excerpt from: Did Your Vote Count? New Coded Ballots May Prove It Did By Sara Robinson , New York Times, March 2, 2004

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With frogs, as with a voter-verified paper trail, voters would still have to trust people to secure the counting process. Mathematical voting systems - developed independently by Dr. Neff and Dr. David Chaum, an independent cryptographer and privacy expert - would ensure that votes were correctly counted, even in the presence of untrustworthy machines and officials.

These systems, based on two decades of cryptography research, would simultaneously satisfy the opposing demands for ballot secrecy and voter records.

Though the two systems differ in several technical respects, they would have similar overall structures. In each system, the counting process would be performed publicly on the Internet. The voters themselves and third party observers would ensure election integrity, and a group of election officials, called trustees, would protect ballot secrecy.

After voting, each voter would receive a receipt - a record of his choices that would be encrypted, or put into code, and could be deciphered only by a collaboration of all the election trustees. After polls closed, all receipts would be posted on the Internet. Each voter could use his serial number to find the image of his receipt, and make sure it matched the one he carried.

Each trustee would perform one step toward decoding the receipts, and the decrypted ballots would also be posted on the Internet, where anyone could count them, but without serial numbers so they could no longer be traced to individual voters. Still, voters and observers who understood the process could mathematically verify that no ballots were added, lost or altered.
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Emanuele Lombardi opinion: I don't think Mathematical voting systems could really solve any problem.

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excerpt from:
Ballot Boxes Go High Tech: From touch screens to digital 'frogs,' technology to make voting more secure is tricky, but it's coming
By Steven Levy, Newsweek, March 29, 2004

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With clever cryptographic algorithms and innovative viewing devices, it's possible to envision a process that provides specific proof after the fact that your vote was included in the total - without compromising the privacy of your selection.

Cryptographer David Chaum, who wrote the first papers on computer-based anonymous voting in the early 1980s, has been experimenting with such schemes. (He's behind the aforementioned VoteMeter.) His latest iteration is Votegrity, involving a device in addition to standard technology (like a touch screen). When you cast your vote, this device generates three images, or "stripes" bar-code-like objects with encoded information. Each stripe contains your vote in encrypted form, but by some form of mathematical magic, when overlaid on top of each other, the stripes display your selections in plain language. As you vote, this readable output is projected on a small screen inside the voting booth so you can check it for accuracy. Then the paper is divided to separate the stripes, and voters may choose which one to take with them. That same image is stored digitally, and officials will use it to register the actual vote. The decryption process involves techniques to ensure that the votes counted are the same ones the voters saw in the booth.

Where's your verification? The codes are all posted to the Web, and using the encoded receipt and a serial number also printed on the paper, you can go online to check that your encrypted vote was tallied. (Of course, since the image is encrypted, no one can know how you voted.) "The Chaum system is the better ballot box," says Mercuri. "It's the first solution that proves to someone that his or her vote counts."
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Emanuele Lombardi opinion: I still don't think Mathematical voting systems could really solve any problem.