Warning: The entirety of this comment might be a bad idea.
There are 124 bits available. (Actually a little less but let's pretend only 4 bits are needed for the version to keep it simple.)
You'll have to decide how many are the ID and how many are the signature. Let's say 32 bits are your ID and the remaining 92 are the signature. (Adjust according to your own needs.)
Let's suppose your ID is 1. Now you need to hash that ID together with a private key using an HMAC algorithm. This signature will have more than 92 bits so trim your signature to this length.
Now build your UUID by combining the 32 bits of your ID with the 92 bits of the signature and four bits specifying version 8 (proprietary).
To test if a claimed UUID is yours, pull out the 32 bits of ID and repeat the process of signature and building a complete UUID. If the bits match, success! If not, its a fake UUID.
Now read the responses to this comment to find out why you shouldn't do this.