secret ballot receipts true voter-verifiable elections richard carback kevin fisher sandi lwin cmsc...

Secret Ballot ReceiptsTrue Voter-Verifiable Elections

Richard CarbackKevin Fisher

Sandi Lwin

CMSC 691vApril 3, 2005

IntroductionSystem Features

•Magic receipt•Vote visible in voting booth•Vote invisible, verifiable outside voting booth

•Trusted voting machines unnecessary•Provisional ballots are ballots, too•Vote from anywhere•Adjudicate today, adjudicate tomorrow•Deeper, more restful sleep•Eliminates common indoor allergens

•Even pet dander!•Boosts gas mileage up to 13%

System from Voter’s Perspective

•Input with touch screen or other input means

•Register printer generates printout• List names of candidate• party affiliations• office sought• others


•Print votes before the final inch

•Printer prints simultaneously both layers

•Review printout

•Indicate layer to keep

•Printer prints final inch


•Printer cuts both layers off, still laminated together and releases them

•Neither layer readable on its own

•Light passing through sandwiched layers without printings on either layers makes choices visible

Example of Ballot Printout

Figure 1. An example part of a ballot printout listing a candidate selected. In

addition to being able to include the candidate’s name, party affiliation, and

office sought, the printout can also include other types of contests and various graphics

options.

Example of Final Inch Together

Figure 2. Last inch of the printout before the two laminated layers are

separated.

Final Inch Separated

Figure 3. Last inch of the printout after it’s separated: (a) the receipt (the layer the voter selects to keep) and (b) the layer

that’s shredded before the voter leaves the polling place.

Leaving the Polling Booth

•Voter gives up the layer marked for surrender

•Layer gets shredded by poll worker

•Same layers get shredded “electronically”

•Only physical layer voter kept and digital version of that same image remains

Election Web Site

•Enter receipt’s serial # to check vote has been counted

•Print image on website and check against the actual receipt

Resistance to Attack

•Posted Receipt == Proper Tabulation (Most likely)

•Votes are private (unless code is broken)

•Malicious Software can only hope:–user will choose one layer–noone will check serial numbers–tally will not be audited

Weaknesses to Attack

•Subliminal Channels•Selectively Malicious DRE•Discarded Receipts•Malicious Tally Software

Visual Cryptography 101Typography

+ =

Newsprinte+ =

Ballot Receipt

Visual Cryptography 101PixelsNewsprint Ballot Receipt

= 0

= 1

0 1=

=

=

=

0

0

1

1

0

1

0

1

0

1

1

0

=

=

=

=

Visual Cryptography 101Message Encoding

+ =

RandomWhite Sheet

=

+ ][

+

Visual Cryptography 101White Sheet Vulnerability

Single encoded message yieldsmultiple plaintext images.

Visual Cryptography 101Mixing Red and White Sheets

+ =

=+

Tabulation

•All receipts are posted•Each trustee decodes a batch

•Batches randomized to protect privacy

Russian Nesting Dolls

•Voted Ballot == Set of dolls (or one big doll)•Each trustee opens one size of dolls•Smallest doll is plaintext ballot

Coded Sheets

•How you do this with computers•Big doll is the summation of the smaller permutations•Each trustee subtracts their permutation mod 2•Original permutation revealed at smallest doll

Tabulation Integrity

•Need to maintain privacy•Each trustee is video-taped doing 2 batches•1 tape is released

–chosen afterwards (auditor or political parties)

Formal Receipt ProcessVoting Phase – Step 1

Ballot image B

President: LincolnSenator: Kennedy

milkeggs

LINCOLN

General Election

Senator:

President:

KENNEDY

Ballot Number 8675309

Separate layers before leaving booth.

Plaintext receipt


< LZ , q , Dt , Db >

Printed 4-tuples



General Election

q: serial number

LZ: ballot layer

Dt: top dollDb: bottom doll



General Election


< Lt , q , Dt , Db >

Visual XOR function

LINCOLN

General Election

Senator:

President:

KENNEDY



< Lb , q , Dt , Db >

=< B , q , Dt , Db >

Mathematical XOR function


Bottom layer: x=bBallot Number 8675309


General Election



General Election

Top layer: x=t


Bottom layer: x=bSeed: sx(q)



General Election

Overall: ox(Lx,q,Dt,Db,sx(q))

“Last Inch”Digital Signature

< sx(q) , ox(Lx,q,Dt,Db,sx(q)) >


Part 1

sx(q)



General Election Consistency Check

(sx)-

1

hash

q


Part 2

sx(q)



General Election

ox(Lx,q,Dt,Db,sx(q))

Consistency Check

(ox)-1

hash

q

hash

Db

hash

Dt

hash

Lx

Formal Receipt ProcessRed and White Matrices



General Election

m

nn/2 n/2

WZRZ




General Election



General Election

Top Layer Bottom Layer

Wt = Lti,[2j – ([i+1]

mod 2)]Rt = Lti,[2j – (i mod 2)] Rb = Lb

i,[2j – ([i+1]

mod 2)]

Wb = Lbi,[2j – (i mod 2)]

WtRt RbWb




General Election



General Election

Top Layer Bottom Layer

Bx = Rx Wy

WtRt RbWb

Formal Receipt ProcessCryptographic Pseudorandom Number Generators

Ballot ID

Key

12345

Ciphertext

AES

AES

12346

1010100..10

0100111..00

N bits

Formal Receipt ProcessCalculating the Noise Matrix

WZi,j = (dZ

k dZk-1 … dZ

1)[mj–

m]+1dZ

k = h’(d’Z

k)d’Z

k = h(sZ(q), k)

sZ(q)

Pseudorandom sequence

h’

h dZk =

101010..110k

Cryptographic pseudorandom number generators

m*n/2 bits

WZi,j = 1

01

010

110

..

n/2

m

Formal Receipt ProcessDoll Construction

d’Zk= doll

ksZ(q)

Pseudorandom sequence

h’

h dZk =

101010..110k

Cryptographic pseudorandom number generators

d’Z

1

)e1

(e2(d’Z

2, ))DZk = ek(d’Z

k, …

Formal Receipt ProcessTally Phase: Doll Processing

DL-1

DL

dL DL

dL

DL-1

d’L-1

eL

h’d’L-1 dL-1

DL-1

dL-1

dZL-1 = h’(d’Z

L-1)

Formal Receipt ProcessTally Phase: Auditing

Stage k k-1 k-2 k-3 k-4

Audit batches

Cryptography

•Computationally secure–breakable with enough computing power applied

•Unconditionally secure–cannot be broken even with applying infinite computing power

Cryptography

•Receipt system uses:–Computationally secure encryption to form layers

•Digital signatures:–last inch contains digital signature for authentication–scanners used to verify signature

Cryptography

•Privacy–Protects privacy using computationally secure encryption.

Cost of System

•Reduces cost of integrity while raising its level dramatically•Hardware cost lower than current black box system

–Government buy at price of open platform PC

•Cost of suitable printers in volume is less than hardware cost saving•Savings in maintenance and upgrades

Similarities in Punchscan

•Splitting the ballot is the same idea–Destroy half the information

•Tabulation is more complicated, but similar to that of Punchscan

–privacy is kept in a similar manner (only choose half of the process to look at)

Similarities in Punchscan

•Definitely an advancement

•Has some security problems at the system level

–not insurmountable

•Kind of complicated

•Not expandable–rank-order would be hard–Not the most scalable

secret ballot receipts true voter-verifiable elections richard carback kevin fisher sandi lwin cmsc...

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