diff --git a/tests/scripts/analyze_outcomes.py b/tests/scripts/analyze_outcomes.py
index 11e4836..20e2ab7 100755
--- a/tests/scripts/analyze_outcomes.py
+++ b/tests/scripts/analyze_outcomes.py
@@ -570,6 +570,11 @@
                     re.compile(r'mbedtls_ct_zeroize_if .*'),
                     re.compile(r'mbedtls_ct_memmove_left .*')
                 ],
+                'test_suite_psa_crypto': [
+                    # We don't support generate_key_ext entry points
+                    # in drivers yet.
+                    re.compile(r'PSA generate key ext: RSA, e=.*'),
+                ],
             }
         }
     },
diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index 1a0f08b..e29e466 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -7482,11 +7482,11 @@
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:PSA_ALG_RSA_PKCS1V15_CRYPT:0:"":PSA_SUCCESS
 
 PSA generate key ext: RSA, e=3
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:PSA_ALG_RSA_PKCS1V15_CRYPT:0:"03":PSA_SUCCESS
 
 PSA generate key ext: RSA, e=3 with leading zeros
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:PSA_ALG_RSA_PKCS1V15_CRYPT:0:"000003":PSA_SUCCESS
 
 # TODO: currently errors with NOT_SUPPORTED because e is converted to an int
@@ -7494,41 +7494,50 @@
 # for leading zeros. This is a very minor bug. Re-enable this test when this
 # bug is fixed.
 #PSA generate key ext: RSA, e=3 with many leading zeros
-#depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
+#depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
 #generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:PSA_ALG_RSA_PKCS1V15_CRYPT:0:"0000000000000000000000000000000003":PSA_SUCCESS
 
 PSA generate key ext: RSA, e=513
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:PSA_ALG_RSA_PKCS1V15_CRYPT:0:"0201":PSA_SUCCESS
 
 PSA generate key ext: RSA, e=65537
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:PSA_ALG_RSA_PKCS1V15_CRYPT:0:"010001":PSA_SUCCESS
 
 PSA generate key ext: RSA, e=2^31-1
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT:INT_MAX>=0x7fffffff
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT:INT_MAX>=0x7fffffff
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:PSA_ALG_RSA_PKCS1V15_CRYPT:0:"7fffffff":PSA_SUCCESS
 
 PSA generate key ext: RSA, e=2^31+3 (too large for built-in RSA)
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:!MBEDTLS_PSA_ACCEL_KEY_TYPE_RSA_KEY_PAIR_GENERATE:INT_MAX<=0x7fffffff
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE:!MBEDTLS_PSA_ACCEL_KEY_TYPE_RSA_KEY_PAIR_GENERATE:INT_MAX<=0x7fffffff
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:0:0:"80000003":PSA_ERROR_NOT_SUPPORTED
 
 PSA generate key ext: RSA, e=2^64+3 (too large for built-in RSA)
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:!MBEDTLS_PSA_ACCEL_KEY_TYPE_RSA_KEY_PAIR_GENERATE:INT_MAX<=0xffffffffffffffff
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE:!MBEDTLS_PSA_ACCEL_KEY_TYPE_RSA_KEY_PAIR_GENERATE:INT_MAX<=0xffffffffffffffff
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:0:0:"010000000000000003":PSA_ERROR_NOT_SUPPORTED
 
 PSA generate key ext: RSA, e=1
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:0:0:"01":PSA_ERROR_INVALID_ARGUMENT
 
 PSA generate key ext: RSA, e=0
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:0:0:"00":PSA_ERROR_INVALID_ARGUMENT
 
 PSA generate key ext: RSA, e=2
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE
 generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:0:0:"02":PSA_ERROR_INVALID_ARGUMENT
 
+# Check that with a driver, we reject a custom e as unsupported,
+# as opposed to silently using the default e.
+# When we add proper driver support, remove this test case and remove
+# the dependency on MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE from
+# the positive/invalid_argument test cases.
+PSA generate key ext: RSA, e=3 with driver and no fallback (not yet supported)
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:!MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE
+generate_key_ext:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:0:0:"03":PSA_ERROR_NOT_SUPPORTED
+
 PSA generate key ext: ECC, flags=0
 depends_on:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_GENERATE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_ECDH
 generate_key_ext:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):256:PSA_KEY_USAGE_DERIVE:PSA_ALG_ECDH:0:"":PSA_SUCCESS