Follow the below steps to enable the ssl to all pages in prestashop 1.5.3.1
1. Enable SSL in admin. Go to admin->preferences->General- Enable SSL
2. If Product Categories are not linked into https, then Go to Classes/ Link.php. Change _PS_BASE_URL_ to _PS_BASE_URL_SSL_
3. If http are not redirecting then change .htaccess file like below:
<IfModule mod_rewrite.c>
RewriteEngine on
RewriteCond %{SERVER_PORT} 80
RewriteRule ^(.*)$ (yoursite in https)$1 [R,L]
</IfModule>