             }
             break;
+#else
+        case PSA_KEY_TYPE_RSA_KEY_PAIR:
+        case PSA_KEY_TYPE_RSA_PUBLIC_KEY:
+            attributes->domain_parameters = NULL;
+            attributes->domain_parameters_size = SIZE_MAX;
+            break;
 #endif /* (defined(MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_IMPORT) && \
         * defined(MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_EXPORT)) ||
         * defined(MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_PUBLIC_KEY) */
diff --git a/library/psa_crypto_client.c b/library/psa_crypto_client.c
index 564463f..472d3d3 100644
--- a/library/psa_crypto_client.c
+++ b/library/psa_crypto_client.c
@@ -53,6 +53,11 @@
     const psa_key_attributes_t *attributes,
     uint8_t *data, size_t data_size, size_t *data_length)
 {
+    if (attributes->domain_parameters == NULL &&
+        attributes->domain_parameters_size == SIZE_MAX) {
+        return PSA_ERROR_NOT_SUPPORTED;
+    }
+
     if (attributes->domain_parameters_size > data_size) {
         return PSA_ERROR_BUFFER_TOO_SMALL;
     }
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index b8acfb5..10a76ec 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -3368,77 +3368,75 @@
     build_and_test_psa_want_key_pair_partial "ECC" "GENERATE"
 }
 
-component_test_psa_crypto_config_accel_rsa_signature () {
-    msg "test: MBEDTLS_PSA_CRYPTO_CONFIG with accelerated RSA signature"
+config_psa_crypto_accel_rsa () {
+    driver_only=$1
 
-    loc_accel_list="ALG_RSA_PKCS1V15_SIGN ALG_RSA_PSS KEY_TYPE_RSA_KEY_PAIR KEY_TYPE_RSA_PUBLIC_KEY"
+    # Start from crypto_full config (no X.509, no TLS)
+    helper_libtestdriver1_adjust_config "crypto_full"
+
+    if [ "$driver_only" -eq 1 ]; then
+        # Remove RSA support and its dependencies
+        scripts/config.py unset MBEDTLS_RSA_C
+        scripts/config.py unset MBEDTLS_PKCS1_V15
+        scripts/config.py unset MBEDTLS_PKCS1_V21
+
+        # We need PEM parsing in the test library as well to support the import
+        # of PEM encoded RSA keys.
+        scripts/config.py -f "$CONFIG_TEST_DRIVER_H" set MBEDTLS_PEM_PARSE_C
+        scripts/config.py -f "$CONFIG_TEST_DRIVER_H" set MBEDTLS_BASE64_C
+    fi
+}
+
+component_test_psa_crypto_config_accel_rsa_crypto () {
+    msg "build: crypto_full with accelerated RSA"
+
+    loc_accel_list="ALG_RSA_OAEP ALG_RSA_PSS \
+                    ALG_RSA_PKCS1V15_CRYPT ALG_RSA_PKCS1V15_SIGN \
+                    KEY_TYPE_RSA_PUBLIC_KEY \
+                    KEY_TYPE_RSA_KEY_PAIR_BASIC \
+                    KEY_TYPE_RSA_KEY_PAIR_GENERATE \
+                    KEY_TYPE_RSA_KEY_PAIR_IMPORT \
+                    KEY_TYPE_RSA_KEY_PAIR_EXPORT"
 
     # Configure
     # ---------
 
-    # Start from default config (no TLS 1.3, no USE_PSA)
-    helper_libtestdriver1_adjust_config "default"
-
-    # It seems it is not possible to remove only the support for RSA signature
-    # in the library. Thus we have to remove all RSA support (signature and
-    # encryption/decryption). AS there is no driver support for asymmetric
-    # encryption/decryption so far remove RSA encryption/decryption from the
-    # application algorithm list.
-    scripts/config.py -f "$CRYPTO_CONFIG_H" unset PSA_WANT_ALG_RSA_OAEP
-    scripts/config.py -f "$CRYPTO_CONFIG_H" unset PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
-
-    # Remove RSA support and its dependencies
-    scripts/config.py unset MBEDTLS_RSA_C
-    scripts/config.py unset MBEDTLS_PKCS1_V15
-    scripts/config.py unset MBEDTLS_PKCS1_V21
-    scripts/config.py unset MBEDTLS_X509_RSASSA_PSS_SUPPORT
-    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_DHE_RSA_ENABLED
-    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_ECDH_RSA_ENABLED
-    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_ECDHE_RSA_ENABLED
-    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_RSA_PSK_ENABLED
-    scripts/config.py unset MBEDTLS_KEY_EXCHANGE_RSA_ENABLED
-
-    # Make sure both the library and the test library support the SHA hash
-    # algorithms and only those ones (SHA256 is included by default). That way:
-    # - the test library can compute the RSA signatures even in the case of a
-    #   composite RSA signature algorithm based on a SHA hash (no other hash
-    #   used in the unit tests).
-    # - the dependency of RSA signature tests on PSA_WANT_ALG_SHA_xyz is
-    #   fulfilled as the hash SHA algorithm is supported by the library, and
-    #   thus the tests are run, not skipped.
-    # - when testing a signature key with an algorithm wildcard built from
-    #   PSA_ALG_ANY_HASH as algorithm to test with the key, the chosen hash
-    #   algorithm based on the hashes supported by the library is also
-    #   supported by the test library.
-    # Disable unwanted hashes here, we'll enable hashes we want in loc_extra_list.
-    scripts/config.py -f "$CRYPTO_CONFIG_H" unset PSA_WANT_ALG_MD5
-    scripts/config.py -f "$CRYPTO_CONFIG_H" unset PSA_WANT_ALG_RIPEMD160_C
-    scripts/config.py unset MBEDTLS_MD5_C
-    scripts/config.py unset MBEDTLS_RIPEMD160_C
-
-    # We need PEM parsing in the test library as well to support the import
-    # of PEM encoded RSA keys.
-    scripts/config.py -f "$CONFIG_TEST_DRIVER_H" set MBEDTLS_PEM_PARSE_C
-    scripts/config.py -f "$CONFIG_TEST_DRIVER_H" set MBEDTLS_BASE64_C
+    config_psa_crypto_accel_rsa 1
 
     # Build
     # -----
 
-    # These hashes are needed for some RSA-PSS signature tests.
+    # These hashes are needed for unit tests.
     loc_extra_list="ALG_SHA_1 ALG_SHA_224 ALG_SHA_256 ALG_SHA_384 ALG_SHA_512 \
-                    ALG_SHA3_224 ALG_SHA3_256 ALG_SHA3_384 ALG_SHA3_512"
+                    ALG_SHA3_224 ALG_SHA3_256 ALG_SHA3_384 ALG_SHA3_512 ALG_MD5"
     helper_libtestdriver1_make_drivers "$loc_accel_list" "$loc_extra_list"
 
     helper_libtestdriver1_make_main "$loc_accel_list"
 
     # Make sure this was not re-enabled by accident (additive config)
-    not grep mbedtls_rsa_rsassa_pkcs1_v15_sign library/rsa.o
-    not grep mbedtls_rsa_rsassa_pss_sign_ext library/rsa.o
+    not grep mbedtls_rsa library/rsa.o
 
     # Run the tests
     # -------------
 
-    msg "test: MBEDTLS_PSA_CRYPTO_CONFIG with accelerated RSA signature"
+    msg "test: crypto_full with accelerated RSA"
+    make test
+}
+
+component_test_psa_crypto_config_reference_rsa_crypto () {
+    msg "build: crypto_full with non-accelerated RSA"
+
+    # Configure
+    # ---------
+    config_psa_crypto_accel_rsa 0
+
+    # Build
+    # -----
+    make
+
+    # Run the tests
+    # -------------
+    msg "test: crypto_full with non-accelerated RSA"
     make test
 }
 
diff --git a/tests/scripts/analyze_outcomes.py b/tests/scripts/analyze_outcomes.py
index ca349d3..d3ea8c0 100755
--- a/tests/scripts/analyze_outcomes.py
+++ b/tests/scripts/analyze_outcomes.py
@@ -501,6 +501,38 @@
                 ],
             }
         }
+    },
+    'analyze_driver_vs_reference_rsa': {
+        'test_function': do_analyze_driver_vs_reference,
+        'args': {
+            'component_ref': 'test_psa_crypto_config_reference_rsa_crypto',
+            'component_driver': 'test_psa_crypto_config_accel_rsa_crypto',
+            'ignored_suites': [
+                # Modules replaced by drivers.
+                'rsa', 'pkcs1_v15', 'pkcs1_v21',
+                # We temporarily don't care about PK stuff.
+                'pk', 'pkwrite', 'pkparse'
+            ],
+            'ignored_tests': {
+                'test_suite_platform': [
+                    # Incompatible with sanitizers (e.g. ASan). If the driver
+                    # component uses a sanitizer but the reference component
+                    # doesn't, we have a PASS vs SKIP mismatch.
+                    'Check mbedtls_calloc overallocation',
+                ],
+                # Following tests depend on RSA_C but are not about
+                # them really, just need to know some error code is there.
+                'test_suite_error': [
+                    'Low and high error',
+                    'Single high error'
+                ],
+                # Constant time operations only used for PKCS1_V15
+                'test_suite_constant_time': [
+                    re.compile(r'mbedtls_ct_zeroize_if .*'),
+                    re.compile(r'mbedtls_ct_memmove_left .*')
+                ],
+            }
+        }
     }
 }
 
diff --git a/tests/src/drivers/test_driver_asymmetric_encryption.c b/tests/src/drivers/test_driver_asymmetric_encryption.c
index c906a66..ff46387 100644
--- a/tests/src/drivers/test_driver_asymmetric_encryption.c
+++ b/tests/src/drivers/test_driver_asymmetric_encryption.c
@@ -46,8 +46,7 @@
         return mbedtls_test_driver_asymmetric_encryption_hooks.forced_status;
     }
 
-#if defined(MBEDTLS_TEST_LIBTESTDRIVER1) && \
-    defined(LIBTESTDRIVER1_MBEDTLS_PSA_BUILTIN_CIPHER)
+#if defined(MBEDTLS_TEST_LIBTESTDRIVER1)
     return libtestdriver1_mbedtls_psa_asymmetric_encrypt(
         (const libtestdriver1_psa_key_attributes_t *) attributes,
         key_buffer, key_buffer_size,
@@ -88,8 +87,7 @@
         return mbedtls_test_driver_asymmetric_encryption_hooks.forced_status;
     }
 
-#if defined(MBEDTLS_TEST_LIBTESTDRIVER1) && \
-    defined(LIBTESTDRIVER1_MBEDTLS_PSA_BUILTIN_CIPHER)
+#if defined(MBEDTLS_TEST_LIBTESTDRIVER1)
     return libtestdriver1_mbedtls_psa_asymmetric_decrypt(
         (const libtestdriver1_psa_key_attributes_t *) attributes,
         key_buffer, key_buffer_size,
diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index e239a44..1bd8b65 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -7342,7 +7342,7 @@
 generate_key_rsa:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:"01":PSA_ERROR_INVALID_ARGUMENT
 
 PSA generate key: RSA, e=2
-generate_key_rsa:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:"01":PSA_ERROR_INVALID_ARGUMENT
+generate_key_rsa:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:"02":PSA_ERROR_INVALID_ARGUMENT
 
 PSA generate key: FFDH, 2048 bits, good
 depends_on:PSA_WANT_ALG_FFDH:PSA_WANT_KEY_TYPE_DH_KEY_PAIR_GENERATE
diff --git a/tests/suites/test_suite_psa_crypto.function b/tests/suites/test_suite_psa_crypto.function
index a510f8e..4c08a90 100644
--- a/tests/suites/test_suite_psa_crypto.function
+++ b/tests/suites/test_suite_psa_crypto.function
@@ -9688,14 +9688,24 @@
     PSA_ASSERT(psa_get_key_attributes(key, &attributes));
     TEST_EQUAL(psa_get_key_type(&attributes), type);
     TEST_EQUAL(psa_get_key_bits(&attributes), bits);
-    PSA_ASSERT(psa_get_key_domain_parameters(&attributes,
-                                             e_read_buffer, e_read_size,
-                                             &e_read_length));
+    psa_status_t status = psa_get_key_domain_parameters(&attributes,
+                                                        e_read_buffer, e_read_size,
+                                                        &e_read_length);
+
+
+#if (defined(MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_IMPORT) && \
+    defined(MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_EXPORT)) || \
+    defined(MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_PUBLIC_KEY)
     if (is_default_public_exponent) {
         TEST_EQUAL(e_read_length, 0);
     } else {
+        TEST_EQUAL(status, PSA_SUCCESS);
         TEST_MEMORY_COMPARE(e_read_buffer, e_read_length, e_arg->x, e_arg->len);
     }
+#else
+    (void) is_default_public_exponent;
+    TEST_EQUAL(status, PSA_ERROR_NOT_SUPPORTED);
+#endif
 
     /* Do something with the key according to its type and permitted usage. */
     if (!mbedtls_test_psa_exercise_key(key, usage, alg)) {