近年來數位簽章在資訊科學領域已經被廣為應用。數位簽章包含有三個重要的參數，分別為：明文、金鑰對、以及簽章。一般來說，明文是給定的並準備被簽署的，金鑰對是由簽章者隨機產生的，而簽章則是根據明文以及金鑰對所計算出來。但在一些特殊的情況下，如果我們可以依據一些條件控制其中一種參數的值，那麼就可以衍生出一些不同型態的簽章，例如「盲簽章」或「潛隱通道」。目前也有一些針對參數選擇以及其他衍生簽章型態之間關係的研究，本篇論文試著從三個參數的自由度去討論，並提出三個實例來說明這個概念。第一個例子是一個「公平盲簽章」的機制，其他兩個例子則是屬於「潛隱通道」的機制。這個參數自由度的觀念應該可以對未來衍生類型數位簽章的研究有所幫助。而這三個新的機制也可以用來說明，如何利用這個觀念來開發或是改進簽章衍生物。

Digital signature is widely used to implement many secure protocols. A digital signature has three parameters. They are the message, the key pair, and the signature. In general, the message is given. The key pair is chosen randomly by the signer. The signature is computed from the message and the key pair. But in some cases, we can choose the value of one of the parameters, this may make it possible to other applications such as blind signatures or subliminal channels. There are some researches to discuss the relations between the parameters and the applications of the digital signatures. In this research, we will propose three new schemes as examples of this technique. The first one is a fair blind signature scheme. The other two are subliminal channel schemes. These three new schemes have some important properties. The concept of this research may help the future researches to find new applications of the digital signature. Meanwhile, these new schemes can show that how the concept can help us to develop or improve applications.

1 Introduction to the Digital Signatures . . . . . . . . . . . . . . . . 1
1.1 Introduction to the Digital Signatures . . . . . . . . . . . . . . 1
1.2 The Digital Signatures and Their Derivatives . . . . . . . . . . . 2
1.3 The Three Parameters of Digital Signatures . . . . . . . . . . . . 4
2 The Freedom of the Message - Fair Blind Signature with Observer. . . . 5
2.1 Introduction to the Fair Blind Signatures. . . . . . . . . . . . . 6
2.2 The Construction of Our Scheme . . . . . . . . . . . . . . . . . . 8
2.3 Security Analysis. . . . . . . . . . . . . . . . . . . . . . . . . 9
3 The Freedom of the Key Pair -
A Subliminal Channel Based on Lamport's One-time Signature. . . . . . 11
3.1 Introduction to the Subliminal Channels . . . . . . . . . . . . . 12
3.2 An Example of Subliminal Channel. . . . . . . . . . . . . . . . . 14
3.3 Review of Lamport’s One-time Signature . . . . . . . . . . . . . 14
3.4 One-time Signatures with Subliminal Channels. . . . . . . . . . . 15
3.4.1 The First Scheme. . . . . . . . . . . . . . . . . . . . . . . 16
3.4.2 The second scheme . . . . . . . . . . . . . . . . . . . . . . 17
3.5 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . 19
4 The Freedom of the Signature -
A Subliminal Channel Based on Rabin's Signature Scheme. . . . . . . . 21
4.1 Introduction to the Freedom of the Signature. . . . . . . . . . . 21
4.2 Review of Rabin’s Signature Scheme . . . . . . . . . . . . . . . 22
4.3 Rabin’s Signature with Subliminal channels . . . . . . . . . . . 23
4.4 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . 24
5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.1 Summary of the Research . . . . . . . . . . . . . . . . . . . . . 25
5.2 Future works. . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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