Punchscan

A marked Punchscan ballot. Full ballot (top), separated ballot (bottom).

A Punchscan ballot has two layers of paper. On the top layer, the candidates are listed with a symbol or letter beside their name. Below the candidate list, there are a series of round holes in the top layer of the ballot. Inside the holes on the bottom layer, the corresponding symbols are printed.

To cast a vote for a candidate, the voter must locate the hole with the symbol corresponding to the symbol beside the candidate's name. This hole is marked with a Bingo-style ink dauber, which is purposely larger than the hole. The voter then separates the ballot, chooses either the top or the bottom layer to keep as a receipt, and shreds the other layer. The receipt is scanned at the polling station for tabulation.

The order of the symbols beside the candidate names is generated randomly for each ballot, and thus differs from ballot to ballot. Likewise for the order of the symbols in the holes. For this reason, the receipt does not contain enough information to determine which candidate the vote was cast for. If the top layer is kept, the order of the symbols through the holes is unknown. If the bottom layer is kept, the order of the symbols beside the candidates name is unknown. Therefore, the voter cannot prove to someone else how they voted, which prevents vote buying or voter intimidation.

As an example, consider a two candidate election between Coke and Pepsi, as illustrated in the preceding diagram. The order of the letters beside the candidates' names could be A and then B, or B and then A. We will call this ordering ${\displaystyle P_{1}}$, and let ${\displaystyle P_{1}}$=0 for the former ordering and ${\displaystyle P_{1}}$=1 for the latter. Therefore,

${\displaystyle P_{1}}$: order of symbols beside candidate list,

${\displaystyle P_{1}\in \{0,1\}=\{{\mbox{AB}},{\mbox{BA}}\}\,}$.

Likewise we can generalize for other parts of a ballot:

${\displaystyle P_{2}}$: order of symbols through the holes,

${\displaystyle P_{2}\in \{0,1\}=\{{\mbox{AB}},{\mbox{BA}}\}\,}$.

${\displaystyle P_{3}}$: which hole is marked,

${\displaystyle P_{3}\in \{0,1\}=\{{\mbox{1st}},{\mbox{2nd}}\}\,}$.

${\displaystyle R}$: result of the ballot,

${\displaystyle R\in \{0,1\}=\{{\mbox{Coke}},{\mbox{Pepsi}}\}\,}$.

Note that the order of the candidates' names are fixed across all ballots. The result of a ballot can be calculated directly as,

${\displaystyle R=P_{1}+P_{2}+P_{3}{\bmod {2}}\,}$ (Equation 1)

However, when one layer of the ballot is shredded, either ${\displaystyle P_{1}}$ or ${\displaystyle P_{2}}$ is destroyed. Therefore, there is insufficient information to calculate ${\displaystyle R}$ from the receipt (which is scanned). In order to calculate the election results, an electronic database is used.

Before the election, the database is created with a series of columns as such. Each row in the database represents a ballot, and the order that the ballots are stored in the database is shuffled (using a cryptographic key that each candidate can contribute to). The first column, ${\displaystyle D_{1}}$, has the shuffled order of the serial numbers. ${\displaystyle D_{2}}$ contains a pseudorandom bitstream generated from the key, and it will act as a stream cipher. ${\displaystyle D_{3}}$ will store an intermediate result. ${\displaystyle D_{4}}$ contains a bit such that:

${\displaystyle D_{2}+D_{4}=P_{1}+P_{2}{\bmod {2}}\,}$

The result of each ballot will be stored in a separate column, ${\displaystyle R}$, where the order of the ballots will be reshuffled again. Thus ${\displaystyle D_{5}}$ contains the row number in the ${\displaystyle R}$ column where the result will be placed.

After the election is run and the ${\displaystyle P_{3}}$ values have been scanned in, ${\displaystyle D_{3}}$ is calculated as:

${\displaystyle D_{3}=P_{3}+D_{2}{\bmod {2}}\,}$

And the result is calculated as,

${\displaystyle R=D_{3}+D_{4}{\bmod {2}}\,}$

This is equivalent to equation 1,

${\displaystyle {\begin{aligned}R&=(D_{3})+D_{4}{\bmod {2}}\\&=(P_{3}+D_{2})+D_{4}{\bmod {2}}\\&=P_{3}+(D_{2}+D_{4}){\bmod {2}}\\&=P_{3}+(P_{1}+P_{2}){\bmod {2}}\end{aligned}}}$

The result column is published and given the ballots have been shuffled (twice), the order of the results column does not indicate which result is from which ballot number. Thus the election authority cannot trace votes to serial numbers.

The voter's ballot receipt does not indicate which candidate the voter cast their ballot for, and therefore it is not secret information. After an election, the election authority will post an image of each receipt online. The voter can look up their ballot by typing in the serial number and they can check that information held by the election authority matches their ballot. This way, the voter can be confident that their ballot was cast as intended.

Any voter or interested party can also inspect part of the database to ensure the results were calculated correctly. They cannot inspect the whole database, otherwise they could link votes to ballot serial numbers. However, half of the database can be safely inspected without breaking privacy. A random choice is made between opening ${\displaystyle \{D_{1},D_{2},D_{3}\}}$ or ${\displaystyle \{D_{3},D_{4},D_{5}\}}$ (this choice can be derived from the secret key or from a true random source, such as dice[2] or the stock market[3]). This procedure allows the voter to be confident that the set of all ballots were counted as cast.

If all ballots are counted as cast and cast as intended, then all ballots are counted as intended. Therefore, the integrity of the election can be proven to a very high probability.

To further increase the integrity of a Punchscan election, several further steps can be taken to protect against a completely corrupt election authority.

• Stream cipher
• Commitment scheme
• Zero-knowledge proof

• Project home page
• Vocomp Submission — a comprehensive 80-page document explaining all aspects of the system
• Electronic Democracy — BBC World's Digital Planet audio interview with David Chaum.
• Making Every E-vote Count — IEEE Spectrum.
• Transparent and Open Voting with Punchscan: Part I and Part II
• Future Tense audio interview with David Chaum.