Conditionnaly add short description to product shortcode

Hello,
I would like to add short description to a product shortcode, but not on all shortcodes.
For exemple with a shortcode like :
[product_category category=”xxxx” show_desc=”true”]

I found a code to display shordcodes :

add_action( 'woocommerce_after_shop_loop_item_title', 'custom_short_description', 45 );

function custom_short_description() {
    global $product;
        ?>   
        <div itemprop="description">
            <?php echo apply_filters( 'woocommerce_short_description', $product->get_short_description() ) ?>
        </div>
        <?php
}

How could I get my option show_desc inside this function to display the description only in this case ?

Thanks