隨著數位簽章日趨成熟的發展和網路的普及,許多公司都開始透過電子簽章與網路來傳遞公文和訊息，以期能節省成本並增進作業效率。且目前現行的電子簽章大多是架構在公開金鑰基礎建設之下，各公司行號會向憑證中心註冊並取得一組屬於自己的憑證，而他人皆可利用憑證中所記載的公鑰來驗證文件是否為此公司所簽署。然而並不是公司內部的每個人皆有使用公司的私鑰來對文件做簽章的權力，一旦公司內部有文件需要向外界發布，便需要持有公司私鑰的負責人簽署，但負責人不會無時無刻都在公司待命。直覺的解決方式是利用代理簽章的機制。負責人授權代理者簽章能力並且給予公司私鑰進行簽署動作。如此一來即使掌管公司金鑰的負責人不在，依然可以順利的完成簽章的動作。此時若有惡意的代理者參與其中，則可能會出現如利用公司私鑰進行偽造簽章等造成公司重大損失的狀況發生。因此我們提出了一個具備安全性之多代理者之指定代理重簽章機制，一方面讓持有公司金鑰的負責人可以一開始就指定多位代理者，而代理者也會在每次的簽署文件中指定轉換的對象，並將各自簽章送給代理伺服器。另一方面，代理伺服器在收到所有代理者所簽署過的文件與負責人的重簽章金鑰之後，才可以轉換為公司的數位簽章。最後，我們亦提出安全分析及證明以說明本機制之安全性。

With the convenience and development of digital signature and network technologies, several companies are beginning to transmit documents and messages over networks.This is expected to reduce costs and improve the efficiency of the working process. Based on the typical digital signature technique over public key infrastructure, each company can apply for its own certificate from the certificate authority to enable people to verify whether a message is signed by the company through the public key within the certificate. Generally, a general manager is responsible for signing
a message to be published. However, the general manager is not always available; hence, the proxy signature scheme can be an efficient solution to this problem. In the typical proxy signature scheme, the delegator will delegate a proxy agent
with the power of signing. The proxy agent can sign and produce the signature of the company on behalf of the general manager. A malicious proxy agent involved in the signing process may cause substantial damage to the company because of misbehaviors, such as signature forgery. Therefore, we propose a provably secure multi-agent designated proxy re-signature scheme. In the proposed
scheme, the general manager designates several agents as delegatees. Each delegatee signs the message and send her/his signature to the proxy. The proxy can re-sign the message to form the signature of the company only when the proxy has obtained signatures from all delegatees. In addition, security definitions and formal proofs are provided in our scheme.

論文審定書...i
誌謝...iii
中文摘要...iv
英文摘要...v
1. Introduction...1
1.1 Contributions...2
1.2 Organization...4
2. Related Works...6
2.1 The Definition of Proxy Re-Signature Scheme...7
2.2 Review of Shao et al.'s Scheme...9
2.3 Review of Libert and Vergnaud’s Scheme...12
3. Preliminaries...15
3.1 Backgrounds... 15
3.1.1 Bilinear Mapping...15
3.1.2 The Decisional Bilinear Diffie-Hellman Problem...16
3.1.3 The Decisional Bilinear Diffie-Hellman Problem Assumption...16
3.1.4 The Flexible Diffie-Hellman Problem...16
3.1.5 The Flexible Diffie-Hellman Problem Assumption...17
3.2 Definitions...17
3.2.1 Multi-Agent Designated Proxy Re-Signature Scheme...17
3.2.2 OMF-MADPRSS...19
3.2.3 DPRA-MADPRSS...22
4 Multi-Agent Designated Proxy Re-signature Scheme...25
4.1 Overview...25
4.2 The Proposed Scheme...26
4.3 Feature Comparisons...33
5 Security Analysis and Proof...37
5.1 Security Analysis...37
5.2 Security Proof...40
6 Conclusions and Future Works...53
6.1 Conclusions...53
6.2 Future Works...54
Bibliography...55

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