PRESENTED BY CHRIS ANDERSON JULY 29, 2009 Using Zero Knowledge Proofs to Validate Electronic Votes

Outline What is the problem? What does zero knowledge mean? Neff’s scheme Challenging the encrypted vote Conclusion

The Problem Trust Two secure voting requirements contradict each other when dealing with e-voting  Privacy  Verifiability Receipt-freeness & uncoercibility

What Does Zero-Knowledge Mean? Task: Prove to a verifier that some fact is true. Parties Involved  Prover  Verifier Follows a challenge/response protocol Rules:  Verifier accepts proof if it is true and both parties follow protocol  Verifier rejects proof it is false and verifier has followed protocol  The prover reveals nothing about the fact that the verifier could not determine without the prover Verifier is unable to prove same fact to someone else

Neff’s Scheme Zero-knowledge protocol developed by Andrew Neff Cast vote is represented by a n x l matrix of ballot match pairs(BMP) called a verifiable choice(VC)  n=number of candidates  l=security parameter Each BMP consists of a pair of plain text b 1, b 2 in {0,1} which are encrypted using a random value If the BMP belongs to the row for the chosen candidate, the BMP will be 0,0 or 1,1 If the BMP belongs to a row for a candidate who was not chosen, the BMP will be 0,1 or 1,0

Verifiable Choice

Neff’s Scheme Voter challenges the candidate by submitting a bit string with length l Each BMP has a pledge bit used to compare BMP with voter’s challenge string If k th bit in string = 0, compare BMP left element to pledge bit If k th bit in string = 1, compare BMP right element to pledge bit

Challenging the Chosen Candidate

Challenging the Other Candidates

Conclusion Neff’s scheme allows voter to verify correctness Solves a major hurdle with e-voting systems Questions?

References Ben Adida. Advances in Cryptographic Voting Systems, Veneta Velyanova. An Analysis Of The Neff’s Voter Verifiable Election Scheme, 2008.