ReadCube always uses SSL (Secure Sockets Layer) for all purchases, whether on www.readcube.com or when checking out on a publisher's website. In some cases, it's possible the checkout frame is embedded in a parent page that is not using SSL (e.g. a regular http site, instead of an https site). Even if the parent page is not using SSL - and you see that you're on a regular http parent page - the ReadCube checkout frame will always use SSL. Your purchases with ReadCube are always 100% SSL-encrypted and safe.
If you want to dig under the hood and check for yourself, please see below for a method to verify that your connection with ReadCube Checkout is SSL-secured:
Verify that a checkout frame is using SSL
In most web browsers, you can inspect the underlying code of a webpage. For example, in Chrome, you can right click on any part of a webpage and choose "Inspect Element." This brings up a hierarchical view of the current webpage.
Look for the sections containing ReadCube "checkout". In the readcube.com web reader, this part of the page is "sidenav/checkout.html".
In the section for the Checkout frame, you will see that frame link is always https (using SSL).