The United States has some of the most sophisticated tech companies in the world. Does anyone really believe that Apple and Google working with the Government (NSA or other agency) could not develop a secure mobile voting app? Of course, they could. All it takes is common sense and a little bit of will.
For voting by app to work you would first have to have to verify the voter. This could easily be done by linking your national id (social security number but I am sure that the NSA could do better) to a face scan and a finger print. Today, we do this just to open our phone.
The next step would be to tie a voter to a location. Every election is tied to a location - Federal, State, city, and township. Geofencing could be used to tie a voter to their address. Your address could give you the appropriate ballot.
I would recommend that “Voting by App” would be limited to the weekend before that election in the voter’s home. This would give the voter the best chance to become informed. If a voter will be away on election day, they would follow absentee voting policy of their State.
Creating a robust secure system is beyond the capability of any single State. It would require a tight partnership between our top tech companies and the Federal Government. However, elections are the domain of the individual states. This authority includes what tools to use. Assuming a robust secure system and process can be created, the individual states could adopt it as a tool.