Can I make my own geocache based upon Geodyssey?

Sure. The easiest way (but certainly not the only way) is to create a puzzle cache that requires the solver to complete the Remote Challenge. On the Remote Challenge Final Page is a 1,024-character one-time pad (randomly generated using that can be used to encrypt your own message that leads your solvers to your cache. See my Geodyssey geocache (GC5CJ31) for an example. FYI: Rumkin has an excellent free tool for encrypting and decrypting messages with one-time pads.