Map incrementing integer range to six-digit base 26 max, but unpredictably

Question

I want to design a URL shortener for a particular use case and type of end-user that I have targetted. I have decided that I want the URLs to be stored internally according

Answer 1

You need a Block Cipher with "Block Space" of 26⁶.

Choose an arbitrary key for the cipher, and you now have a transformation that is reversible by you, yet unpredictable for everyone else.

Your block size is a bit unusual, so you probably won't find a ready-made good block cipher for your size. But as suggested by kquinn you can design one on your own that mimics other ciphers.