diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index 32c7274..06ed561 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -6935,6 +6935,18 @@
 depends_on:PSA_WANT_ALG_PBKDF2_AES_CMAC_PRF_128:PSA_WANT_ALG_CMAC:PSA_WANT_KEY_TYPE_AES:!MBEDTLS_AES_ONLY_128_BIT_KEY_LENGTH
 derive_key_type:PSA_ALG_PBKDF2_AES_CMAC_PRF_128:"706173737764":"01":"73616c74":PSA_KEY_TYPE_AES:256:"28e288c6345bb5ecf7ca70274208a3ba0f1148b5868537d5e09d3ee6813b1f52"
 
+PSA key derivation custom: default -> AES-128
+depends_on:PSA_WANT_ALG_HKDF:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_AES
+derive_key_custom:PSA_ALG_HKDF(PSA_ALG_SHA_256):"0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b":"000102030405060708090a0b0c":"f0f1f2f3f4f5f6f7f8f9":PSA_KEY_TYPE_AES:128:0:"":PSA_SUCCESS:"3cb25f25faacd57a90434f64d0362f2a"
+
+PSA key derivation custom: flags=1 -> AES-128
+depends_on:PSA_WANT_ALG_HKDF:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_AES
+derive_key_custom:PSA_ALG_HKDF(PSA_ALG_SHA_256):"0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b":"000102030405060708090a0b0c":"f0f1f2f3f4f5f6f7f8f9":PSA_KEY_TYPE_AES:128:1:"":PSA_ERROR_INVALID_ARGUMENT:""
+
+PSA key derivation custom: data non-empty -> AES-128
+depends_on:PSA_WANT_ALG_HKDF:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_AES
+derive_key_custom:PSA_ALG_HKDF(PSA_ALG_SHA_256):"0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b":"000102030405060708090a0b0c":"f0f1f2f3f4f5f6f7f8f9":PSA_KEY_TYPE_AES:128:0:"2a":PSA_ERROR_INVALID_ARGUMENT:""
+
 PSA key derivation: default params -> AES-128
 depends_on:PSA_WANT_ALG_HKDF:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_AES
 derive_key_ext:PSA_ALG_HKDF(PSA_ALG_SHA_256):"0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b":"000102030405060708090a0b0c":"f0f1f2f3f4f5f6f7f8f9":PSA_KEY_TYPE_AES:128:0:"":PSA_SUCCESS:"3cb25f25faacd57a90434f64d0362f2a"
@@ -7520,6 +7532,83 @@
 depends_on:PSA_WANT_ALG_FFDH:PSA_WANT_KEY_TYPE_DH_KEY_PAIR_GENERATE
 generate_key:PSA_KEY_TYPE_DH_KEY_PAIR(PSA_DH_FAMILY_RFC7919):1024:PSA_KEY_USAGE_EXPORT:PSA_ALG_FFDH:PSA_ERROR_NOT_SUPPORTED:0
 
+PSA generate key custom: RSA, flags=1
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE
+generate_key_custom:PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_VENDOR_RSA_GENERATE_MIN_KEY_BITS:PSA_KEY_USAGE_ENCRYPT | PSA_KEY_USAGE_DECRYPT:0:1:"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA generate key custom: RSA, empty e
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:PSA_WANT_ALG_RSA_PKCS1V15_CRYPT
+generate_key_custom: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 custom: RSA, e=3
+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_custom: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 custom: RSA, e=3 with leading zeros
+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_custom: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
+# and the conversion errors out if there are too many digits without checking
+# for leading zeros. This is a very minor bug. Re-enable this test when this
+# bug is fixed.
+#PSA generate key custom: RSA, e=3 with many leading zeros
+#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_custom: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 custom: RSA, e=513
+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_custom: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 custom: RSA, e=65537
+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_custom: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 custom: RSA, e=2^31-1
+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_custom: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 custom: RSA, e=2^31+3 (too large for built-in RSA)
+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_custom: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 custom: RSA, e=2^64+3 (too large for built-in RSA)
+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_custom: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 custom: RSA, e=1
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE
+generate_key_custom: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 custom: RSA, e=0
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE
+generate_key_custom: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 custom: RSA, e=2
+depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE:MBEDTLS_PSA_BUILTIN_KEY_TYPE_RSA_KEY_PAIR_GENERATE
+generate_key_custom: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 custom: 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_custom: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 custom: 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_custom:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):256:PSA_KEY_USAGE_DERIVE:PSA_ALG_ECDH:0:"":PSA_SUCCESS
+
+PSA generate key custom: ECC, flags=1
+depends_on:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_GENERATE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_ECDH
+generate_key_custom:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):256:PSA_KEY_USAGE_DERIVE:PSA_ALG_ECDH:1:"":PSA_ERROR_INVALID_ARGUMENT
+
+PSA generate key custom: ECC, data non-empty
+depends_on:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_GENERATE:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_ECDH
+generate_key_custom:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):256:PSA_KEY_USAGE_DERIVE:PSA_ALG_ECDH:0:"2a":PSA_ERROR_INVALID_ARGUMENT
+
 PSA generate key ext: RSA, params.flags=1
 depends_on:PSA_WANT_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:0:1:"":PSA_ERROR_INVALID_ARGUMENT
diff --git a/tests/suites/test_suite_psa_crypto.function b/tests/suites/test_suite_psa_crypto.function
index 0c8552b..7f47f27 100644
--- a/tests/suites/test_suite_psa_crypto.function
+++ b/tests/suites/test_suite_psa_crypto.function
@@ -9592,6 +9592,77 @@
 /* END_CASE */
 
 /* BEGIN_CASE */
+void derive_key_custom(int alg_arg,
+                       data_t *key_data,
+                       data_t *input1,
+                       data_t *input2,
+                       int key_type_arg, int bits_arg,
+                       int flags_arg,
+                       data_t *custom_data,
+                       psa_status_t expected_status,
+                       data_t *expected_export)
+{
+    mbedtls_svc_key_id_t base_key = MBEDTLS_SVC_KEY_ID_INIT;
+    mbedtls_svc_key_id_t derived_key = MBEDTLS_SVC_KEY_ID_INIT;
+    const psa_algorithm_t alg = alg_arg;
+    const psa_key_type_t key_type = key_type_arg;
+    const size_t bits = bits_arg;
+    psa_custom_key_parameters_t custom = PSA_CUSTOM_KEY_PARAMETERS_INIT;
+    custom.flags = flags_arg;
+    psa_key_derivation_operation_t operation = PSA_KEY_DERIVATION_OPERATION_INIT;
+    const size_t export_buffer_size =
+        PSA_EXPORT_KEY_OUTPUT_SIZE(key_type, bits);
+    uint8_t *export_buffer = NULL;
+    psa_key_attributes_t base_attributes = PSA_KEY_ATTRIBUTES_INIT;
+    psa_key_attributes_t derived_attributes = PSA_KEY_ATTRIBUTES_INIT;
+    size_t export_length;
+
+    TEST_CALLOC(export_buffer, export_buffer_size);
+    PSA_ASSERT(psa_crypto_init());
+
+    psa_set_key_usage_flags(&base_attributes, PSA_KEY_USAGE_DERIVE);
+    psa_set_key_algorithm(&base_attributes, alg);
+    psa_set_key_type(&base_attributes, PSA_KEY_TYPE_DERIVE);
+    PSA_ASSERT(psa_import_key(&base_attributes, key_data->x, key_data->len,
+                              &base_key));
+
+    if (mbedtls_test_psa_setup_key_derivation_wrap(
+            &operation, base_key, alg,
+            input1->x, input1->len,
+            input2->x, input2->len,
+            PSA_KEY_DERIVATION_UNLIMITED_CAPACITY, 0) == 0) {
+        goto exit;
+    }
+
+    psa_set_key_usage_flags(&derived_attributes, PSA_KEY_USAGE_EXPORT);
+    psa_set_key_algorithm(&derived_attributes, 0);
+    psa_set_key_type(&derived_attributes, key_type);
+    psa_set_key_bits(&derived_attributes, bits);
+
+    TEST_EQUAL(psa_key_derivation_output_key_custom(
+                   &derived_attributes, &operation,
+                   &custom, custom_data->x, custom_data->len,
+                   &derived_key),
+               expected_status);
+
+    if (expected_status == PSA_SUCCESS) {
+        PSA_ASSERT(psa_export_key(derived_key,
+                                  export_buffer, export_buffer_size,
+                                  &export_length));
+        TEST_MEMORY_COMPARE(export_buffer, export_length,
+                            expected_export->x, expected_export->len);
+    }
+
+exit:
+    mbedtls_free(export_buffer);
+    psa_key_derivation_abort(&operation);
+    psa_destroy_key(base_key);
+    psa_destroy_key(derived_key);
+    PSA_DONE();
+}
+/* END_CASE */
+
+/* BEGIN_CASE */
 void derive_key_ext(int alg_arg,
                     data_t *key_data,
                     data_t *input1,
@@ -10153,6 +10224,71 @@
 /* END_CASE */
 
 /* BEGIN_CASE */
+void generate_key_custom(int type_arg,
+                         int bits_arg,
+                         int usage_arg,
+                         int alg_arg,
+                         int flags_arg,
+                         data_t *custom_data,
+                         int expected_status_arg)
+{
+    mbedtls_svc_key_id_t key = MBEDTLS_SVC_KEY_ID_INIT;
+    psa_key_type_t type = type_arg;
+    psa_key_usage_t usage = usage_arg;
+    size_t bits = bits_arg;
+    psa_algorithm_t alg = alg_arg;
+    psa_status_t expected_status = expected_status_arg;
+    psa_key_attributes_t attributes = PSA_KEY_ATTRIBUTES_INIT;
+    psa_custom_key_parameters_t custom = PSA_CUSTOM_KEY_PARAMETERS_INIT;
+    custom.flags = flags_arg;
+    psa_key_attributes_t got_attributes = PSA_KEY_ATTRIBUTES_INIT;
+
+    PSA_ASSERT(psa_crypto_init());
+
+    psa_set_key_usage_flags(&attributes, usage);
+    psa_set_key_algorithm(&attributes, alg);
+    psa_set_key_type(&attributes, type);
+    psa_set_key_bits(&attributes, bits);
+
+    /* Generate a key */
+    psa_status_t status =
+        psa_generate_key_custom(&attributes,
+                                &custom, custom_data->x, custom_data->len,
+                                &key);
+
+    TEST_EQUAL(status, expected_status);
+    if (expected_status != PSA_SUCCESS) {
+        goto exit;
+    }
+
+    /* Test the key information */
+    PSA_ASSERT(psa_get_key_attributes(key, &got_attributes));
+    TEST_EQUAL(psa_get_key_type(&got_attributes), type);
+    TEST_EQUAL(psa_get_key_bits(&got_attributes), bits);
+
+#if defined(PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_GENERATE)
+    if (type == PSA_KEY_TYPE_RSA_KEY_PAIR) {
+        TEST_ASSERT(rsa_test_e(key, bits, custom_data));
+    }
+#endif
+
+    /* Do something with the key according to its type and permitted usage. */
+    if (!mbedtls_test_psa_exercise_key(key, usage, alg, 0)) {
+        goto exit;
+    }
+
+exit:
+    /*
+     * Key attributes may have been returned by psa_get_key_attributes()
+     * thus reset them as required.
+     */
+    psa_reset_key_attributes(&got_attributes);
+    psa_destroy_key(key);
+    PSA_DONE();
+}
+/* END_CASE */
+
+/* BEGIN_CASE */
 void generate_key_ext(int type_arg,
                       int bits_arg,
                       int usage_arg,