Do Photoshop have portable version?

Online authentication on any computer is how the Creative Cloud apps for desktop and mobile already work. Any time you are in front of a random computer that meets the system requirements and you have admin access to, you can install and online activate Photoshop on that computer.

For example, you can install Photoshop on any number of Windows or Mac computers you want. The limitation is that only two of those installations can be activated for your account at any time, and that activation is, as you said, online authentication. As long as a computer has Internet access, you can easily deauthenticate the installation on one computer and authenticate another computer at any time so that the two computer limit is not exceeded.

So the online authentication part is not the obstacle, they have already had that in place and working for years. The real obstacle is Adobe has chosen not to make the application fully portable. It is partially portable in that you can have it install on a volume other than the C drive. But it is not totally portable in that the Creative Cloud background processes are still installed and run from the boot volume, and user configuration and preferences are still installed and retrieved from the user account folder on the C drive.