I would like to give customers a random-looking order number but use 0, 1, 2, … in the backend. That way the customer gets a non-password-protected order status URL with the encrypted order number and they cannot look at other customers’ order numbers by adding or subtracting 1. This might replace a scheme where random order keys are generated, checked for uniqueness among all the previous orders, and re-generated until unique. When the web server gets a request to view an order, it decrypts the order number and retrieves the order.
To keep the URL short, what ‘good’ encryption algorithm has the shortest block size? Is this scheme a good idea? (What if I was encrypting Apple, Inc. employee ids to keep Steve Jobs from asking for Employee #0?)
Observe that all the package tracking websites allow you to track packages without authentication. It would be fine to limit the amount of information shown on the password-free order status page.
Most block ciphers are going to use larger than 32-bit sized blocks, for security reasons.
However, I found one that is made specifically for what you are doing: Skip32
You may consider using a GUID, but perhaps you have reasons you want to avoid that. (Say, your app is done already.)
Edit: Actually, if a GUID is permissible, then that gives you a range of 128 bits. You could easily use any other block cipher. The benefit to having a larger space (at the cost of long ID strings) is that you’ll have much more protection from people guessing IDs. (Not that it an order ID by itself should be a security token anyways…)