Election and voting play crucial roles in democratic society for an elactorate to make a collective decision. E-voting is one of the most challenging problems in cryptographic research to provide multiple dimensions security assurances. In this paper, we study an important voting paradigm, score voting, with privacy protection, which has not been investigated in previous work. We propose a blockchain based self-tallying election system to support score voting, dubbed “PriScore”, where the ballots are recorded on blockchain to prevent vote forgery or tampering. PriScore makes it possible for each voter to assign different evaluation scores (within a certain range) for the candidates as ranked-choice, where the sum of the scores in each ballot should be a predefined constant, and the evaluation scores are encrypted to maintain confidentiality. A major challenge in score voting is to simultaneously prove two constraint conditions: range proof and sum proof. We introduce a new technique, called dual zero-knowledge proof (dual-ZKP), to prove the scores satisfying two crucial requirements, which integrates “1-out-of- $K$ ” proof and distributed ElGamal crypto in a non-trivial way. The self-tallying mechanism in PriScore enables any party in the system to calculate and verify the election result, which provides fairness, dispute-freeness. The security analysis demonstrates that PriScore achieves completeness, soundness, eligibility, universal/individual verifiability and multiple-voting detection. We evaluate the performance of PriScore on modern workbench to test the performance, and also on a blockchain platform to measure the resource consumption. The experiments show that PriScore preserves privacy of score voting with reasonable overheads.

中文翻译：

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PriScore：支持分数投票的基于区块链的自计票选举系统

选举和投票在民主社会中发挥着至关重要的作用，让选民可以做出集体决定。电子投票是密码学研究中最具挑战性的问题之一，以提供多维度的安全保证。在本文中，我们研究了一个重要的投票范式，评分投票，具有隐私保护，这在以前的工作中没有被研究过。我们提出了一个基于区块链的自计票选举系统来支持评分投票，称为“PriScore”，其中选票记录在区块链上以防止投票伪造或篡改。PriScore 使得每个投票者可以为候选人分配不同的评估分数（在一定范围内）作为排名选择，其中每次投票的分数总和应该是一个预定义的常数，并且评估分数被加密以保持机密性. 分数投票的一个主要挑战是同时证明两个约束条件：范围证明和总和证明。我们引入了一种称为双重零知识证明（dual-ZKP）的新技术来证明满足两个关键要求的分数，它集成了“1-out-of- $K$ ”以一种非平凡的方式证明和分发 ElGamal 加密货币。PriScore 中的自统计机制使系统中的任何一方都可以计算和验证选举结果，从而提供公平、无争议。安全性分析表明，PriScore 实现了完整性、稳健性、合格性、通用/个体可验证性和多投票检测。我们在现代工作台上评估 PriScore 的性能以测试性能，并在区块链平台上测量资源消耗。实验表明，PriScore 以合理的开销保护了评分投票的隐私。