隨著科技進步的推波助瀾，人類的生活模式紛紛順應這股洪流，投向數位化的懷抱；若談到當前最受到世界矚目的一項電子化應用，則非電子投票莫屬；毫無疑問，選舉為民主社會中最為重要的表徵，而投票則是民主的具體實踐行為，因此格外備受各界關注，同時電子投票也被認為是邁向高度開發國家的一個關鍵性指標。簡而言之，電子投票的特色與優勢在於導入科技以節省傳統紙張投票中所需要的人力、物力，並且能夠在短時間之內完成投開票，縮短時間上的消耗。毫無疑問，一個電子投票系統必須滿足各項投票行為所需之安全特性，以保證投票過程的正當性及結果的正確性；這些特性包含抗暴力脅迫、投票者匿名性與選票可驗證性等。但由於電子化的影響，使得電子投票也衍生出一些額外問題尚待解決；買賣票甚至有心人士的暴力脅迫即為當中最為棘手的問題，由於在電子投票系統中為了讓投票者足以確認投票過程的正確性，因而通常會讓投票者持有“收據”， 而這個收據則會導致暴力脅迫與買賣票成功的可能性增加。因此在本論文中，我們分析了植基於盲簽章之電子投票系統中可能導致暴力脅迫與買賣票成功\\\的四項因素，並發現了具隨機化之盲簽章技術則是解決暴力脅迫這個問題的必要條件之一； 意即若所採用的盲簽章不具隨機化的特性，則暴力脅迫就無法避免。承襲與延伸上述的研究成果，我們將提出兩個植基於不同密碼底層之隨機化盲簽章協定並分別針對其所需之安全特性進行理論證明；而所提出的隨機化盲簽章機制均能協助電子投票系統，使其滿足抗暴力脅迫與抗買賣票的特性。

Due to resource-saving and efficiency consideration, electronic voting (e-voting) gradually replaces traditional paper-based voting in some developed countries. An anonymous e-voting system that can be used in elections with large electorates must meet various security requirements, such as anonymity, uncoercibility, tally correctness, unrecastability, verifiability, and so on. Especially, the uncoercibility property is an essential property which can greatly reduce the possibility of coercion and bribe. Since each voter can obtain one and only one voting receipt in an electronic voting system, coercers or bribers can enforce legal voters to show their voting receipts to identify whether the enforced voters follow their will or not. It turns out that the coercion and bribe will succeed more easily in digital environments than that in traditional paper-based voting. In this dissertation, we analyze four possible scenarios leading to coercion and discover that the randomization property is necessary to blind-signature-based e-voting systems against coercion. Based on this result, we extend our research and come up with two provably secure randomized blind signature schemes from different cryptographic primitives, which can be adopted as key techniques for an electronic voting system against coercion and bribery.

英文審定書. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . iii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . vi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Coercion and Bribery Issues in Electronic Voting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3
1.2 Dissertation Orientation and Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5
2 Preliminary and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 7
2.1 Prerequisites of Electronic Voting Systems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . 7
2.2 Previous Solutions to Coercion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2.2.1 Receipt Freeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2.3 Analysis of Possible Coercions in Electronic Voting Systems . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Some Generic Ideas Against Coercion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 15
2.5 The Significance of Randomization . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 19
2.5.1 Chaum’s Blind Signature Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
2.5.2 Coercion in Blind-signature-based E-Voting Protocol . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . .. . . . . . 20
2.5.3 Remark . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 The Generic Concept of E-Voting System with Uncoercibility . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . .. . . . . . . 25
3.1 Generic Randomized Blind Signature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .. . . . . . . . 25
3.2 An Uncoercible Anonymous E-Voting System Based on Generic Representation . . . . . . . .. .. . . . . . . . . . 29
3.2.1 The Ways Against Coercion and Bribery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .. . . 33
3.3 Property Examination . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 Fast Randomization Schemes for Chaum’s Blind Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 45
4.1 The Proposed Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 45
4.1.1 The Message-Free Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Formal Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . . . 48
4.2.1 Correctness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 48
4.2.2 Unlinkability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . 49
4.2.3 Unforgeability and Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 53
4.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 65
4.4 Extension: An Uncoercible Anonymous E-Voting System Based on FRCBS . . . . . . . . . . . . . . . . . . . . . . . .70
5 Randomized Blind Signature Scheme Based on Bilinear Pairing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
5.1 Bilinear Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 The Proposed Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . 75
5.3 Formal Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . .78
5.3.1 Correctness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . .. . 78
5.3.2 Unlinkability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
5.3.3 Unforgeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. .82
5.3.4 Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 89
5.4 Performance and Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4.1 Performance Analysis . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. . . . . . 92
5.4.2 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6 Concluding Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 96
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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