How do zero-knowledge proofs solve the three e-voting cheats while keeping ballots secret?

Each encrypted vote carries ZK proofs that the votes sum to exactly one, that it is a valid binary value, and that the voter actually knows the plaintext they submitted — all checkable without decrypting the ballot.

The three solutions map directly onto the three cheats:

• Proof the votes sum to 1: proves the voter selected exactly one option — neither more nor zero — defeating the "invalid sum" cheat.
• Proof of binary value: a ZK proof that the encrypted vote is exactly 0 or 1 — nothing else — kills the "invalid value" cheat.
• Proof you know your vote: the voter proves they actually know the plaintext (the vote, or its decryption key) behind the ciphertext they submitted, so they can't blindly copy and resubmit someone else's encrypted ballot — defeating the copy-paste attack.

Crucially, every proof is verified on the ciphertext — the system confirms the vote is well-formed and counted without ever seeing the plaintext choice. Secrecy and verifiability coexist.