diff --git a/library/psa_crypto.c b/library/psa_crypto.c
index fba1936..dba244a 100644
--- a/library/psa_crypto.c
+++ b/library/psa_crypto.c
@@ -1044,6 +1044,12 @@
     ret = mbedtls_rsa_export( rsa, NULL, NULL, NULL, NULL, &mpi );
     if( ret != 0 )
         goto exit;
+    if( mbedtls_mpi_cmp_int( &mpi, 65537 ) == 0 )
+    {
+        /* It's the default value, which is reported as an empty string,
+         * so there's nothing to do. */
+        goto exit;
+    }
 
     buflen = mbedtls_mpi_size( &mpi );
     buffer = mbedtls_calloc( 1, buflen );