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How Elections Should Really Be Run
Josh BenalohSenior CryptographerMicrosoft Research
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Disclaimer
Any opinions presented in this talk are my own and do not necessary represent those of the Microsoft Corporation or any subsidiary or partner thereof.
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The Year Is …
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2
Sophisticated Mathematics
0 54 2008.00
1.99 Remainder appears to be statistically near to zero.
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This year …
… there will be a U.S. Presidential election.
(Don’t tell, maybe no one will notice.)
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The Current Voting Landscape
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The Current Voting Landscape
• Hand-Counted Paper
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The Current Voting Landscape
• Hand-Counted Paper• Punch Cards
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The Current Voting Landscape
• Hand-Counted Paper• Punch Cards• Lever Machines
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The Current Voting Landscape
• Hand-Counted Paper• Punch Cards• Lever Machines• Optical Scan Ballots
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The Current Voting Landscape
• Hand-Counted Paper• Punch Cards• Lever Machines• Optical Scan Ballots• Touch-Screen Terminals
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The Current Voting Landscape
• Hand-Counted Paper• Punch Cards• Lever Machines• Optical Scan Ballots• Touch-Screen Terminals• Various Hybrids
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Vulnerabilities and Trust
• All of these systems have substantial vulnerabilities.
• All of these systems require trust in the honesty and expertise of election officials.
Can we do better?
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End-to-End Voter-Verifiability
As a voter, I can be sure that• My vote is
– Cast as intended– Counted as cast
• All votes are counted as cast… without having to trust anyone or
anything.
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Lloyd Bentsen Syndrome:
I know computers…I’ve worked with computers…You cannot trust computers.
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More specifically …
There are a million ways to tamper with software:
• Insider attacks• Exploitation of bugs and vulnerabilities• Configuration errors• etc.How can one trust an election to software?
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A Web-Based Election
• Voters post their names and votes to a public web site.
• Anyone who cares to do so can– Check that their own votes are correctly posted– Check that other voters are legitimate– Check that the totals are correct
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But wait …
This isn’t a secret-ballot election.Quite true, but it’s enough to show
that voter-verifiability is possible … and also to falsify arguments
that electronic elections are inherently untrustworthy.
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Privacy
• The only ingredient missing from this “toy” web-based election is privacy – and the things which flow from privacy (e.g. protection from coercion).
• Performing tasks while preserving privacy is the bailiwick of cryptography.
• Cryptographic techniques can enable end-to-end verifiable elections while preserving voter privacy.
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End-to-End Verifiable Elections
• Voters post their names and encrypted votes to a public web site.
• At the end of the election, administrators post the tally together with a cryptographic proof that the tally “matches” the set of encrypted votes.
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End-to-End Verifiable Elections
• Anyone who cares to do so can– Check that their own encrypted votes are
correctly posted– Check that other voters are legitimate– Check the cryptographic proof of the
correctness of the announced tally
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Is it Really This Easy?
Yes …
… but there are lots of details to get right.
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Some Important Details
• How is the ballot encryption and decryption done?
• How is the cryptographic proof of the tally done?
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Fundamental Tallying Decision
You have essentially two paradigms to choose from …
• Anonymized Ballots (Mix Networks)• Ballotless Tallying (Homomorphic Encryption)
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Anonymized Ballots
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Ballotless Tallying
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Pros and Cons of Ballots
• Ballots simplify write-ins.
• Ballots make it harder to enforce privacy.
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BallotlessTallying
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The Homomorphic Paradigm
Benaloh (Cohen), Fischer (1985) …
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The Homomorphic Paradigm
Tally
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The Homomorphic Paradigm
Tally
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Homomorphic Encryption
It is possible to construct public-key encryption functions such that if A is an encryption of a and B is an encryption of b then AB is an encryption of a+b.
(AE(a)) (BE(b)) (ABE(a+b))
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Homomorphic Encryption
In particular, given an encryption ME(m) , one can create a different M’E(m) by generating an encryption of zero ZE(0) and forming M’=MZ.
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Homomorphic Encryption
Some Homomorphic Functions
• RSA: E(m) = me mod n• ElGamal: E(m,r) = (gr,mhr) mod p• Benaloh: E(m,r) = rxgm mod n• Pallier: E(m,r) = rngm mod n2
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Homomorphic Techniques
Alice 0Bob 0
Carol 1David 0
Eve 1
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Homomorphic Techniques
Alice 0Bob 0
Carol 1David 0
Eve 1
=
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Homomorphic Techniques
Alice 0Bob 0
Carol 1David 0
Eve 1
=2
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Homomorphic Techniques
Alice 0Bob 0
Carol 1David 0
Eve 1
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Homomorphic Techniques
Alice 0Bob 0
Carol 1David 0
Eve 1
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Homomorphic Techniques
Alice 0Bob 0
Carol 1David 0
Eve 1
=2
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Homomorphic Techniques
Alice 0Bob 0
Carol 1David 0
Eve 1
=2
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Homomorphic Techniques
The product of the encryptions of the votes constitutes an encryption of the sum of the votes.
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The Homomorphic Paradigm
Tally
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AnonymizedBallots
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The Mix-Net Paradigm
Chaum (1981) …
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The Mix-Net Paradigm
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The Mix-Net Paradigm
MIX
Vote
Vote
Vote
Vote
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The Mix-Net Paradigm
MIX
Vote
Vote
Vote
Vote
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A Re-encryption Mix
MIX
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A Re-encryption Mix
MIX
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Verifiability
The mix provides a proof that its output is a permutation of re-encryptions of its input.
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Multiple Re-encryption Mixes
MIX
Vote
Vote
Vote
Vote
MIX
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Verifiability
Each re-encryption mix provides a mathematical proof that it’s output is a permutation of re-encryptions of its input.
Any observer can verify this proof.The decryptions are also proven to be correct.If a mix’s proof is invalid, its mixing will be
bypassed.
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Faulty Mixes
MIX
Vote
Vote
Vote
Vote
MIX
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A Simple Verifiable Re-encryption Mix
Input Ballot Set Output Ballot Set
MIX
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Operation of a Re-encryption Mix
Input Ballot Set Output Ballot Set
MIX
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MIX
Operation of a Re-encryption Mix
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27182818
31415926
16180339
14142135
81828172
62951413
93308161
53124141
Operation of a Re-encryption Mix
Inputs Outputs
81828172
62951413
93308161
53124141
81828172
62951413
93308161
53124141
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Re-encryption
• Each value is re-encrypted by multiplying it by an encryption of zero.
• This can be done without knowing the decryptions.
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27182818
31415926
16180339
14142135
81828172
62951413
93308161
53124141
Verifying a Re-encryption
MIX27182818
31415926
16180339
14142135
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A Simple Verifiable Re-encryption Mix
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Is This “Proof” Absolute?
• The proof can be “defeated” if and only if every left/right decision can be predicted by the prover in advance.
• If there are 100 intermediate ballot sets, the chance of this happening is 1 in 2100.
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Who Chooses?
If you choose, then you are convinced.But this won’t convince me.
We can each make some of the choices.But this can be inefficient.
We can co-operate on the choices.But this is cumbersome.
We can agree on a random source.But what source?
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Who Chooses?
The Fiat-Shamir Heuristic• Prepare all of the ballot sets as above.• Put all of the data into a one-way hash.• Use the hash output to make the choices.
This allows a proof of equivalence to be “published” by the mix.
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Mix-Net Properties
• The integrity of a mix-net is not dependent on any unproven assumptions – only the inability of a mix to predict the challenges it receives (except possibly the hash).
• Privacy in a mix-net is dependent upon the mixes and is no better than that provided by the encryption – a cryptographic break-through could compromise privacy.
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So WhatAbout BallotEncryption?
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The Encryption Phase
How can voters turn their intentions into encrypted ballots?
Any device that can perform this task could have vulnerabilities, intentional back doors, be subject to viruses, etc.
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Prêt à Voter Ballot
Joe SmithJohn CitizenJane DoeFred RubbleMary Hill
17320508
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The Encryption Phase
Requirements of ballot encryption devices
• Must accurately encrypt voter intentions• Need not know voter identities• Need not authenticate voters right to vote• Need not limit people to a single use• Need not cast votes
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Auditing
Note that it’s not necessary for all voters to audit vote encryption devices – a tiny random fraction of voters and/or election inspectors can suffice.
E.g. 100 random auditing events would probably detect a 1% fraud rate.
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Unstructured Auditing
• Anyone … voter/inspector/observer is free to create votes at any time during an election.
• Any “uncast” votes are opened (decrypted) for verification.
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In Practice?
Typical Voter• Go to a polling station, sign in, receive a token.• Go to a stand-alone voting station.• Enter preferences interactively.• Receive a printed encryption of the completed ballot.• Get the question: “Do you want to cast this ballot?”• Answer “yes” and insert token to receive a copy of the
encrypted ballot on the token signed as good for casting.• Leave token with poll worker.• Take printed receipt home and (if desired) use it to verify
on-line that the vote hasn’t been altered.
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In Practice?
Suspicious Voter or Observer• Go to a voting station.• Enter preferences interactively.• Receive a printed encryption of the completed
ballot.• Get the question:
“Do you want to cast this ballot?”• Answer “no” and receive a printed verifiable
decryption of the encrypted ballot.• [Later] Verify the decryption of the ballot.• [Optional] Verify the posted ballot mixing and
decryptions using posted proofs.
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In Practice?
Election Officials• Receive all votes and post them on-line (perhaps
even together with voter names).• Allow anyone to (sequentially) scramble (mix) the
votes and provide a proof of correct mixing. Post all such mixings and proofs on-line.
• Have the final mixed ballots decrypted together with proof of correct decryption. Post the decryptions together with their proofs.
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Properties
• Cryptographically verified election technologies can achieve universal end-to-end verifiabilty, while pure paper and “voter-verifiable paper audit trail (VVPAT)” systems only provide administrative and limited voter verifiability.
• This is a substantially different paradigm that emphasizes certification of elections rather than election equipment.
• The integrity of a cryptographic election can be verified externally without ever having to inspect the system hardware or software.
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Scorecard
CryptoBased
PaperBased
Accuracy/ Verifiability
Privacy/ Coercibility
Robustness/ Availability
Usability/ Voter Error
Overall
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Scorecard
CryptoBased
PaperBased
Accuracy/ Verifiability
Fully end-to-end verifiable by anyone
Voter can only verify as far as ballot box
Privacy/ Coercibility
Robustness/ Availability
Usability/ Voter Error
Overall
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Scorecard
CryptoBased
PaperBased
Accuracy/ Verifiability
Fully end-to-end verifiable by anyone
Voter can only verify as far as ballot box
Privacy/ Coercibility
Cannot be proven absolutely
Cannot be proven absolutely
Robustness/ Availability
Usability/ Voter Error
Overall
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Scorecard
CryptoBased
PaperBased
Accuracy/ Verifiability
Fully end-to-end verifiable by anyone
Voter can only verify as far as ballot box
Privacy/ Coercibility
Cannot be proven absolutely
Cannot be proven absolutely
Robustness/ Availability
Wholesale failure is possible
Only retail failure is possible
Usability/ Voter Error
Overall
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Scorecard
CryptoBased
PaperBased
Accuracy/ Verifiability
Fully end-to-end verifiable by anyone
Voter can only verify as far as ballot box
Privacy/ Coercibility
Cannot be proven absolutely
Cannot be proven absolutely
Robustness/ Availability
Wholesale failure is possible
Only retail failure is possible
Usability/ Voter Error
Fully-interactive voting device
Paper
Overall
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Scorecard
CryptoBased
PaperBased
Accuracy/ Verifiability
Fully end-to-end verifiable by anyone
Voter can only verify as far as ballot box
Privacy/ Coercibility
Cannot be proven absolutely
Cannot be proven absolutely
Robustness/ Availability
Wholesale failure is possible
Only retail failure is possible
Usability/ Voter Error
Fully-interactive voting device
Paper
Overall ? ?
![Page 82: How Elections Should Really Be Run](https://reader036.vdocuments.net/reader036/viewer/2022062521/568168d0550346895ddfc082/html5/thumbnails/82.jpg)
Conclusions
• Keep an open mind.
• Think critically.
• Vote!
![Page 83: How Elections Should Really Be Run](https://reader036.vdocuments.net/reader036/viewer/2022062521/568168d0550346895ddfc082/html5/thumbnails/83.jpg)
Resources
Seehttp://research.microsoft.com/crypto/voting/ for some pointers to further information.