I’m experiencing this too on one of my sites, although the error is different (it now throws an exception):
Fatal error: Uncaught exception 'Exception' with message 'Plugin was unable to generate an RSA security key that is needed for secure communication with the CodeGuard.com backup service.' in /.../public/wordpress/wp-content/plugins/codeguard/codeguard-plugin.php:650
Stack trace:
#0 /.../public/wordpress/wp-content/plugins/codeguard/codeguard-plugin.php(155): CodeGuard_WP_Plugin::generate_plugin_keys()
#1 [internal function]: CodeGuard_WP_Plugin::install('')
#2 /.../public/wordpress/wp-includes/plugin.php(406): call_user_func_array(Array, Array)
#3 /.../public/wordpress/wp-admin/plugins.php(150): do_action('activate_codegu...')
#4 {main} thrown in /.../public/wordpress/wp-content/plugins/codeguard/codeguard-plugin.php on line 650
My guess is my host (and yours) doesn’t provide the required PHP extension for this to work.
PHP.net’s page on the openssl_pkey_new() function has a commenter suggesting developers to adopt the phpseclib library instead, as it works with or without PHP’s OpenSLL extension. Maybe CodeGuard’s folks could look into it?