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Efficient Receipt-Free
    Ballot Casting
 Resistant to Covert
      Channels
           Ben Adida
        C. Andrew Neff

         EVT / WOTE
       August 11th, 2009
       Montreal, Canada
Andy uses a voting machine
   to prepare a ballot.

 Andy wants to verify that
  the machine properly
  encrypted the ballot.
             2
Neff ’s MarkPledge
         and Moran-Naor.

           Two Problems.
1) 2 ciphertexts per challenge bit (40-50)
2) machine can use ballot to leak plaintext.



                     3
MarkPledge2
efficient ballot encoding:
2 ciphertexts for any challenge length
covert-channel resistance:
no leakage via the ballot.
voting machine is significantly simplified.
➡   simpler voting machine = less chance of errors.



                           4
Voter Experience




       5
Voter Experience
    Voter
   Check-in

Andy   _________
Ben    _________




                   5
Voter Experience
    Voter
   Check-in

Andy     VHTI
       _________
Ben    _________




                   5
Voter Experience
     Voter
    Check-in

Andy         VHTI
           _________
Ben        _________




 Hillary

 Barack

 John

 Bill



                       5
Voter Experience
     Voter
    Check-in

Andy         VHTI
           _________
Ben        _________




 Hillary

 Barack

 John

 Bill



                       5
Voter Experience
     Voter
    Check-in

Andy         VHTI
           _________
Ben        _________




 Hillary

 Barack                Barack
 John                  8DX5
 Bill



                                5
Voter Experience
     Voter
    Check-in

Andy         VHTI
           _________
Ben        _________




 Hillary

 Barack                Barack       Challenge?
 John                  8DX5
 Bill



                                5
Voter Experience
     Voter
    Check-in

Andy         VHTI
           _________
Ben        _________




 Hillary

 Barack                Barack       Challenge?
 John                  8DX5          VHTI
 Bill



                                5
Voter Experience
     Voter                                         Receipt
    Check-in
                                                 Hillary    MCN3
Andy         VHTI
           _________                             Barack     8DX5
Ben        _________                             John       I341
                                                 Bill       LQ21
                                                     Challenge

 Hillary                                             VHTI
 Barack                Barack       Challenge?
 John                  8DX5          VHTI
 Bill



                                5
Voter Experience
     Voter                                         Receipt
    Check-in
                                                 Hillary    MCN3
Andy         VHTI
           _________                             Barack     8DX5
Ben        _________                             John       I341
                                                 Bill       LQ21
                                                     Challenge

 Hillary                                             VHTI
 Barack                Barack       Challenge?
 John                  8DX5          VHTI
 Bill



                                5
Voter Experience
     Voter                                         Receipt
    Check-in
                                                 Hillary    MCN3
Andy         VHTI
           _________                             Barack     8DX5
Ben        _________                             John       I341
                                                 Bill       LQ21
                                                     Challenge

 Hillary                                             VHTI
 Barack                Barack       Challenge?
 John                  8DX5          VHTI
 Bill



                                5
Special Bit Encryption
 Hillary   0

 Barack    1
                   Encrypt a 0 or 1
 John
                   for each candidate
           0

 Bill      0
                   Special proof protocol
                   ➡ for bit b=1
                   ➡ meaningful short strings
                     as part of the commitment
                   ➡ short challenge strings
                     for real and simulated proofs



               6
Special Bit Encryption
     Hillary     0

     Barack      1
                            Encrypt a 0 or 1
     John
                            for each candidate
                 0

     Bill        0
                            Special proof protocol
                            ➡ for bit b=1
                            ➡ meaningful short strings
<ciphertexts>, "8DX5"
                              as part of the commitment
                            ➡ short challenge strings
                              for real and simulated proofs



                        6
Special Bit Encryption
     Hillary     0

     Barack      1
                            Encrypt a 0 or 1
     John
                            for each candidate
                 0

     Bill        0
                            Special proof protocol
                            ➡ for bit b=1
                            ➡ meaningful short strings
<ciphertexts>, "8DX5"
                              as part of the commitment
        "VHTI"              ➡ short challenge strings
                              for real and simulated proofs



                        6
Special Bit Encryption
     Hillary     0

     Barack      1
                            Encrypt a 0 or 1
     John
                            for each candidate
                 0

     Bill        0
                            Special proof protocol
                            ➡ for bit b=1
                            ➡ meaningful short strings
<ciphertexts>, "8DX5"
                              as part of the commitment
        "VHTI"              ➡ short challenge strings
                              for real and simulated proofs
  reveal enc factors



                        6
Voter Experience (II)
Hillary      0

Barack       1

John         0

Bill         0

                 7
Voter Experience (II)
                     <ciphertexts>, !!!!!!!!!!


Hillary      0
                     <ciphertexts>, "8DX5"

Barack       1
                     <ciphertexts>, !!!!!!!!!!

John         0
                     <ciphertexts>, !!!!!!!!!!

Bill         0

                 7
Voter Experience (II)
                     <ciphertexts>, !!!!!!!!!!


Hillary
                              "VHTI"
             0
                     <ciphertexts>, "8DX5"

Barack       1                "VHTI"



                     <ciphertexts>, !!!!!!!!!!

John         0                "VHTI"


                     <ciphertexts>, !!!!!!!!!!

Bill         0
                              "VHTI"




                 7
Voter Experience (II)
                     <ciphertexts>, "MCN3"


Hillary
                            "VHTI"
             0
                     <ciphertexts>, "8DX5"

Barack       1              "VHTI"



                     <ciphertexts>, "I341"

John         0              "VHTI"


                     <ciphertexts>, "LQ21"

Bill         0
                            "VHTI"




                 7
Voter Experience (II)
                     <ciphertexts>, "MCN3"


Hillary
                            "VHTI"
             0         reveal enc factors

                     <ciphertexts>, "8DX5"

Barack       1              "VHTI"
                       reveal enc factors

                     <ciphertexts>, "I341"

John         0              "VHTI"
                       reveal enc factors

                     <ciphertexts>, "LQ21"

Bill         0
                            "VHTI"
                       reveal enc factors




                 7
Voter Experience (II)
                     <ciphertexts>, "MCN3"


Hillary
                            "VHTI"           MCN3
             0         reveal enc factors

                     <ciphertexts>, "8DX5"

Barack       1              "VHTI"
                       reveal enc factors
                                             8DX5
                     <ciphertexts>, "I341"

John         0              "VHTI"
                       reveal enc factors
                                             I341
                     <ciphertexts>, "LQ21"

Bill         0
                            "VHTI"
                       reveal enc factors    LQ21
                 7
MarkPledge & Moran-Naor
   BitEnc(1)         0 0 1 1   ...   0 0

       Pledge        0    1    ...   0

    Challenge        1    1    ...   0

       Reveal        0 0 1 1   ...   0 0


          unique
   BitEnc(0)         1 0 0 1   ...   0 1
      that fits the
        challenge



                      8
Markpledge 2
  different bit encryption
  (α, β) ∈    Zq ,
               2
                     with α + β = 1
                          2   2

   ➡ isomorphic to SO(2, q)
   ➡ operation is rotation (matrix mult.)


  Designate 1-, 0-, and T-vectors
   ➡ any pair of a 1-vector and 0-vector
     bisected by a test vector
   ➡ dot-product with test vector.




          9
Same pattern emerges
                      MarkPledge         MarkPledge2

BitEnc(1)         0 0 1 1   ...    0 0     xi        yi

    Pledge        0    1    ...    0             i

 Challenge        1    1    ...    0         xC,yC

    Reveal        0 0 1 1   ...    0 0    xCxi + yCyi

                                          m0,i
                                                 chal
       unique
                                                        xi,yi
BitEnc(0)         1 0 0 1   ...    0 1
   that fits the
     challenge



                              10
Covert Channel
Raised by Karloff, Sastry & Wagner
If the voting machine chooses the
random factor, it can embed info
Can we make the voting machine
fully deterministic given a voter ID
and a selection in a given race?


                   11
Covert Channel
                  Ballot #42

              1   0 0 0 0
                               2, r'1
 Trustee #1
              0   0 1 0 0                    Ballot #42

                                              7 = 2 mod 5
                               1, r'2
 Trustee #2
              0   0 0 1 0                    r'1 + r'2 + r'3
                                                               Voting Machine
                               4, r'3
 Trustee #3
              0   0 1 0 0

                                                      Bulletin Board

                                                       Ballot #42
                                                0     0 1 0 0


Pre-generate ciphertexts with trustees
Rotate them on voter selection
                                        12
Why is this receipt-free?

What can the coercer ask the voter
to do that affects the ballot / receipt?
Only the challenge, which is selected
before the voter enters the booth.
All proofs will look the same,
whether real or simulated.


                    13
Questions?



14

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Efficient Receipt-Free Ballot Casting

  • 1. Efficient Receipt-Free Ballot Casting Resistant to Covert Channels Ben Adida C. Andrew Neff EVT / WOTE August 11th, 2009 Montreal, Canada
  • 2. Andy uses a voting machine to prepare a ballot. Andy wants to verify that the machine properly encrypted the ballot. 2
  • 3. Neff ’s MarkPledge and Moran-Naor. Two Problems. 1) 2 ciphertexts per challenge bit (40-50) 2) machine can use ballot to leak plaintext. 3
  • 4. MarkPledge2 efficient ballot encoding: 2 ciphertexts for any challenge length covert-channel resistance: no leakage via the ballot. voting machine is significantly simplified. ➡ simpler voting machine = less chance of errors. 4
  • 6. Voter Experience Voter Check-in Andy _________ Ben _________ 5
  • 7. Voter Experience Voter Check-in Andy VHTI _________ Ben _________ 5
  • 8. Voter Experience Voter Check-in Andy VHTI _________ Ben _________ Hillary Barack John Bill 5
  • 9. Voter Experience Voter Check-in Andy VHTI _________ Ben _________ Hillary Barack John Bill 5
  • 10. Voter Experience Voter Check-in Andy VHTI _________ Ben _________ Hillary Barack Barack John 8DX5 Bill 5
  • 11. Voter Experience Voter Check-in Andy VHTI _________ Ben _________ Hillary Barack Barack Challenge? John 8DX5 Bill 5
  • 12. Voter Experience Voter Check-in Andy VHTI _________ Ben _________ Hillary Barack Barack Challenge? John 8DX5 VHTI Bill 5
  • 13. Voter Experience Voter Receipt Check-in Hillary MCN3 Andy VHTI _________ Barack 8DX5 Ben _________ John I341 Bill LQ21 Challenge Hillary VHTI Barack Barack Challenge? John 8DX5 VHTI Bill 5
  • 14. Voter Experience Voter Receipt Check-in Hillary MCN3 Andy VHTI _________ Barack 8DX5 Ben _________ John I341 Bill LQ21 Challenge Hillary VHTI Barack Barack Challenge? John 8DX5 VHTI Bill 5
  • 15. Voter Experience Voter Receipt Check-in Hillary MCN3 Andy VHTI _________ Barack 8DX5 Ben _________ John I341 Bill LQ21 Challenge Hillary VHTI Barack Barack Challenge? John 8DX5 VHTI Bill 5
  • 16. Special Bit Encryption Hillary 0 Barack 1 Encrypt a 0 or 1 John for each candidate 0 Bill 0 Special proof protocol ➡ for bit b=1 ➡ meaningful short strings as part of the commitment ➡ short challenge strings for real and simulated proofs 6
  • 17. Special Bit Encryption Hillary 0 Barack 1 Encrypt a 0 or 1 John for each candidate 0 Bill 0 Special proof protocol ➡ for bit b=1 ➡ meaningful short strings <ciphertexts>, "8DX5" as part of the commitment ➡ short challenge strings for real and simulated proofs 6
  • 18. Special Bit Encryption Hillary 0 Barack 1 Encrypt a 0 or 1 John for each candidate 0 Bill 0 Special proof protocol ➡ for bit b=1 ➡ meaningful short strings <ciphertexts>, "8DX5" as part of the commitment "VHTI" ➡ short challenge strings for real and simulated proofs 6
  • 19. Special Bit Encryption Hillary 0 Barack 1 Encrypt a 0 or 1 John for each candidate 0 Bill 0 Special proof protocol ➡ for bit b=1 ➡ meaningful short strings <ciphertexts>, "8DX5" as part of the commitment "VHTI" ➡ short challenge strings for real and simulated proofs reveal enc factors 6
  • 20. Voter Experience (II) Hillary 0 Barack 1 John 0 Bill 0 7
  • 21. Voter Experience (II) <ciphertexts>, !!!!!!!!!! Hillary 0 <ciphertexts>, "8DX5" Barack 1 <ciphertexts>, !!!!!!!!!! John 0 <ciphertexts>, !!!!!!!!!! Bill 0 7
  • 22. Voter Experience (II) <ciphertexts>, !!!!!!!!!! Hillary "VHTI" 0 <ciphertexts>, "8DX5" Barack 1 "VHTI" <ciphertexts>, !!!!!!!!!! John 0 "VHTI" <ciphertexts>, !!!!!!!!!! Bill 0 "VHTI" 7
  • 23. Voter Experience (II) <ciphertexts>, "MCN3" Hillary "VHTI" 0 <ciphertexts>, "8DX5" Barack 1 "VHTI" <ciphertexts>, "I341" John 0 "VHTI" <ciphertexts>, "LQ21" Bill 0 "VHTI" 7
  • 24. Voter Experience (II) <ciphertexts>, "MCN3" Hillary "VHTI" 0 reveal enc factors <ciphertexts>, "8DX5" Barack 1 "VHTI" reveal enc factors <ciphertexts>, "I341" John 0 "VHTI" reveal enc factors <ciphertexts>, "LQ21" Bill 0 "VHTI" reveal enc factors 7
  • 25. Voter Experience (II) <ciphertexts>, "MCN3" Hillary "VHTI" MCN3 0 reveal enc factors <ciphertexts>, "8DX5" Barack 1 "VHTI" reveal enc factors 8DX5 <ciphertexts>, "I341" John 0 "VHTI" reveal enc factors I341 <ciphertexts>, "LQ21" Bill 0 "VHTI" reveal enc factors LQ21 7
  • 26. MarkPledge & Moran-Naor BitEnc(1) 0 0 1 1 ... 0 0 Pledge 0 1 ... 0 Challenge 1 1 ... 0 Reveal 0 0 1 1 ... 0 0 unique BitEnc(0) 1 0 0 1 ... 0 1 that fits the challenge 8
  • 27. Markpledge 2 different bit encryption (α, β) ∈ Zq , 2 with α + β = 1 2 2 ➡ isomorphic to SO(2, q) ➡ operation is rotation (matrix mult.) Designate 1-, 0-, and T-vectors ➡ any pair of a 1-vector and 0-vector bisected by a test vector ➡ dot-product with test vector. 9
  • 28. Same pattern emerges MarkPledge MarkPledge2 BitEnc(1) 0 0 1 1 ... 0 0 xi yi Pledge 0 1 ... 0 i Challenge 1 1 ... 0 xC,yC Reveal 0 0 1 1 ... 0 0 xCxi + yCyi m0,i chal unique xi,yi BitEnc(0) 1 0 0 1 ... 0 1 that fits the challenge 10
  • 29. Covert Channel Raised by Karloff, Sastry & Wagner If the voting machine chooses the random factor, it can embed info Can we make the voting machine fully deterministic given a voter ID and a selection in a given race? 11
  • 30. Covert Channel Ballot #42 1 0 0 0 0 2, r'1 Trustee #1 0 0 1 0 0 Ballot #42 7 = 2 mod 5 1, r'2 Trustee #2 0 0 0 1 0 r'1 + r'2 + r'3 Voting Machine 4, r'3 Trustee #3 0 0 1 0 0 Bulletin Board Ballot #42 0 0 1 0 0 Pre-generate ciphertexts with trustees Rotate them on voter selection 12
  • 31. Why is this receipt-free? What can the coercer ask the voter to do that affects the ballot / receipt? Only the challenge, which is selected before the voter enters the booth. All proofs will look the same, whether real or simulated. 13