Coercion-Resistant Remote Voting

1. Coercion-Resistant Remote Voting JCJ and Civitas Michael ClarksonCornell University SecVote Summer School September 3, 2010 Coin (ca. 63 B.C.) commemorating introduction of secret ballot in 137 B.C.

4. Remote Voting

6. Receipt Freeness . Voters do not obtain information (a receipt) that proves how they voted. [Benaloh & Tuinstra 1994, Okamoto 1997, Delaune, Kremer & Ryan 2006, Jonker and Pieters 2006, Jonker and de Vink 2007, Backes, Hritcu & Maffei 2008, …]

7. Attacks • Randomization • Forced abstention • Simulation [Schoenmakers 2000, Juels, Catalano & Jakobsson 2005]

8. Coercion Resistance Coercer can observe and interact with voter during remote voting… …must prevent coercers from trusting their own observations… …must enable voters to lie to coercers.

9. Coercion Resistance The adversary cannot learn how voters vote, even if voters collude and interact with the adversary. (RF + defense against three attacks) [Juels, Catalano & Jakobsson 2005, Delaune, Kremer & Ryan 2006, Moran & Naor 2006, Backes, Hritcu & Maffei 2008, Küsters, Truderung & Vogt 2010]

10. JCJ Ari Juels, Dario Catalano & Markus Jakobsson.Coercion-resistant electronic elections. In Proc. Workshop in Privacy in the Electronic Society, 2005.

11. Civitas Michael Clarkson, Stephen Chong, Andrew Myers. Civitas: Toward a Secure Voting System.In Proc. IEEE Symposium on Security and Privacy, 2008.

12. Civitas LOC

13. JCJ Key techniques: • Coercion-resistant credentials • Plaintext equivalence test (PET)[Jakobsson & Juels 2000, MacKenzie, Shrimpton & Jakobsson 2002] Based on mix networks…

14. Mixnet Schemes • V → BB: sign(enc(vote; KT); kV) • Talliers: • check and remove signatures • mix votes • decrypt votes

15. JCJ V → BB: enc(cred; KT), enc(vote; KT) • Talliers: • Anonymize all submissions with mixnets • Remove submissions with unauthorized credentials • Decrypt votes

16. JCJ V → BB: enc(cred; KT), enc(vote; KT) Want voters to be able to fake credentials

17. Resisting Coercion

18. Resisting Coercion Defeats randomization attacks Defeats forced abstention attacks Defeats simulation attacks

19. CredentialsDesired Properties • Verifiable • Unsalable • Unforgeable • Anonymous

20. JCJ Scheme bulletinboard Registrar Tallier Voter

21. JCJ Scheme Registrar Tallier R1 T1 bulletinboard R2 T2 R3 T3 Voter

22. Assumption 0 At least one of each type of authority is honest (Needed for CR, not for verifiability)

23. JCJ Phases: • Setup • Registration • Vote submission • Tabulation

24. Setup Registrar Tallier R1 T1 bulletinboard R2 T2 R3 T3 Voter

25. Setup • Agree on El Gamal group G • Generate Tallier’s public encryption key KT, distribute private key kT • Post KT on BB

26. Assumption 1 DDH (also RSA, random oracle) Civitas

27. Registration Registrar Tallier R1 T1 bulletinboard R2 T2 R3 T3 Voter

28. Registration • Registrar: authenticate V • Registrar: s ← G • Registrar → BB: enc(s; KT) • Registrar → V [untap.]: s s = private credential enc(s) = S = public credential

29. Registration • Registrar: authenticate V • Registrar: s ← G • Registrar → BB: enc(s; KT) • Registrar → V [untap.]: s Electoral roll: list of all public credentials, signed by Registrar s = private credential enc(s) = S = public credential

30. Assumption 2 Initial voter authenticationis correct & Untappable channel (In person registration?)

31. Registration How many registrars? How trusted? • One, trusted • Many, untrusted

32. Registration One, untrusted registrar: 4. Registrar → V [untap.]: s, DVP(“S encrypts s”, V)

33. DVP Designated Verifier Proof [Jakobsson, Sako & Impagliazzo 1996] DVP(Φ, A) proves in ZK that “Φ holds, or prover knows A’s private key”

34. Registration One, untrusted registrar: 4. Registrar → V [untap.]: s, DVP(“S encrypts s”, V) DVP ensures proof isn’t receipt

35. Registration Civitas Many, untrusted registrars: For each registrar Ri: • Ri: authenticate V • Ri: si ← G • Ri → BB: enc(si; KT) which is Si • Ri → V [unt.]: si, DVP(“Si encrypts si”, V) …

36. Registration Civitas …Voter calculates credential: s = ∏isi S = ∏iSi S= ∏iSi = ∏ienc(si) = enc(∏isi) = enc(s)

37. Faking Credentials Voter V: • Picks registrar Ri • Substitutes new ŝi for si • Invents DVP(“Si encrypts ŝi”, V)

38. Assumption 3 Trusted Ri (Need untappable channel only to that registrar.)

39. CredentialsDesired Properties • Verifiable ✓ • Unsalable ✓ • Unforgeable✓ • Anonymous

40. Vote Submission Registrar Tallier R1 T1 bulletinboard R2 T2 R3 T3 Voter

41. Vote Submission • V: select choice (candidate) c • V → BB [anon.]: enc(s; KT), enc(c; KT)

42. Assumption 4 Anonymous channel

43. Assumption 5 Voter client doesn’t leak credential & Voter client encrypts correctly

44. Assumption 5 Voter client doesn’t leak credential & Voter client encrypts correctly

45. Vote Submission • V: select choice (candidate) c • V → BB [anon.]: enc(s; KT), enc(c; KT) Problems: replay attacks, malformed choices

46. Vote Submission • V: select choice (candidate) c • V → BB [anon.]: enc(s; KT), enc(c; KT) Problems: replay attacks, malformed choices Solution: zero-knowledge proofs

47. Vote Submission • V: select choice (candidate) c • V → BB [anon.]: enc(s; KT), enc(c; KT), Pk,Pw Pk: signature of knowledge[Camenisch & Stadler 1997] Pw: 1-out-of-L reencryption proof [Hirt & Sako 2000]

48. Vote Submission • V: select choice (candidate) c • V → BB [anon.]: enc(s; KT), enc(c; KT), Pk,Pw Problem: scalability, reliability of BB

49. Vote Submission • V: select choice (candidate) c • V → BB [anon.]: enc(s; KT), enc(c; KT), Pk,Pw Problem: scalability, reliability of BB Solution: distributed ballot boxes Civitas

50. Vote Submission Registrar Tallier R1 T1 bulletinboard R2 T2 R3 T3 Voter