End-to-End Verifiability for Ranking-based E-Voting Systems

有许多不同的制度来进行选举或公民投票并决定其结果。一种比较流行的选举制度是多数制：得票最多的候选人赢得选举。我们使用“得票最多者当选”（FPTP）一词来指选举单一成员或政党的多元化制度。FPTP经常被批评产生的结果不代表其参与者所投的选票;大党往往代表过多，而小党往往代表不足。排名投票系统的存在是为了提供比多数系统更公平和更有代表性的结果。孔多塞方法是一种排名投票系统，它使用所有选择之间的成对比较来宣布赢家，但循环模糊性可能会导致没有赢家。排名投票系统的另一个例子是单一可转移投票（Single Transferable Vote，STV），其目的是通过允许选民直接对他们的选择进行排名来实现代表性。STV选举多个获胜者，所以如果选民的第一个选择没有在STV下获胜，那么他们的投票将被应用于他们的下一个最高排名的选择。重复这个过程，直到所有的选择都被用尽。虽然我们可以在许多不同的投票系统之间做出决定，但在这些系统中投票的方式很少。传统的投票方法是亲自到当地投票站投票。一个人不能前往当地投票站投票的情况往往有多种原因：一个人可能住得离投票站太远，一个人的工作时间可能与投票站的工作时间冲突，残疾人可能难以到达投票站。一些投票系统允许以邮寄选票的形式进行远程投票;然而，这些通常需要在选举前几个月登记邮寄投票，邮寄延迟可能会延迟投票。这激发了对在本地投票是不可能的情况下可用的安全的远程电子投票（e-voting）系统的需要。这些远程投票系统应该是端到端（E2 E）可验证的，并且不具有统计权限，允许选民验证他们的选票是按预期投出的，并且验证每一张选票都被正确地统计以产生选举结果，而不需要信任潜在的腐败权限（诸如DRE-ip），然而，缺乏用于基于排名的系统（包括Condorcet和STV）的这种协议。该项目的目标是：1。探索E2 E验证没有理货当局孔多塞方法; 2。扩大对STV的探索; 3.为正在进行的电子投票试验作出贡献。

There are many different systems for conducting and deciding the result of an election or referendum. One of the more popular electoral systems is the plurality system: the candidate with the most votes wins the election. We use the term "First Past the Post" (FPTP) to refer to a plurality system which elects a single member or party. FPTP is often criticized for producing results which are unrepresentative of the votes cast by its participants; large parties are often over-represented whilst smaller parties are often under-represented. Ranked voting systems exist to provide a fairer and more representative result compared to plurality systems. The Condorcet method is one ranked voting system which uses pairwise comparisons between all choices to declare a winner, however circular ambiguities may result in no winner. Another example of a ranked voting system is Single Transferable Vote (STV), which aims to achieve representation by allowing voters to rank their choices directly. STV elects multiple winners, so if a voter's first choice does not win under STV, then their vote is applied to their next highest ranked choice. This process repeats until all choices are exhausted. Whilst we may decide between many different voting systems, there are few ways to cast votes within these systems. The traditional method involves voting in person at a local polling station. It is often the case that a person cannot visit their local polling station to cast their vote for many reasons: a person may live too far away from their polling station, a person's working hours may clash with those of the polling station and individuals with disabilities may find it difficult to reach their polling station. Some voting systems allow remote voting in the form of posted ballots; however, these often require registering for a postal vote some months in advance of an election and postal delays may delay the vote. This motivates the need for a secure, remote electronic voting (e-voting) system usable in the case where local voting is impossible. These remote voting systems should be End-to-End (E2E) verifiable and have no tallying authority, allowing voters to verify that their votes were casted as intended and to verify that every vote was tallied correctly to produce the result of the election, without the need to trust a potentially corrupt authority.E2E verifiable voting systems without tallying authorities have been proposed for FPTP (such as DRE-ip), however there is a lack of such protocols for ranking based systems including Condorcet and STV. The aims of this project are to: 1. Explore E2E verifiability without tallying authorities for the Condorcet method; 2. Extend the exploration for STV; 3. Contribute to ongoing trials for e-voting.