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 random.org) 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.