1) The document proposes an improved method called MarkPledge2 for efficient receipt-free voting that addresses problems with previous methods.
2) MarkPledge2 uses a more efficient ballot encoding that requires only 2 ciphertexts for any challenge length, providing covert-channel resistance by preventing ballot information from being leaked.
3) This simpler approach significantly simplifies the voting machine design, reducing the chances of errors.
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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
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
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
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