摘  要:密电子投票技术已经发展了40多年，但在实际应用中仍然面临潜在的安全问题。主要的挑战是如何设计一个令选民信任的系统。以密码学为核心技术，本论文试图对电子投票的设计作全面的回顾。我们介绍了3类基本电子投票协议和2类高级投票协议中关键技术；总结了无收据、抗胁迫性等开放性问题。研究了当前区块链等技术在投票设计中的应用，与未来发展方向。我们希望这篇论文可以作为电子投票设计的一个很好的介绍。

关键词:密码学;盲签名;混合网络;同态加密;抗胁迫性;区块链;

Abstract: Electronic voting technology has been developed for more than 40 years.  However, there is still a long way to go before practical applications.  The main challenge is how to design a system that makes voters trust.  With cryptography as the core technology, this paper attempts to make a comprehensive review of the design of electronic voting.  We introduced three types of basic electronic voting protocols and two types of key technologies in advanced voting protocols; we concluded that receipt-free and coercion-resistance are still open issues.  The application of current blockchain and other technologies in voting design and the future development direction are studied.  We hope this paper can serve as a good introduction to electronic voting design.

Key words: Cryptography; Blind signature; mix network; Homomorphic encryption; coercion-resistance; Blockchain;

1. Introduction

The electronic voting technology has undergone more than 40 years of development and has achieved outstanding results both in theory and practice.  Compared with paper voting, electronic voting has the characteristics of low cost and fast counting.  The majority electronic voting system allows voters to vote online remotely, which improves the voter participation rate and voting management efficiency, which is of great significance to the promotion of the democratic process.  An electronic voting system is a system that directly records votes in electronic form.  It has gone through such a process, from punch card voting, optical identification voting, to direct recording electronic voting system, and now remote online voting[1].  In 1981, Chaum proposed the first cryptographically significant electronic voting scheme, which inspired the research enthusiasm of electronic voting.  In 1995, Horster et al. proposed the theory of electronic election protocol  based which  the Sensus system[2]and the EU Cybervote system had been achieved. Subsequently, the United States, South Korea, English, Japan, Estonia and other countries all actively implemented electronic voting.  During the local elections in October 2005, Estonia used electronic voting for the first time.  Estonia became the first country to use the Internet as a means of voting for legally binding general elections, with 9,317 people voting online.  In 2007, Estonia held the world's first national Internet elections[3]. However, in the deployment of online voting, various countries are facing security threats such as user privacy leakage and unauditability [4],The main problems are embodied in software and hardware systems, hacker attacks, mechanical failures, election social management, etc., but the cryptographic voting protocol itself is safe. There are three basic voting protocols: an electronic voting scheme based on obfuscated networks, an electronic voting scheme based on blind signatures, and an electronic voting scheme based on homomorphic encryption. These voting schemes provide the basic security requirements for elections:  the anonymity of voters, the privacy of votes, the fairness of the election process, and the consistency of election results.  With the frequent occurrence of bribery and coercion in online voting, how voters cast their votes according to their wishes has gradually become the focus of attention.  In order to solve these problems, the system needs to ensure stronger privacy protection: no receipt and resistance to coercion.  In addition, the rapid development of technologies such as blockchain and cloud computing in recent years has provided a broad application environment for online voting.

The organization structure of the paper: Section 2 describes the development and current situation of secure voting, including basic voting protocol design and advanced voting protocol design. Section 3 introduces the new results of secure voting, and finally summarizes the key issues and development directions in this field.

2. Development and current situation of secure electronic voting

a) Main process of electronic voting

1) Classification of electronic voting protocols

Classified according to the types of commonly used tickets:

(1) yes/no voting :Voters can only submit two ballots yes or no;

(2) 1out-of-L voting :Choose one from L possible choices;

(3) K-out-o f-L voting :Choose K from L possible choices, these K elements have no order relationship;

(4) K-out-o f-L order voting :Choose K from L possible choices, these K elements are in order;

(5) 1-L-K voting :Voters first choose one from the set of L and then choose K from the corresponding set;

(6) write-in voting :When voting, you can cast votes that are not on the list of candidates.

Groth[5] proposed four types of elections:

1.Limited voting:There are L candidates in total. N is a constant (0<n<L). Voters can choose N different candidates from L candidates;

2. Approval voting: There are L candidates in total, and voters can choose K different candidates arbitrarily.

3.Disiabled voting: In the first two types of elections, each candidate can receive up to one vote per ballot. In divisible elections, voters can cast more than one vote for a candidate at a time;

4. Borda voting: This election is used to count the degree of support of candidates. It is assumed that there are L candidates. For the candidate most satisfactory to the voters, the voters cast L votes. Secondly, for candidates with poor satisfaction, voters cast L − 1 votes. In this order, the number decreases... For the candidate who is most dissatisfied with him, the voter will vote 1 vote.

Sort by ticket weight:

① equal-voting :The weight of each voter's vote is the same;

② weighted‐voting :The weight of voters' votes is not the same.

According to the different voting places, it can be divided into polling place voting, constituency voting, voting booth voting and network voting.  Network electronic voting refers to the way that voters use computers to vote through remote networks.