Question about HTTPS

I am a newbie to the Arduino world.

I want to start a project with arduino that will talk to a RESTful service when a button is pressed.

This seems easy as long as I am not talking over HTTPS.

Looking around it seems the arduino is not powerful enough to handle https. If that is the case what are my alternatives?

I know I could set up a local proxy to a server and send the HTTPS that way, but I would rather make the device without this dependency.

Is the Intel Edison an answer to this problem?