臺灣博碩士論文加值系統

過去數位簽章 (Digital Signature) 及加密 (Encryption) 一直是密碼學領域所熱衷研究的兩大區塊，但始終是各據山頭各自發展鮮少有把兩研究課題結合，即便是有先簽章而後加密的方法提出，但不可避免的因為步驟繁雜造成成本過高的現象。然而於1994年，由 Horster、Michels 與 Petersen 三位學者共同提出鑑別加密法 (Authenticated Encryption Scheme) 後便打破這長久以來的藩籬，其目的是可以在單一的步驟中，同時達到數位簽章與加密之功能，並且它的計算成本或是通訊成本都遠低於傳統的先簽後加密之方法。隨後，由 Zheng 於1997年Crypto’ 97會議中提出另一種類似的技術稱之為簽章加密法 (Signcryption) 其目的仍跳脫不開鑑別加密法所賦予的任務。近年，德國學者 Paillier 提出一項基於 的機率式密碼學，其具有不可辨識性 (Indistinguishability)、同形性 (Homomorphism)，成為另一種密碼安全機制，其相關應用有資訊加密、投票系統技術與一般簽章。本論文所提出的以 Paillier 加密系統架構為基準衍生出來的鑑別加密法，皆符合於鑑別加密法的基本精神，除了提供電子商務安全的解決方案外也針對 Paillier 的理論領域上提出新的應用。

第一章 緒論 4
1.1 研究背景與動機 4
1.2 研究目的 6
1.3 論文架構 7
第二章 文獻探討 8
2.1 數位簽章 8
2.1.1 RSA 數位簽章機制 9
2.1.2 ElGamal 數位簽章機制 9
2.1.3 DSA 數位簽章機制 10
2.2鑑別加密法 11
2.2.1 Lee 與 Chang 之鑑別加密法 11
2.2.2 訊息可連結之鑑別加密法 13
2.2.3 訊息連結鑑別加密法之改進 14
2.3貝利爾密碼學 ..20
2.3.1 Paillier 的加密程序 23
2.3.2 另一項單向暗門函數的 Paillier 加密程序 26
2.3.3 Paillier 的簽章程序 27
第三章 植基於貝力爾系統之可驗證公鑰鑑別加密方法 29
第四章 安全性分析 32
4.1 機密性分析 32
4.2 不可偽造性與完整性分析 33
4.3 公鑰可驗證性分析 33
4.4 可鑑別性分析 34
第五章 效率分析 35
第六章 結論與未來研究 36
參考文獻 37

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