Cryptography for vote is super easy : each voter submits a secret prime number with the ballot and then the product of all such numbers is published together with the vote. It's as secret as factorization and everybody can check if their vote has been counted.
Does this stop multiple votes by same person? Votes by imaginary people? Does this stop keeping your secret prime number but discarding or changing your vote?
No, it also does not cure cancer and does not ensure the world peace. It only ensures that one can prove they voted and makes re-counting possible if needed.
Well, the grandparent's comment isn't asking if your scheme cures cancer and ensures world peace. Instead they're asking if your scheme is at least as secure as other current cryptographic voting protocols out there, the answer to which is "no."
If this problem were so trivial, then I think some of the big names in crypto would not have wasted their time on studying solutions. As it is, though, I don't think there are any convincing arguments for why this problem is "trivial." Instead, there's a laundry list of properties you want a good voting protocol to have, and developing a cryptographically secure protocol that satisfies those properties is highly nontrivial.
This scheme is more secure than paper ballots, which are advocated as better than the current cryptographic protocols, whichever they are. Better in a sense that every property of paper ballots can be also applied to the prime multiplication plus it allows verification that you cannot have with the paper ballots.
My opponent did not question particular properties of this scheme but instead went on the tangent of properties, which none of voting methods currently has. Hence, she or he could as well request cancer cure.
If we know all the primes issued by voters we can verify everything. It's a problem of splitting a set of primes between two disjoint sets. Knowing the product of both sets defines pretty much everything you want to know about them (including the fact that the sets are not disjoint or have members other than from the original set).
