diff --git a/library/psa_crypto.c b/library/psa_crypto.c
index f031654..8fc021a 100644
--- a/library/psa_crypto.c
+++ b/library/psa_crypto.c
@@ -424,8 +424,10 @@
     }
 }
 
-static mbedtls_ecp_group_id mbedtls_ecc_group_of_psa( psa_ecc_curve_t curve )
+static mbedtls_ecp_group_id mbedtls_ecc_group_of_psa( psa_ecc_curve_t curve,
+                                                      size_t byte_length )
 {
+    (void) byte_length;
     switch( curve )
     {
         case PSA_ECC_CURVE_SECP192R1:
@@ -602,6 +604,8 @@
 
 #if defined(MBEDTLS_ECP_C)
 static psa_status_t psa_prepare_import_ec_key( psa_ecc_curve_t curve,
+                                               size_t data_length,
+                                               int is_public,
                                                mbedtls_ecp_keypair **p_ecp )
 {
     mbedtls_ecp_group_id grp_id = MBEDTLS_ECP_DP_NONE;
@@ -610,8 +614,23 @@
         return( PSA_ERROR_INSUFFICIENT_MEMORY );
     mbedtls_ecp_keypair_init( *p_ecp );
 
+    if( is_public )
+    {
+        /* A public key is represented as:
+         * - The byte 0x04;
+         * - `x_P` as a `ceiling(m/8)`-byte string, big-endian;
+         * - `y_P` as a `ceiling(m/8)`-byte string, big-endian.
+         * So its data length is 2m+1 where n is the key size in bits.
+         */
+        if( ( data_length & 1 ) == 0 )
+            return( PSA_ERROR_INVALID_ARGUMENT );
+        data_length = data_length / 2;
+    }
+
     /* Load the group. */
-    grp_id = mbedtls_ecc_group_of_psa( curve );
+    grp_id = mbedtls_ecc_group_of_psa( curve, data_length );
+    if( grp_id == MBEDTLS_ECP_DP_NONE )
+        return( PSA_ERROR_INVALID_ARGUMENT );
     return( mbedtls_to_psa_error(
                 mbedtls_ecp_group_load( &( *p_ecp )->grp, grp_id ) ) );
 }
@@ -626,7 +645,7 @@
     psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
     mbedtls_ecp_keypair *ecp = NULL;
 
-    status = psa_prepare_import_ec_key( curve, &ecp );
+    status = psa_prepare_import_ec_key( curve, data_length, 1, &ecp );
     if( status != PSA_SUCCESS )
         goto exit;
 
@@ -668,7 +687,7 @@
     if( PSA_BITS_TO_BYTES( PSA_ECC_CURVE_BITS( curve ) ) != data_length )
         return( PSA_ERROR_INVALID_ARGUMENT );
 
-    status = psa_prepare_import_ec_key( curve, &ecp );
+    status = psa_prepare_import_ec_key( curve, data_length, 0, &ecp );
     if( status != PSA_SUCCESS )
         goto exit;
 
@@ -5578,7 +5597,8 @@
     if ( PSA_KEY_TYPE_IS_ECC( type ) && PSA_KEY_TYPE_IS_KEY_PAIR( type ) )
     {
         psa_ecc_curve_t curve = PSA_KEY_TYPE_GET_CURVE( type );
-        mbedtls_ecp_group_id grp_id = mbedtls_ecc_group_of_psa( curve );
+        mbedtls_ecp_group_id grp_id =
+            mbedtls_ecc_group_of_psa( curve, PSA_BITS_TO_BYTES( bits ) );
         const mbedtls_ecp_curve_info *curve_info =
             mbedtls_ecp_curve_info_from_grp_id( grp_id );
         mbedtls_ecp_keypair *ecp;
diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index b70fc63..0205eea 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -304,11 +304,7 @@
 
 PSA import EC public key: key pair
 depends_on:MBEDTLS_PK_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED
-# For consistency with ECpub as ECpair, RSApub as RSApair and RSApair as RSApub,
-# one would expect the status to be PSA_ERROR_INVALID_ARGUMENT. But the
-# Mbed TLS pkparse module returns MBEDTLS_ERR_PK_INVALID_ALG, I think because
-# it's looking for an OID where there is no OID.
-import_with_data:"3078020101042100ab45435712649cb30bbddac49197eebf2740ffc7f874d9244c3460f54f322d3aa00a06082a8648ce3d030107a14403420004dea5e45d0ea37fc566232a508f4ad20ea13d47e4bf5fa4d54a57a0ba012042087097496efc583fed8b24a5b9be9a51de063f5a00a8b698a16fd7f29b5485f320":PSA_KEY_TYPE_ECC_PUBLIC_KEY(PSA_ECC_CURVE_SECP256R1):0:PSA_ERROR_NOT_SUPPORTED
+import_with_data:"3078020101042100ab45435712649cb30bbddac49197eebf2740ffc7f874d9244c3460f54f322d3aa00a06082a8648ce3d030107a14403420004dea5e45d0ea37fc566232a508f4ad20ea13d47e4bf5fa4d54a57a0ba012042087097496efc583fed8b24a5b9be9a51de063f5a00a8b698a16fd7f29b5485f320":PSA_KEY_TYPE_ECC_PUBLIC_KEY(PSA_ECC_CURVE_SECP256R1):0:PSA_ERROR_INVALID_ARGUMENT
 
 PSA import EC keypair: valid key but RSA
 depends_on:MBEDTLS_PK_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_BP512R1_ENABLED:MBEDTLS_RSA_C