数学代写|密码学作业代写Cryptography代考|CIS556

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数学代写|密码学作业代写Cryptography代考|HOW TO USE A VOTING SCHEME

While we have not followed this convention, it is sometimes convenient to distinguish between a scheme and a protocol in the following sense: The former is essentially a collection of (interactive) algorithms, perhaps with a few sets attached, while the latter is a collection of interactive algorithms attached to roles, along with a description of user sets and infrastructures the protocol relies on, such as networks and public key infrastructures, again perhaps with a few sets attached. For the former, the adversary is allowed to reveal key material, while for the latter the adversary corrupts players.

The objects we have studied so far in this book would all be cryptographic schemes under this classification. But when relevant there is mostly a trivial and obvious cryptographic protocol built on top of a public key infrastructure and some suitable network. It is also mostly obvious how the security properties of the cryptographic scheme imply security for the application. We have studied schemes instead of protocols because schemes are easier to analyse.
For voting schemes, it is far less obvious how to build a protocol, and in fact a single voting scheme can be used in different ways to achieve different election security goals. This section gives a brief overview of how we can build and analyse cryptographic voting protocols. We note that a proper discussion of these topics is no longer pure cryptography, but a multi-disciplinary study involving psychology, human-computer-interaction, game theory and other fields. This is beyond the scope of this book.

数学代写|密码学作业代写Cryptography代考|A Cryptographic Protocol

Design Figure 14.2 describes one possible way to use a cryptographic voting scheme to achieve useful election security properties. The election proceeds in three phases: setup, casting and counting.

During the setup phase, the setup algorithm is run by a trusted party, which distributes the ballot casting key to every player and one counting key share to each counter. This is not shown in the figure.

Remark. We do not want a trusted party to run the setup algorithm. Since this process happens before the election, it is usually not very time critical. Standard multiparty computation will usually be sufficient to distribute setup. Faster and more convenient methods are often available.

In the casting phase, the voters input their ballots to their ballot casting devices, which run the casting algorithm with appropriate associated data. The output and the associated data is given to the voter and the ballot box. The voters accept their ballots as cast when they receive the device output.
The ballot box serves as storage and conduit for encrypted ballots and their corresponding associated data and ballot proofs. When the counting phase starts, the ballot box selects the encrypted ballots to be counted and sends them to the first shuffle server. The ballot box will follow some for now unspecified rule to select the ballots, but in particular it will never select an encrypted ballot with a ballot argument that does not verify, nor will the ballot box select two ballots with identical associated data.

The shuffle servers simply apply the shuffle algorithm to the encrypted ballots they receive, passing the output encrypted ballots to the next shuffle server. The final shuffle server sends the output to the counters.

The counters run the counting algorithm on their counting key share and the encrypted ballots they receive, sending result shares to the auditor. The auditor runs the result reconstruction algorithm and announces the result.
In order to ensure that the encrypted ballots have been properly processed, the ballot box and the shuffle servers all send their inputs and outputs to all the counters, who individually verify this information before running the counting algorithm with their counting key shares. The counters include this information in the associated data they use. The auditor also receives and verifies this information, before running the reconstruction algorithm and making the result public.

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