diff --git a/tests/include/test/drivers/key_management.h b/tests/include/test/drivers/key_management.h
index 7b5c4c7..1d9bc43 100644
--- a/tests/include/test/drivers/key_management.h
+++ b/tests/include/test/drivers/key_management.h
@@ -26,8 +26,10 @@
     /* Count the amount of times one of the key management driver functions
      * is called. */
     unsigned long hits;
-    /* Subset of hits which only counts key operations with EC key */
+    /* Subset of hits which only counts public key export operations */
     unsigned long hits_export_public_key;
+    /* Subset of hits which only counts key generation operations */
+    unsigned long hits_generate_key;
     /* Location of the last key management driver called to import a key. */
     psa_key_location_t location;
 } mbedtls_test_driver_key_management_hooks_t;
@@ -36,7 +38,7 @@
  * sense that no PSA specification will assign a meaning to this location
  * (stated first in version 1.0.1 of the specification) and that it is not
  * used as a location of an opaque test drivers. */
-#define MBEDTLS_TEST_DRIVER_KEY_MANAGEMENT_INIT { NULL, 0, PSA_SUCCESS, 0, 0, 0x800000 }
+#define MBEDTLS_TEST_DRIVER_KEY_MANAGEMENT_INIT { NULL, 0, PSA_SUCCESS, 0, 0, 0, 0x800000 }
 static inline mbedtls_test_driver_key_management_hooks_t
 mbedtls_test_driver_key_management_hooks_init(void)
 {
diff --git a/tests/src/drivers/test_driver_key_management.c b/tests/src/drivers/test_driver_key_management.c
index 866b31e..2a87899 100644
--- a/tests/src/drivers/test_driver_key_management.c
+++ b/tests/src/drivers/test_driver_key_management.c
@@ -193,6 +193,7 @@
     uint8_t *key, size_t key_size, size_t *key_length)
 {
     ++mbedtls_test_driver_key_management_hooks.hits;
+    ++mbedtls_test_driver_key_management_hooks.hits_generate_key;
 
     if (mbedtls_test_driver_key_management_hooks.forced_status != PSA_SUCCESS) {
         return mbedtls_test_driver_key_management_hooks.forced_status;
diff --git a/tests/suites/test_suite_psa_crypto_driver_wrappers.data b/tests/suites/test_suite_psa_crypto_driver_wrappers.data
index 37c15ee..54e0892 100644
--- a/tests/suites/test_suite_psa_crypto_driver_wrappers.data
+++ b/tests/suites/test_suite_psa_crypto_driver_wrappers.data
@@ -238,10 +238,11 @@
 generate_ec_key:PSA_SUCCESS:"ab45435712649cb30bbddac49197eebf2740ffc7f874d9244c3460f54f322d3a":PSA_SUCCESS
 
 generate_ec_key through transparent driver: in-driver
+depends_on:MBEDTLS_PSA_ACCEL_KEY_TYPE_ECC_KEY_PAIR_GENERATE
 generate_ec_key:PSA_SUCCESS:"":PSA_SUCCESS
 
 generate_ec_key through transparent driver: fallback
-depends_on:MBEDTLS_PSA_BUILTIN_KEY_TYPE_ECC_KEY_PAIR_GENERATE
+depends_on:MBEDTLS_PSA_BUILTIN_KEY_TYPE_ECC_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_ECC_SECP_R1_256
 generate_ec_key:PSA_ERROR_NOT_SUPPORTED:"":PSA_SUCCESS
 
 generate_ec_key through transparent driver: fallback not available
diff --git a/tests/suites/test_suite_psa_crypto_driver_wrappers.function b/tests/suites/test_suite_psa_crypto_driver_wrappers.function
index a788827..e7925dd 100644
--- a/tests/suites/test_suite_psa_crypto_driver_wrappers.function
+++ b/tests/suites/test_suite_psa_crypto_driver_wrappers.function
@@ -748,7 +748,7 @@
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:PSA_WANT_ALG_ECDSA:PSA_WANT_ECC_SECP_R1_256:MBEDTLS_PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_GENERATE */
+/* BEGIN_CASE depends_on:PSA_WANT_ALG_ECDSA:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_GENERATE */
 void generate_ec_key(int force_status_arg,
                      data_t *fake_output,
                      int expected_status_arg)
@@ -782,13 +782,14 @@
                 fake_output->len;
     }
 
-    mbedtls_test_driver_key_management_hooks.hits = 0;
-    mbedtls_test_driver_key_management_hooks.forced_status = force_status;
-
     PSA_ASSERT(psa_crypto_init());
 
+    mbedtls_test_driver_key_management_hooks.hits = 0;
+    mbedtls_test_driver_key_management_hooks.hits_generate_key = 0;
+    mbedtls_test_driver_key_management_hooks.forced_status = force_status;
+
     actual_status = psa_generate_key(&attributes, &key);
-    TEST_EQUAL(mbedtls_test_driver_key_management_hooks.hits, 1);
+    TEST_EQUAL(mbedtls_test_driver_key_management_hooks.hits_generate_key, 1);
     TEST_EQUAL(actual_status, expected_status);
 
     if (actual_status == PSA_SUCCESS) {
diff --git a/tests/suites/test_suite_psa_crypto_pake.data b/tests/suites/test_suite_psa_crypto_pake.data
index baebded..49e97a9 100644
--- a/tests/suites/test_suite_psa_crypto_pake.data
+++ b/tests/suites/test_suite_psa_crypto_pake.data
@@ -211,19 +211,19 @@
 ecjpake_rounds_inject:PSA_ALG_JPAKE:PSA_PAKE_PRIMITIVE(PSA_PAKE_PRIMITIVE_TYPE_ECC, PSA_ECC_FAMILY_SECP_R1, 256):PSA_ALG_SHA_256:0:"abcdef":ERR_INJECT_ROUND2_SERVER_ZK_PROOF:PSA_ERROR_DATA_INVALID:1
 
 PSA PAKE: inject ERR_INJECT_EXTRA_OUTPUT
-depends_on:MBEDTLS_PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
+depends_on:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
 ecjpake_rounds_inject:PSA_ALG_JPAKE:PSA_PAKE_PRIMITIVE(PSA_PAKE_PRIMITIVE_TYPE_ECC, PSA_ECC_FAMILY_SECP_R1, 256):PSA_ALG_SHA_256:0:"abcdef":ERR_INJECT_EXTRA_OUTPUT:PSA_ERROR_BAD_STATE:0
 
 PSA PAKE: inject ERR_INJECT_EXTRA_INPUT
-depends_on:MBEDTLS_PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
+depends_on:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
 ecjpake_rounds_inject:PSA_ALG_JPAKE:PSA_PAKE_PRIMITIVE(PSA_PAKE_PRIMITIVE_TYPE_ECC, PSA_ECC_FAMILY_SECP_R1, 256):PSA_ALG_SHA_256:1:"abcdef":ERR_INJECT_EXTRA_INPUT:PSA_ERROR_BAD_STATE:0
 
 PSA PAKE: inject ERR_INJECT_EXTRA_OUTPUT_AT_END
-depends_on:MBEDTLS_PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
+depends_on:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
 ecjpake_rounds_inject:PSA_ALG_JPAKE:PSA_PAKE_PRIMITIVE(PSA_PAKE_PRIMITIVE_TYPE_ECC, PSA_ECC_FAMILY_SECP_R1, 256):PSA_ALG_SHA_256:1:"abcdef":ERR_INJECT_EXTRA_OUTPUT_AT_END:PSA_ERROR_BAD_STATE:1
 
 PSA PAKE: inject ERR_INJECT_EXTRA_INPUT_AT_END
-depends_on:MBEDTLS_PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
+depends_on:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_DERIVE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
 ecjpake_rounds_inject:PSA_ALG_JPAKE:PSA_PAKE_PRIMITIVE(PSA_PAKE_PRIMITIVE_TYPE_ECC, PSA_ECC_FAMILY_SECP_R1, 256):PSA_ALG_SHA_256:0:"abcdef":ERR_INJECT_EXTRA_INPUT_AT_END:PSA_ERROR_BAD_STATE:1
 
 PSA PAKE: ecjpake size macros
diff --git a/tests/suites/test_suite_psa_crypto_se_driver_hal.function b/tests/suites/test_suite_psa_crypto_se_driver_hal.function
index e3681ba..37a72d9 100644
--- a/tests/suites/test_suite_psa_crypto_se_driver_hal.function
+++ b/tests/suites/test_suite_psa_crypto_se_driver_hal.function
@@ -13,6 +13,19 @@
 #include "psa/internal_trusted_storage.h"
 #endif
 
+/* Same in library/psa_crypto.c */
+#if defined(MBEDTLS_PSA_BUILTIN_ALG_HKDF) ||          \
+    defined(MBEDTLS_PSA_BUILTIN_ALG_HKDF_EXTRACT) ||  \
+    defined(MBEDTLS_PSA_BUILTIN_ALG_HKDF_EXPAND)
+#define BUILTIN_ALG_ANY_HKDF 1
+#endif
+#if defined(BUILTIN_ALG_ANY_HKDF) || \
+    defined(MBEDTLS_PSA_BUILTIN_ALG_TLS12_PRF) || \
+    defined(MBEDTLS_PSA_BUILTIN_ALG_TLS12_PSK_TO_MS) || \
+    defined(MBEDTLS_PSA_BUILTIN_ALG_TLS12_ECJPAKE_TO_PMS) || \
+    defined(PSA_HAVE_SOFT_PBKDF2)
+#define AT_LEAST_ONE_BUILTIN_KDF
+#endif
 
 /****************************************************************/
 /* Test driver helpers */
@@ -720,7 +733,7 @@
                                         buffer, sizeof(buffer), NULL, 0,
                                         buffer, sizeof(buffer), &length));
 
-#if defined(PSA_WANT_ALG_SHA_256)
+#if defined(PSA_WANT_ALG_SHA_256) && defined(MBEDTLS_PSA_BUILTIN_ALG_HKDF)
     /* Try the key in a plain key derivation. */
     PSA_ASSERT(psa_key_derivation_setup(&derivation_operation,
                                         PSA_ALG_HKDF(PSA_ALG_SHA_256)));
@@ -753,7 +766,9 @@
                          alg, key, buffer, length,
                          buffer, sizeof(buffer), &length));
     }
-#endif /* PSA_WANT_ALG_SHA_256 */
+#else
+    (void) derivation_operation;
+#endif /* PSA_WANT_ALG_SHA_256 && MBEDTLS_PSA_BUILTIN_ALG_HKDF */
 
     ok = 1;
 
diff --git a/tests/suites/test_suite_ssl.data b/tests/suites/test_suite_ssl.data
index d6bf16a..c96b4ad 100644
--- a/tests/suites/test_suite_ssl.data
+++ b/tests/suites/test_suite_ssl.data
@@ -117,7 +117,7 @@
 move_handshake_to_state:MBEDTLS_SSL_IS_CLIENT:MBEDTLS_SSL_VERSION_TLS1_2:MBEDTLS_SSL_SERVER_HELLO:1
 
 TLS 1.2:Move client handshake to SERVER_CERTIFICATE
-depends_on:MBEDTLS_SSP_PROTO_TLS1_2:MBEDTLS_CAN_HANDLE_RSA_TEST_KEY
+depends_on:MBEDTLS_SSL_PROTO_TLS1_2:MBEDTLS_CAN_HANDLE_RSA_TEST_KEY
 move_handshake_to_state:MBEDTLS_SSL_IS_CLIENT:MBEDTLS_SSL_VERSION_TLS1_2:MBEDTLS_SSL_SERVER_CERTIFICATE:1
 
 TLS 1.2:Move client handshake to SERVER_KEY_EXCHANGE
diff --git a/tests/suites/test_suite_x509parse.data b/tests/suites/test_suite_x509parse.data
index 754660c..89d4578 100644
--- a/tests/suites/test_suite_x509parse.data
+++ b/tests/suites/test_suite_x509parse.data
@@ -330,8 +330,8 @@
 depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_MD_CAN_SHA224:MBEDTLS_RSA_C:!MBEDTLS_X509_REMOVE_INFO
 mbedtls_x509_csr_info:"data_files/parse_input/server1.req.sha224":"CSR version   \: 1\nsubject name  \: C=NL, O=PolarSSL, CN=PolarSSL Server 1\nsigned using  \: RSA with SHA-224\nRSA key size  \: 2048 bits\n"
 
-X509 CSR Information RSA with SHA-256
-depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_MD_CAN_SHA256:MBEDTLS_RSA_C:MBEDTS_X509_INFO
+X509 CSR Information RSA with SHA256
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_MD_CAN_SHA256:MBEDTLS_RSA_C:!MBEDTLS_X509_REMOVE_INFO
 mbedtls_x509_csr_info:"data_files/parse_input/server1.req.sha256":"CSR version   \: 1\nsubject name  \: C=NL, O=PolarSSL, CN=PolarSSL Server 1\nsigned using  \: RSA with SHA-256\nRSA key size  \: 2048 bits\n"
 
 X509 CSR Information RSA with SHA384
@@ -342,8 +342,8 @@
 depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_MD_CAN_SHA512:MBEDTLS_RSA_C:!MBEDTLS_X509_REMOVE_INFO
 mbedtls_x509_csr_info:"data_files/parse_input/server1.req.sha512":"CSR version   \: 1\nsubject name  \: C=NL, O=PolarSSL, CN=PolarSSL Server 1\nsigned using  \: RSA with SHA-512\nRSA key size  \: 2048 bits\n"
 
-X509 CSR Information RSA with SHA-256, containing commas
-depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_MD_CAN_SHA256:MBEDTLS_RSA_C:MBEDTS_X509_INFO
+X509 CSR Information RSA with SHA256, containing commas
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_MD_CAN_SHA256:MBEDTLS_RSA_C:!MBEDTLS_X509_REMOVE_INFO
 mbedtls_x509_csr_info:"data_files/parse_input/server1.req.commas.sha256":"CSR version   \: 1\nsubject name  \: C=NL, O=PolarSSL\\, Commas, CN=PolarSSL Server 1\nsigned using  \: RSA with SHA-256\nRSA key size  \: 2048 bits\n"
 
 X509 CSR Information EC with SHA1
@@ -386,8 +386,8 @@
 depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_X509_RSASSA_PSS_SUPPORT:MBEDTLS_MD_CAN_SHA512:!MBEDTLS_X509_REMOVE_INFO
 mbedtls_x509_csr_info:"data_files/parse_input/server9.req.sha512":"CSR version   \: 1\nsubject name  \: C=NL, O=PolarSSL, CN=localhost\nsigned using  \: RSASSA-PSS (SHA512, MGF1-SHA512, 0x3E)\nRSA key size  \: 1024 bits\n\nkey usage         \: Digital Signature, Non Repudiation, Key Encipherment\n"
 
-X509 CSR Information RSA with SHA-256 - Microsoft header
-depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_MD_CAN_SHA256:MBEDTLS_RSA_C
+X509 CSR Information RSA with SHA256 - Microsoft header
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_MD_CAN_SHA256:MBEDTLS_RSA_C:!MBEDTLS_X509_REMOVE_INFO
 mbedtls_x509_csr_info:"data_files/parse_input/server1-ms.req.sha256":"CSR version   \: 1\nsubject name  \: C=NL, O=PolarSSL, CN=PolarSSL Server 1\nsigned using  \: RSA with SHA-256\nRSA key size  \: 2048 bits\n"
 
 X509 CSR Information v3 extensions #1 (all)