Zero Knowledge Proofs

Zero-Knowledge Proofs

What are Zero-Knowledge Proofs?

A Zero-Knowledge Proof is a type of cryptographic tool that allows someone to prove that a mathematical operation was carried out correctly without revealing any private information involved in the mathematical operation.

This property is particularly useful in situations where the prover has some sensitive information that they don't want to share, but still want to demonstrate the validity of the information to the verifier.

SIV's Zero-Knowledge Proofs

SIV uses multiple Zero-Knowledge Proofs (ZKPs) to prove that an election is correctly conducted, that every vote was counted, and it all added up to one person winning with a particular total.

SIV's two main Zero Knowledge Proofs are:

  1. In Step 4: Zero Knowledge Proof of a Valid Shuffle
  2. In Step 5: Zero Knowledge Proof of a Valid Partial Decryption

These ZK Proofs, in particular the Shuffle Proof, come from Dr. Andrew Neff's 2001 paper "A Verifiable Secret Shuffle and its Application to E-Voting (opens in a new tab)". They are used to safely implement a cryptographic mixnet, so that votes can be anonymized by multiple indepedent parties, without risk that any of the parties could have possibly switched out or modified any of the underlying vote content.

During Steps 4 and 5, every election Privacy Protector who takes part in the cryptographic shuffle generates their own ZK Proofs. All of these proofs are automatically verified by SIV itself and all of the other Privacy Protectors.

SIV also enables a third ZK Proof: Proof of Voting in a SIV Election, without revealing the underlying vote. This proof is not required to carry out a SIV election, but it can be used to strengthen Post-Election Audits, as well as enabling further civic participation with strong authentication.

Defense in Depth

Although these Zero Knowledge Proofs are incredibly powerful, and allow independent verifiers to confirm the entire set of all votes at once, we must also acknowledge they are highly technical and involve a high barrier for understanding. For this reason, they are intentionally not the only method to confirm that SIV results are correct. SIV also provides the far simpler Personal Voter Verification methods, based on Verification #s, that are quick to check and easy to understand, and widely accessible for all voters to gain confidence.

Further Reading

For further study of Steps 4 & 5 of a SIV election: