Delete all the Prestashop tables from the database, unlock the server to server whitelist from the AlterVista control panel (look at the PHP settings), then in the file of Prestashop classes/Tools.php find
PHP Code:
if (in_array(ini_get('allow_url_fopen'), array('On', 'on', '1')) || !preg_match('/^https?:\/\//', $url))
and replace it with
PHP Code:
/*if (in_array(ini_get('allow_url_fopen'), array('On', 'on', '1')) || !preg_match('/^https?:\/\//', $url))
below that, find
PHP Code:
elseif (function_exists('curl_init'))
and replace it with
PHP Code:
else*/if (function_exists('curl_init'))
And finally try again the installation procedure.
Let me know if you have any other issue.