That's implicitly assuming that you can't do cryptographic voting protocols with paper ballots. That is false. You can in fact make a cryptographic voting system where:
1. Voters vote by marking ovals with a marker pen on paper ballots.
3. The paper ballots can be counted by the optical scan machines that are already widely used in many places.
4. The paper ballots can be hand counted.
5. All the ballots can be published, allowing anyone to independently verify the counts.
6. An individual voter if they choose to can make a note of short alphanumeric code that is revealed when they vote for a candidate, and using that note later can verify that their vote was included in the total and went to the correct candidate.
7. An individual voter cannot prove to a third party that they voted for a particular candidate.
Almost all of the cryptographic mojo takes place when the ballots are printed, so no modifications are required to the scanners. You do have to use a special marker to mark the ballots.
Doing the cryptographic verification of all the votes would almost certainly be done by software, but as all the ballots are published and the system is completely open and documented, independent parties can easily do their own counts. The software is also fairly simple.
1. Voters vote by marking ovals with a marker pen on paper ballots.
3. The paper ballots can be counted by the optical scan machines that are already widely used in many places.
4. The paper ballots can be hand counted.
5. All the ballots can be published, allowing anyone to independently verify the counts.
6. An individual voter if they choose to can make a note of short alphanumeric code that is revealed when they vote for a candidate, and using that note later can verify that their vote was included in the total and went to the correct candidate.
7. An individual voter cannot prove to a third party that they voted for a particular candidate.
Here is a paper on such a system: https://eprint.iacr.org/2010/502.pdf
Wikipedia article on it: https://en.wikipedia.org/wiki/Scantegrity
Here is a paper showing how it satisfies item #7: https://eprint.iacr.org/2010/502
Almost all of the cryptographic mojo takes place when the ballots are printed, so no modifications are required to the scanners. You do have to use a special marker to mark the ballots.
Doing the cryptographic verification of all the votes would almost certainly be done by software, but as all the ballots are published and the system is completely open and documented, independent parties can easily do their own counts. The software is also fairly simple.