Shouldn't be signatures.
Should be thumbprints.
The voter should have to submit a thumbprint to register to vote, and that print must be matched against the database of US citizens before the registration is allowed.
Then the thumbprint must be scanned at the poll, in person, before the paper ballot is issued. And the thumb should be then inked so it cannot again be scanned that day, after the ballot is read into the machine.
Also, why the heck not, the thumbprint should be accessible to law enforcement agencies after the election in case the cops are looking for felons or other Democrats on the run who like to vote.