diff --git a/oqs-template/oqsprov/oqsprov_keys.c/oqsnames.fragment b/oqs-template/oqsprov/oqsprov_keys.c/oqsnames.fragment
index d523d39c..a8a2d86b 100644
--- a/oqs-template/oqsprov/oqsprov_keys.c/oqsnames.fragment
+++ b/oqs-template/oqsprov/oqsprov_keys.c/oqsnames.fragment
@@ -30,9 +30,9 @@
 static oqs_nid_name_t nid_names[NID_TABLE_LEN] = {
 #ifdef OQS_KEM_ENCODERS
 {% for kem in config['kems'] %}
-  { 0, "{{ kem['name_group'] }}", {{ kem['oqs_alg'] }}, KEY_TYPE_KEM, {{ kem['bit_security'] }} },
+  { 0, "{{ kem['name_group'] }}", {{ kem['oqs_alg'] }}, KEY_TYPE_KEM, {{ kem['bit_security'] }}, 0 },
 {%- for hybrid in kem['hybrids'] %}
-  { 0, "{% if 'standard_name' in hybrid %}{{hybrid['standard_name']}}{% else %}{{ hybrid['hybrid_group'] }}_{{ kem['name_group'] }}{% endif %}", {{ kem['oqs_alg'] }}, {% if hybrid['hybrid_group'].startswith('p') -%} KEY_TYPE_ECP_HYB_KEM {% else %} KEY_TYPE_ECX_HYB_KEM {% endif %}, {{ kem['bit_security'] }} },
+  { 0, "{% if 'standard_name' in hybrid %}{{hybrid['standard_name']}}{% else %}{{ hybrid['hybrid_group'] }}_{{ kem['name_group'] }}{% endif %}", {{ kem['oqs_alg'] }}, {% if hybrid['hybrid_group'].startswith('p') -%} KEY_TYPE_ECP_HYB_KEM {% else %} KEY_TYPE_ECX_HYB_KEM {% endif %}, {{ kem['bit_security'] }}, {% if 'fips_standard' in kem and not hybrid['hybrid_group'].startswith('p') %}1{% else %}0{% endif %} },
 {%- endfor -%}
 {%- endfor %}
 
diff --git a/oqsprov/oqs_encode_key2any.c b/oqsprov/oqs_encode_key2any.c
index 54939a61..83ff6554 100644
--- a/oqsprov/oqs_encode_key2any.c
+++ b/oqsprov/oqs_encode_key2any.c
@@ -636,8 +636,13 @@ static int oqsx_pki_priv_to_der(const void *vxkey, unsigned char **pder) {
         OQS_ENC_PRINTF2("OQS ENC provider: saving priv+pubkey of length %d\n",
                         buflen);
         memcpy(buf, oqsxkey->privkey, privkeylen);
-        memcpy(buf + privkeylen, oqsxkey->comp_pubkey[oqsxkey->numkeys - 1],
-               oqsx_key_get_oqs_public_key_len(oqsxkey));
+        if (oqsxkey->reverse_share) {
+            memcpy(buf + privkeylen, oqsxkey->comp_pubkey[0],
+                   oqsx_key_get_oqs_public_key_len(oqsxkey));
+        } else {
+            memcpy(buf + privkeylen, oqsxkey->comp_pubkey[oqsxkey->numkeys - 1],
+                   oqsx_key_get_oqs_public_key_len(oqsxkey));
+        }
 #endif
 
         oct.data = buf;
diff --git a/oqsprov/oqsprov_keys.c b/oqsprov/oqsprov_keys.c
index 226a3ff2..507d3b26 100644
--- a/oqsprov/oqsprov_keys.c
+++ b/oqsprov/oqsprov_keys.c
@@ -45,6 +45,7 @@ typedef struct {
     char *oqsname;
     int keytype;
     int secbits;
+    int reverseshare;
 } oqs_nid_name_t;
 
 static int oqsx_key_recreate_classickey(OQSX_KEY *key, oqsx_key_op_t op);
@@ -60,69 +61,74 @@ static int oqsx_key_recreate_classickey(OQSX_KEY *key, oqsx_key_op_t op);
 static oqs_nid_name_t nid_names[NID_TABLE_LEN] = {
 #ifdef OQS_KEM_ENCODERS
 
-    {0, "frodo640aes", OQS_KEM_alg_frodokem_640_aes, KEY_TYPE_KEM, 128},
+    {0, "frodo640aes", OQS_KEM_alg_frodokem_640_aes, KEY_TYPE_KEM, 128, 0},
     {0, "p256_frodo640aes", OQS_KEM_alg_frodokem_640_aes, KEY_TYPE_ECP_HYB_KEM,
-     128},
+     128, 0},
     {0, "x25519_frodo640aes", OQS_KEM_alg_frodokem_640_aes,
-     KEY_TYPE_ECX_HYB_KEM, 128},
-    {0, "frodo640shake", OQS_KEM_alg_frodokem_640_shake, KEY_TYPE_KEM, 128},
+     KEY_TYPE_ECX_HYB_KEM, 128, 0},
+    {0, "frodo640shake", OQS_KEM_alg_frodokem_640_shake, KEY_TYPE_KEM, 128, 0},
     {0, "p256_frodo640shake", OQS_KEM_alg_frodokem_640_shake,
-     KEY_TYPE_ECP_HYB_KEM, 128},
+     KEY_TYPE_ECP_HYB_KEM, 128, 0},
     {0, "x25519_frodo640shake", OQS_KEM_alg_frodokem_640_shake,
-     KEY_TYPE_ECX_HYB_KEM, 128},
-    {0, "frodo976aes", OQS_KEM_alg_frodokem_976_aes, KEY_TYPE_KEM, 192},
+     KEY_TYPE_ECX_HYB_KEM, 128, 0},
+    {0, "frodo976aes", OQS_KEM_alg_frodokem_976_aes, KEY_TYPE_KEM, 192, 0},
     {0, "p384_frodo976aes", OQS_KEM_alg_frodokem_976_aes, KEY_TYPE_ECP_HYB_KEM,
-     192},
+     192, 0},
     {0, "x448_frodo976aes", OQS_KEM_alg_frodokem_976_aes, KEY_TYPE_ECX_HYB_KEM,
-     192},
-    {0, "frodo976shake", OQS_KEM_alg_frodokem_976_shake, KEY_TYPE_KEM, 192},
+     192, 0},
+    {0, "frodo976shake", OQS_KEM_alg_frodokem_976_shake, KEY_TYPE_KEM, 192, 0},
     {0, "p384_frodo976shake", OQS_KEM_alg_frodokem_976_shake,
-     KEY_TYPE_ECP_HYB_KEM, 192},
+     KEY_TYPE_ECP_HYB_KEM, 192, 0},
     {0, "x448_frodo976shake", OQS_KEM_alg_frodokem_976_shake,
-     KEY_TYPE_ECX_HYB_KEM, 192},
-    {0, "frodo1344aes", OQS_KEM_alg_frodokem_1344_aes, KEY_TYPE_KEM, 256},
+     KEY_TYPE_ECX_HYB_KEM, 192, 0},
+    {0, "frodo1344aes", OQS_KEM_alg_frodokem_1344_aes, KEY_TYPE_KEM, 256, 0},
     {0, "p521_frodo1344aes", OQS_KEM_alg_frodokem_1344_aes,
-     KEY_TYPE_ECP_HYB_KEM, 256},
-    {0, "frodo1344shake", OQS_KEM_alg_frodokem_1344_shake, KEY_TYPE_KEM, 256},
+     KEY_TYPE_ECP_HYB_KEM, 256, 0},
+    {0, "frodo1344shake", OQS_KEM_alg_frodokem_1344_shake, KEY_TYPE_KEM, 256,
+     0},
     {0, "p521_frodo1344shake", OQS_KEM_alg_frodokem_1344_shake,
-     KEY_TYPE_ECP_HYB_KEM, 256},
-    {0, "kyber512", OQS_KEM_alg_kyber_512, KEY_TYPE_KEM, 128},
-    {0, "p256_kyber512", OQS_KEM_alg_kyber_512, KEY_TYPE_ECP_HYB_KEM, 128},
-    {0, "x25519_kyber512", OQS_KEM_alg_kyber_512, KEY_TYPE_ECX_HYB_KEM, 128},
-    {0, "kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_KEM, 192},
-    {0, "p384_kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_ECP_HYB_KEM, 192},
-    {0, "x448_kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_ECX_HYB_KEM, 192},
-    {0, "x25519_kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_ECX_HYB_KEM, 192},
-    {0, "p256_kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_ECP_HYB_KEM, 192},
-    {0, "kyber1024", OQS_KEM_alg_kyber_1024, KEY_TYPE_KEM, 256},
-    {0, "p521_kyber1024", OQS_KEM_alg_kyber_1024, KEY_TYPE_ECP_HYB_KEM, 256},
-    {0, "mlkem512", OQS_KEM_alg_ml_kem_512, KEY_TYPE_KEM, 128},
-    {0, "p256_mlkem512", OQS_KEM_alg_ml_kem_512, KEY_TYPE_ECP_HYB_KEM, 128},
-    {0, "x25519_mlkem512", OQS_KEM_alg_ml_kem_512, KEY_TYPE_ECX_HYB_KEM, 128},
-    {0, "mlkem768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_KEM, 192},
-    {0, "p384_mlkem768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_ECP_HYB_KEM, 192},
-    {0, "x448_mlkem768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_ECX_HYB_KEM, 192},
-    {0, "X25519MLKEM768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_ECX_HYB_KEM, 192},
-    {0, "SecP256r1MLKEM768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_ECP_HYB_KEM, 192},
-    {0, "mlkem1024", OQS_KEM_alg_ml_kem_1024, KEY_TYPE_KEM, 256},
-    {0, "p521_mlkem1024", OQS_KEM_alg_ml_kem_1024, KEY_TYPE_ECP_HYB_KEM, 256},
-    {0, "p384_mlkem1024", OQS_KEM_alg_ml_kem_1024, KEY_TYPE_ECP_HYB_KEM, 256},
-    {0, "bikel1", OQS_KEM_alg_bike_l1, KEY_TYPE_KEM, 128},
-    {0, "p256_bikel1", OQS_KEM_alg_bike_l1, KEY_TYPE_ECP_HYB_KEM, 128},
-    {0, "x25519_bikel1", OQS_KEM_alg_bike_l1, KEY_TYPE_ECX_HYB_KEM, 128},
-    {0, "bikel3", OQS_KEM_alg_bike_l3, KEY_TYPE_KEM, 192},
-    {0, "p384_bikel3", OQS_KEM_alg_bike_l3, KEY_TYPE_ECP_HYB_KEM, 192},
-    {0, "x448_bikel3", OQS_KEM_alg_bike_l3, KEY_TYPE_ECX_HYB_KEM, 192},
-    {0, "bikel5", OQS_KEM_alg_bike_l5, KEY_TYPE_KEM, 256},
-    {0, "p521_bikel5", OQS_KEM_alg_bike_l5, KEY_TYPE_ECP_HYB_KEM, 256},
-    {0, "hqc128", OQS_KEM_alg_hqc_128, KEY_TYPE_KEM, 128},
-    {0, "p256_hqc128", OQS_KEM_alg_hqc_128, KEY_TYPE_ECP_HYB_KEM, 128},
-    {0, "x25519_hqc128", OQS_KEM_alg_hqc_128, KEY_TYPE_ECX_HYB_KEM, 128},
-    {0, "hqc192", OQS_KEM_alg_hqc_192, KEY_TYPE_KEM, 192},
-    {0, "p384_hqc192", OQS_KEM_alg_hqc_192, KEY_TYPE_ECP_HYB_KEM, 192},
-    {0, "x448_hqc192", OQS_KEM_alg_hqc_192, KEY_TYPE_ECX_HYB_KEM, 192},
-    {0, "hqc256", OQS_KEM_alg_hqc_256, KEY_TYPE_KEM, 256},
-    {0, "p521_hqc256", OQS_KEM_alg_hqc_256, KEY_TYPE_ECP_HYB_KEM, 256},
+     KEY_TYPE_ECP_HYB_KEM, 256, 0},
+    {0, "kyber512", OQS_KEM_alg_kyber_512, KEY_TYPE_KEM, 128, 0},
+    {0, "p256_kyber512", OQS_KEM_alg_kyber_512, KEY_TYPE_ECP_HYB_KEM, 128, 0},
+    {0, "x25519_kyber512", OQS_KEM_alg_kyber_512, KEY_TYPE_ECX_HYB_KEM, 128, 0},
+    {0, "kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_KEM, 192, 0},
+    {0, "p384_kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_ECP_HYB_KEM, 192, 0},
+    {0, "x448_kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_ECX_HYB_KEM, 192, 0},
+    {0, "x25519_kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_ECX_HYB_KEM, 192, 0},
+    {0, "p256_kyber768", OQS_KEM_alg_kyber_768, KEY_TYPE_ECP_HYB_KEM, 192, 0},
+    {0, "kyber1024", OQS_KEM_alg_kyber_1024, KEY_TYPE_KEM, 256, 0},
+    {0, "p521_kyber1024", OQS_KEM_alg_kyber_1024, KEY_TYPE_ECP_HYB_KEM, 256, 0},
+    {0, "mlkem512", OQS_KEM_alg_ml_kem_512, KEY_TYPE_KEM, 128, 0},
+    {0, "p256_mlkem512", OQS_KEM_alg_ml_kem_512, KEY_TYPE_ECP_HYB_KEM, 128, 0},
+    {0, "x25519_mlkem512", OQS_KEM_alg_ml_kem_512, KEY_TYPE_ECX_HYB_KEM, 128,
+     1},
+    {0, "mlkem768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_KEM, 192, 0},
+    {0, "p384_mlkem768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_ECP_HYB_KEM, 192, 0},
+    {0, "x448_mlkem768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_ECX_HYB_KEM, 192, 1},
+    {0, "X25519MLKEM768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_ECX_HYB_KEM, 192, 1},
+    {0, "SecP256r1MLKEM768", OQS_KEM_alg_ml_kem_768, KEY_TYPE_ECP_HYB_KEM, 192,
+     0},
+    {0, "mlkem1024", OQS_KEM_alg_ml_kem_1024, KEY_TYPE_KEM, 256, 0},
+    {0, "p521_mlkem1024", OQS_KEM_alg_ml_kem_1024, KEY_TYPE_ECP_HYB_KEM, 256,
+     0},
+    {0, "p384_mlkem1024", OQS_KEM_alg_ml_kem_1024, KEY_TYPE_ECP_HYB_KEM, 256,
+     0},
+    {0, "bikel1", OQS_KEM_alg_bike_l1, KEY_TYPE_KEM, 128, 0},
+    {0, "p256_bikel1", OQS_KEM_alg_bike_l1, KEY_TYPE_ECP_HYB_KEM, 128, 0},
+    {0, "x25519_bikel1", OQS_KEM_alg_bike_l1, KEY_TYPE_ECX_HYB_KEM, 128, 0},
+    {0, "bikel3", OQS_KEM_alg_bike_l3, KEY_TYPE_KEM, 192, 0},
+    {0, "p384_bikel3", OQS_KEM_alg_bike_l3, KEY_TYPE_ECP_HYB_KEM, 192, 0},
+    {0, "x448_bikel3", OQS_KEM_alg_bike_l3, KEY_TYPE_ECX_HYB_KEM, 192, 0},
+    {0, "bikel5", OQS_KEM_alg_bike_l5, KEY_TYPE_KEM, 256, 0},
+    {0, "p521_bikel5", OQS_KEM_alg_bike_l5, KEY_TYPE_ECP_HYB_KEM, 256, 0},
+    {0, "hqc128", OQS_KEM_alg_hqc_128, KEY_TYPE_KEM, 128, 0},
+    {0, "p256_hqc128", OQS_KEM_alg_hqc_128, KEY_TYPE_ECP_HYB_KEM, 128, 0},
+    {0, "x25519_hqc128", OQS_KEM_alg_hqc_128, KEY_TYPE_ECX_HYB_KEM, 128, 0},
+    {0, "hqc192", OQS_KEM_alg_hqc_192, KEY_TYPE_KEM, 192, 0},
+    {0, "p384_hqc192", OQS_KEM_alg_hqc_192, KEY_TYPE_ECP_HYB_KEM, 192, 0},
+    {0, "x448_hqc192", OQS_KEM_alg_hqc_192, KEY_TYPE_ECX_HYB_KEM, 192, 0},
+    {0, "hqc256", OQS_KEM_alg_hqc_256, KEY_TYPE_KEM, 256, 0},
+    {0, "p521_hqc256", OQS_KEM_alg_hqc_256, KEY_TYPE_ECP_HYB_KEM, 256, 0},
 
 #endif /* OQS_KEM_ENCODERS */
     {0, "dilithium2", OQS_SIG_alg_dilithium_2, KEY_TYPE_SIG, 128},
@@ -218,6 +224,15 @@ static int get_secbits(int nid) {
     return 0;
 }
 
+static int get_reverseshare(int nid) {
+    int i;
+    for (i = 0; i < NID_TABLE_LEN; i++) {
+        if (nid_names[i].nid == nid)
+            return nid_names[i].reverseshare;
+    }
+    return 0;
+}
+
 static int get_keytype(int nid) {
     int i;
     for (i = 0; i < NID_TABLE_LEN; i++) {
@@ -470,7 +485,8 @@ static OQSX_KEY *oqsx_key_new_from_nid(OSSL_LIB_CTX *libctx, const char *propq,
     }
 
     return oqsx_key_new(libctx, get_oqsname(nid), tls_algname, get_keytype(nid),
-                        propq, get_secbits(nid), get_oqsalg_idx(nid), 0);
+                        propq, get_secbits(nid), get_oqsalg_idx(nid),
+                        get_reverseshare(nid));
 }
 
 /* Workaround for not functioning EC PARAM initialization
@@ -912,9 +928,14 @@ static OQSX_KEY *oqsx_key_op(const X509_ALGOR *palg, const unsigned char *p,
             if (key->numkeys == 2) {
                 unsigned char *pubkey = (unsigned char *)key->pubkey;
                 ENCODE_UINT32(pubkey, key->evp_info->length_public_key);
-                memcpy(pubkey + SIZE_OF_UINT32 +
-                           key->evp_info->length_public_key,
-                       p + actualprivkeylen, plen - actualprivkeylen);
+                if (key->reverse_share) {
+                    memcpy(pubkey + SIZE_OF_UINT32, p + actualprivkeylen,
+                           plen - actualprivkeylen);
+                } else {
+                    memcpy(pubkey + SIZE_OF_UINT32 +
+                               key->evp_info->length_public_key,
+                           p + actualprivkeylen, plen - actualprivkeylen);
+                }
             } else
                 memcpy(key->pubkey, p + key->privkeylen,
                        plen - key->privkeylen);
diff --git a/test/oqs_test_evp_pkey_params.c b/test/oqs_test_evp_pkey_params.c
index b20aab93..b00c05c2 100644
--- a/test/oqs_test_evp_pkey_params.c
+++ b/test/oqs_test_evp_pkey_params.c
@@ -559,7 +559,6 @@ int main(int argc, char **argv) {
     }
 
     for (; algs->algorithm_names != NULL; ++algs) {
-        // if (strcmp(algs->algorithm_names, "x25519_mlkem768")) continue;
         if (!is_signature_algorithm_hybrid(algs->algorithm_names)) {
             continue;
         }
@@ -583,7 +582,6 @@ int main(int argc, char **argv) {
         goto unload_oqs_provider;
     }
     for (; algs->algorithm_names != NULL; ++algs) {
-        // if (strcmp(algs->algorithm_names, "x25519_mlkem768")) continue;
         if (!is_kem_algorithm_hybrid(algs->algorithm_names)) {
             continue;
         }