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Cryptographic elections
Alon RosenIDC Herzliya
September 14th, 2008
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Thanks
• Ben Adida (Harvard University)
• Yuval Kedem (Gallileo)
• David Movshovitz (IDC Herzlyia)
• Shimon Schocken (IDC Herzlyia)
• Amnon Ta-Shma (Tel Aviv University)
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This Talk
! Current voting technology has serious flaws.
! Voting is hard.
! Commonly proposed solutions fall short.
! Cryptographic voting has the potentialto revolutionize how we audit elections.
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http://www.nytimes.com/2008/01/06/magazine/06Vote-t.html
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Voting in the US
http://www.cs.uiowa.edu/~jones/voting/pictures/
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Voting in the US
http://www.cs.uiowa.edu/~jones/voting/pictures/
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Voting in the US
http://www.cs.uiowa.edu/~jones/voting/pictures/
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Voting in the US
http://www.cs.uiowa.edu/~jones/voting/pictures/
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Voting in the US
http://www.cs.uiowa.edu/~jones/voting/pictures/
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Voting in the US
http://www.cs.uiowa.edu/~jones/voting/pictures/
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Voting in the US
http://www.cs.uiowa.edu/~jones/voting/pictures/
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• HAVA - Help America Vote Act
• 4 Billion dollars allocated
• Mostly to replace voting machines
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• HAVA - Help America Vote Act
• 4 Billion dollars allocated
• Mostly to replace voting machines
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The Princeton Report
• Diebold touch-screen runs executable code loaded from memory card
• All audit logs modifiedto be consistent
• Can spread virally by memory card.
[FHF2006]
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• New Mexico (March 2006)
• California (August 2007)
• Florida (December 2007)
• Ohio (January 2008)
• Iowa (March 2008)
• ...
• States that mandate paper trail.
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http://xkcd.com/463/
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• Simple and reliable system
• Voter secrecy
• Quick count
• And in addition: transparency (open audit).
What does Everbody Want?
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What is Transparency?
Anyone can verify that:
• their vote was cast as intended
• the votes were count as cast
And, in case of a problem, can recount and obtain the correct result (e.g. paper trail)
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Paper vs. Electronic
Electronic elections today:
• Global attacks
• Undetectable
• Unrecoverable
• No transparency
Paper elections:
• Local attacks
• No transparency
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Paper vs. Electronic
Electronic elections today:
• Global attacks
• Undetectable
• Unrecoverable
• No transparency
Paper elections:
• Local attacks
• No transparency
Ideally:
• No local/global attacks
• Full transparency
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Software Independence [Rivest, Wack’06]
“A voting system is software independent if an undetected change or error in its software cannot cause an undetectable change or error in an election outcome”
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Examples
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Examples
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Non-examples
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Non-examples
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The Israeli Perspective
• Nov ’07 - Pilot of electronic voting with touch screens in several municipalities.
• Nov ’07 - Minister of interior announces plan to move to electronic elections
• Apr ’08 - TEHILA are given mandate to run pilot in 3 municipalities in Oct ’08 election.
• Aug’08 - Speedy legislation underway to accommodate pilot.
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The process:
• No public scrutiny
• No open design
The result:
• No paper trail
• No software independence
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Why is Votingso Hard?
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The Point of An Election
“The People have spoken....the bastards!”
Dick Tuck1966 Concession Speech
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The Point of An Election
“The People have spoken....the bastards!”
Dick Tuck1966 Concession Speech
Provide enough evidenceto convince the loser.
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Secret Ballot vs. Verifiability
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Secret Ballot vs.Verifiability
Voting System
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Secret Ballot vs.Verifiability
Voting System
Alice
convince
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Secret Ballot vs.Verifiability
Voting System
Alice
convince
Carl the Coercer
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Secret Ballot vs.Verifiability
Voting System
Alice
convince
Carl the Coercer
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Desired Properties
(1)Alice verifies her vote.
(2)Everyone verifies tallying.
(3)Alice cannot be coerced by Eve.
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http://www.cs.uiowa.edu/~jones/voting/pictures/
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http://www.cs.uiowa.edu/~jones/voting/pictures/
1892 - Australian Ballot
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The Breakfast Election
Salty Sweet
http://www.flickr.com/photos/35034346243@N01/91524057/
http://en.wikipedia.org/wiki/Image:FoodOmelete.jpg
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The Ballot Handoff
Alice the Voter
Sweet
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The Ballot Handoff
Alice the Voter
Sweet
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The Ballot Handoff
Alice the Voter
Sweet
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The Ballot Handoff
Alice the Voter
Sweet
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Salty
Sweet
Salty
SweetSweet
The Ballot Handoff
Alice the Voter
Sweet
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Salty
Sweet
Salty
SweetSweet
The Ballot Handoff
Alice the Voter
Sweet
Black Box
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Chain of Custody
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Chain of Custody
Vendor
/*
* source
* code
*/
if (...
1
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Chain of Custody
VotingMachine
2
Vendor
/*
* source
* code
*/
if (...
1
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Chain of Custody
VotingMachine
2
Vendor
/*
* source
* code
*/
if (...
1
Polling Location
3
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Chain of Custody
VotingMachine
2
Vendor
/*
* source
* code
*/
if (...
1
Polling Location
3L
4
Alice
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Chain of Custody
VotingMachine
2
Vendor
/*
* source
* code
*/
if (...
1
Polling Location
3L
4
Alice
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Chain of Custody
VotingMachine
2
Vendor
/*
* source
* code
*/
if (...
1
Polling Location
3
Ballot Box Collection
5
L
4
Alice
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Chain of Custody
VotingMachine
2
Vendor
/*
* source
* code
*/
if (...
1
Polling Location
3
Ballot Box Collection
5
Results
.....6
L
4
Alice
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Chain of Custody
VotingMachine
2
Vendor
/*
* source
* code
*/
if (...
1
Polling Location
3
Ballot Box Collection
5
Results
.....6
4
Alice
VotingVVMachine
2
VendorVV
/*
* source
* code
*/
if (...
1
Polling Location
3L
4 Paper Trail Bypass
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Chain of Custody
VotingMachine
2
Vendor
/*
* source
* code
*/
if (...
1
Polling Location
3
Ballot Box Collection
5
Results
.....6
4
Alice
VotingVVMachine
2
VendorVV
/*
* source
* code
*/
if (...
1
Polling Location
3L
4 Paper Trail Bypass
Black Box
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The Cost of Secrecy
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The Cost of Secrecy
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The Cost of Secrecy
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The Cost of Secrecy
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The Cost of Secrecy
![Page 70: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/70.jpg)
Is Secrecy Important?
![Page 71: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/71.jpg)
Is Secrecy Important?
“Secret ballots and transparency in government are mutually exclusive concepts.”
Lynn Landes - Nov. 2005
![Page 72: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/72.jpg)
Is Secrecy Important?
“Secret ballots and transparency in government are mutually exclusive concepts.”
Lynn Landes - Nov. 2005
http://votebymailproject.org
![Page 73: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/73.jpg)
Is Secrecy Important?
“Secret ballots and transparency in government are mutually exclusive concepts.”
Lynn Landes - Nov. 2005
http://votebymailproject.org
![Page 74: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/74.jpg)
Is Secrecy Important?
“Secret ballots and transparency in government are mutually exclusive concepts.”
Lynn Landes - Nov. 2005
http://votebymailproject.org
![Page 75: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/75.jpg)
Actually, it is.
Secret Ballot implemented in Chile in 1958.
“the secrecy of the ballot [...] has first-order implications for resource
allocation, political outcomes, and social efficiency.”
[BalandRobinson 2004]
![Page 76: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/76.jpg)
So what can we do?
![Page 77: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/77.jpg)
Cryptographic (open audit) elections
[Chaum81], [Benaloh85], [PIK93], [BenalohTuinstra92], [SK94], [Neff2001] ,[FS2001], [Chaum2004], [Neff2004], [Ryan2004], [Chaum2005], [MoranNaor06], [Rivest2006],[CCCEPRRSS20080]
Cryptography provides more than confidentiality.
Cryptography can provide verifiabilitywhile mantaining ballot secrecy.
Anyone can audit!
![Page 78: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/78.jpg)
Bulletin Board
Public Ballots
Bridget:Sweet
Carol:Salty
![Page 79: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/79.jpg)
Bulletin Board
Public Ballots
Bridget:Sweet
Carol:Salty
Alice
![Page 80: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/80.jpg)
Bulletin Board
Public Ballots
Alice:Sweet
Bridget:Sweet
Carol:Salty
Alice
![Page 81: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/81.jpg)
Bulletin Board
Public Ballots
Alice:Sweet
Bridget:Sweet
Carol:Salty
Tally
Sweet.......2Salty..........1
Alice
![Page 82: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/82.jpg)
Encrypted Public BallotsBulletin Board
Alice:Rice
Bridget:Clinton
Carol:Rice
Tally
Sweet.......2Salty..........1
Alice
![Page 83: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/83.jpg)
Encrypted Public BallotsBulletin Board
Alice:Rice
Bridget:Clinton
Carol:Rice
Tally
Sweet.......2Salty..........1
Alice
Alice verifies her vote
![Page 84: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/84.jpg)
Encrypted Public BallotsBulletin Board
Alice:Rice
Bridget:Clinton
Carol:Rice
Tally
Sweet.......2Salty..........1
Alice
Alice verifies her voteEveryo
ne verifies the tally
![Page 85: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/85.jpg)
How can we verify operations on
encrypted data?
![Page 86: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/86.jpg)
Public-Key Encryption
![Page 87: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/87.jpg)
Public-Key Encryption
Keypair consists of a public key and a secret key .skpk
![Page 88: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/88.jpg)
Public-Key Encryption
Keypair consists of a public key and a secret key .skpk
"Salty" 8b5637Encpk
![Page 89: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/89.jpg)
Public-Key Encryption
Keypair consists of a public key and a secret key .skpk
"Salty" 8b5637Encpk
c5de34Encpk"Sweet"
![Page 90: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/90.jpg)
Public-Key Encryption
Keypair consists of a public key and a secret key .skpk
"Salty" 8b5637Encpk
c5de34Encpk"Sweet"
a4b395Encpk"Salty"
![Page 91: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/91.jpg)
Threshold Decryption
8b5637
Secret key is shared amongst multiple parties:all (or at least a quorum) need to cooperate to decrypt.
![Page 92: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/92.jpg)
Threshold Decryption
8b5637
b739cbDecsk1
Secret key is shared amongst multiple parties:all (or at least a quorum) need to cooperate to decrypt.
![Page 93: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/93.jpg)
Threshold Decryption
8b5637
b739cbDecsk1
261ad7Decsk2
Secret key is shared amongst multiple parties:all (or at least a quorum) need to cooperate to decrypt.
![Page 94: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/94.jpg)
Threshold Decryption
8b5637
b739cbDecsk1
261ad7Decsk2
7231bcDecsk3
Secret key is shared amongst multiple parties:all (or at least a quorum) need to cooperate to decrypt.
![Page 95: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/95.jpg)
Threshold Decryption
8b5637
b739cbDecsk1
261ad7Decsk2
7231bcDecsk3
8239baDecsk4
Secret key is shared amongst multiple parties:all (or at least a quorum) need to cooperate to decrypt.
![Page 96: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/96.jpg)
Threshold Decryption
8b5637
b739cbDecsk1
261ad7Decsk2
7231bcDecsk3
8239baDecsk4
"Salty"
Secret key is shared amongst multiple parties:all (or at least a quorum) need to cooperate to decrypt.
![Page 97: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/97.jpg)
The Voting Process
![Page 98: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/98.jpg)
Alice
Identification
2
Polling stationcommittee
![Page 99: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/99.jpg)
Alice
Identification
2
ID
Polling stationcommittee
![Page 100: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/100.jpg)
Alice
Identification
2
ID
Ballot(s)
Polling stationcommittee
![Page 101: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/101.jpg)
The Ballot
Fold
Tear
![Page 102: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/102.jpg)
Alice
+
Producing Encrypted Ballot
![Page 103: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/103.jpg)
Alice
+
Producing Encrypted Ballot
![Page 104: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/104.jpg)
Alice
+
Producing Encrypted Ballot
![Page 105: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/105.jpg)
Alice
+
Producing Encrypted Ballot
Sweet
![Page 106: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/106.jpg)
Encrypted Ballot
Sweet Sweet
![Page 107: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/107.jpg)
Ballot Casting
1
![Page 108: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/108.jpg)
Ballot Casting
1
2
![Page 109: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/109.jpg)
Ballot Casting
4
Alice
3
1
2
![Page 110: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/110.jpg)
Ballot Casting
4
Alice
3
1
2
Receipt4
![Page 111: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/111.jpg)
Homomorphic Tabulation
Enc(m1)× Enc(m2)= Enc(m1 + m2)
![Page 112: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/112.jpg)
Homomorphic Tabulation
Yes = Enc(1)
No = Enc(0)
Enc(m1)× Enc(m2)= Enc(m1 + m2)
![Page 113: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/113.jpg)
Homomorphic Tabulation
Yes = Enc(1)
No = Enc(0)
Bulletin Board
Alice:Bridget:
Carol:
Enc(ma)Enc(mb)
Enc(mc)
Enc(m1)× Enc(m2)= Enc(m1 + m2)
![Page 114: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/114.jpg)
Homomorphic Tabulation
Yes = Enc(1)
No = Enc(0)
Bulletin Board
Alice:Bridget:
Carol:
Enc(ma)Enc(mb)
Enc(mc)
EncryptedTally = Enc(ma)× Enc(mb)× Enc(mc)
= Enc(ma + mb + mc)
Enc(m1)× Enc(m2)= Enc(m1 + m2)
![Page 115: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/115.jpg)
Verifying Validity of Encryption
Given Enc(m) How can I verify that it is not an encryption of more than one vote?
Zero-Knowledge proofs: Can prove validity of Enc(m) without revealing anything else!
Revolutionary concept: only need to verify that machine is computing right functionality...
![Page 116: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/116.jpg)
Verifying Consistency [Benaloh]
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
![Page 117: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/117.jpg)
Verifying Consistency [Benaloh]
Alice
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
![Page 118: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/118.jpg)
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
![Page 119: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/119.jpg)
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
![Page 120: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/120.jpg)
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
![Page 121: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/121.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
![Page 122: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/122.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
![Page 123: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/123.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
DecryptedBallot
EncryptedBallot
VERIFICATION
![Page 124: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/124.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
DecryptedBallot
EncryptedBallot
VERIFICATION
![Page 125: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/125.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
DecryptedBallot
EncryptedBallot
VERIFICATION
"AUDIT"
Alice
DecryptedBallot
DecryptedBallot
EncryptedBallot
VERIFICATIONVERIFICAVERIFICA
![Page 126: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/126.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
Alice
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
DecryptedBallot
EncryptedBallot
VERIFICATION
"AUDIT"
Alice
DecryptedBallot
DecryptedBallot
EncryptedBallot
VERIFICATIONVERIFICAVERIFICA
![Page 127: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/127.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
Alice
"CAST"
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
DecryptedBallot
EncryptedBallot
VERIFICATION
"AUDIT"
Alice
DecryptedBallot
DecryptedBallot
EncryptedBallot
VERIFICATIONVERIFICAVERIFICA
![Page 128: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/128.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
Alice
"CAST"
SignedEncryptedBallot
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
DecryptedBallot
EncryptedBallot
VERIFICATION
"AUDIT"
Alice
DecryptedBallot
DecryptedBallot
EncryptedBallot
VERIFICATIONVERIFICAVERIFICA
![Page 129: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/129.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
Alice
"CAST"
SignedEncryptedBallot
Alice
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
DecryptedBallot
EncryptedBallot
VERIFICATION
"AUDIT"
Alice
DecryptedBallot
DecryptedBallot
EncryptedBallot
VERIFICATIONVERIFICAVERIFICA
![Page 130: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/130.jpg)
"AUDIT"
Verifying Consistency [Benaloh]
Alice
"Vote for Sweet"
EncryptedBallot
Alice
DecryptedBallot
Alice
"CAST"
SignedEncryptedBallot
Alice
http://en.wikipedia.org/wiki/Image:Barcode-scanner.jpg
SignedEncryptedBallot
DecryptedBallot
EncryptedBallot
VERIFICATION
"AUDIT"
Alice
DecryptedBallot
DecryptedBallot
EncryptedBallot
VERIFICATIONVERIFICAVERIFICA
![Page 131: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/131.jpg)
Putting It Together
Voting Equipment & Ballot Flow
Verification
![Page 132: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/132.jpg)
Putting It Together
Voting Equipment & Ballot Flow
Verification
Polling Location
VotingMachine
Vendor
/*
* source
* code
*/
if (...
![Page 133: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/133.jpg)
Putting It Together
Voting Equipment & Ballot Flow
Verification
Polling Location
VotingMachine
Vendor
/*
* source
* code
*/
if (...
Public
Ballot Box
Alice
![Page 134: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/134.jpg)
Putting It Together
Voting Equipment & Ballot Flow
Verification
Polling Location
VotingMachine
Vendor
/*
* source
* code
*/
if (...
Results
.....
Public
Ballot Box
Alice
![Page 135: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/135.jpg)
Putting It Together
Voting Equipment & Ballot Flow
Verification
Polling Location
VotingMachine
Vendor
/*
* source
* code
*/
if (...
Receipt
1
Results
.....
Public
Ballot Box
Alice
![Page 136: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/136.jpg)
Putting It Together
Voting Equipment & Ballot Flow
Verification
Polling Location
VotingMachine
Vendor
/*
* source
* code
*/
if (...
Receipt
1 2
Results
.....
Public
Ballot Box
Alice
![Page 137: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/137.jpg)
Open-Audit Elections
• Alice verifies her vote.
• Everyone verifies the tally.
• Incoercibility is enforced.
![Page 138: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/138.jpg)
Open-Audit Elections
• Alice verifies her vote.
• Everyone verifies the tally.
• Incoercibility is enforced.
Anyone can Audit.
![Page 139: Cryptographic elections - OWASP · The Israeli Perspective • Nov ’07 - Pilot of electronic voting with touch screens in several municipalities. • Nov ’07 - Minister of interior](https://reader033.vdocuments.us/reader033/viewer/2022042017/5e756672e8fe83789f328779/html5/thumbnails/139.jpg)
Questions?