Here's how I see this can work. I am going to generalize this quite a bit. Every registered voter who wants to sign up for mobile voting would have to go sign up. Just register for online or mobile voting. Also, the voter would have to provide a passcode. Again, this will have to be online.
Then the voter would get a special letter from the government with a special code authorizing online voting. This letter would also have a randomly generated code that the voter must enter along with the passcode they created when they sign up for online voting. If they match, the voting process can begin.
Okay again, I'm generalizing. I'm sure you folks out there will have a better scheme for mobile voting and can come up with a better security system for doing this. Right now, each time I sign in to do banking, I am emailed a code by my bank each time I log in from a different PC. I'm fine when it's on my mobile apps from the bank.
Also, Google has added security layer when you sign into Google accounts. They can text you a passcode that you have to enter after you've entered your login name and password. Perhaps there are even more robust security measure. You can be asked a series of questions before you start voting.
But I think it's time we start exploring mobile voting. Right now, I think this works better than voting on your PC given the greater security risks. And if we do this in the United States, we would not be alone. Estonia did it as far back as 2007.
Heck, Astronauts already do this from space. Here are more examples of other countries allowing online voting via Wikipedia. So, this has been done. If the government is still by the people and for the people, it's time we make this happen.