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研究生:陳冠宇
研究生(外文):Chen, Kuan-Yu
論文名稱:代理重簽章的功能性延伸及隱私權強化
論文名稱(外文):Proxy Re-signatures with Extended Functionalities and Enhanced Privacy
指導教授:林熙中
指導教授(外文):Lin, Hsi-Chung
口試委員:顏嵩銘薛智誠
口試委員(外文):Yen, Sung-MingHsueh, Chih-Cheng
口試日期:2013-01-16
學位類別:碩士
校院名稱:真理大學
系所名稱:資訊工程學系碩士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:英文
論文頁數:46
中文關鍵詞:代理重簽章代理簽章隱私權門檻式授權結構指定驗證者簽章
外文關鍵詞:Proxy Re-signatureProxy SignaturePrivacyThreshold DelegationDesignated Verifier Signature
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在現今的生活之中,數位簽章已漸漸地被使用在許多的電子商業應用中。在早期簡單的電子商業應用中,只需使用基本型數位簽章驗證訊息的完整性及來源;但基本型數位簽章已經無法滿足現今複雜的電子商業應用,因此許多研究學者開始著手研究,使其功能更為強大且更為實用。在本篇論文中,所討論的兩種簽章系統都著重於簽章權力轉移的功能。
在前期簽章權力轉移的研究結果之中,代理簽章系統被許多學者廣泛討論,其系統提供原始簽章者轉移簽章權力給指定參與者之能力,其簽署出的簽章如同由原始簽章者親自簽署般。然而,惡意的指定參與者具有簽署任意訊息之能力,此行為會損害原始簽章者的權益,因此學者們投入巧思提出許多能限制指定參與者簽署能力的方案。而近期簽章權力轉移的研究結果之中,代理重簽章系統提供原始簽章者,轉移簽章權力給指定參與者及半信任方之能力。換句話說,原始簽章者將簽章權力轉移給指定參與者,指定參與者利用自己擁有的私密金鑰產生數位簽章,再交由半信任方,將其數位簽章轉換成原始簽章者的簽章。
但是,在大多數的代理重簽章文獻中,代理重簽章具有安全性、效率及隱私保護上的缺失。於安全性的缺失方面,惡意的指定參與者能欺騙半信任方,將其對任意訊息所簽署的簽章轉換成原始簽章者的簽章,進而損害原始簽章者的權益。於效率的缺失方面,原始簽章者必須使用互動式協定與指定參與者及半信任方進行互動,進而達成簽章權力轉移,但使用互動式協定完成簽章權力轉移的方式,對於所有參與者而言效率極差。此外,指定參與者所產生的簽章,可被任意的第三方驗證,對於指定參與者的隱私來說非常沒有保障。因此,本篇論文將提出新型態之代理重簽章系統,以改善上述三項缺失。同時,本篇論文不僅討論原始簽章者如何將簽章權力轉移給單一指定參與者,更進一步思考如何以門檻式授權的結構,將簽章權力轉移給多個指定參與者與單一半信任方。

Nowadays, digital signatures are widely used in various kinds of e-commerce applications. In previous e-commerce systems with simple application scenario, message origin and integrity are sufficient for overall system security, thus ordinary digital signature schemes are suitable and applicable. Unfortunately. Functionalities of ordinary signature scheme not strong enough for novel e-commerce systems with complex application scenario; thus, many researchers investigate new signature variants with powerful and practical functionalities for these modern applications. In this thesis, two signature schemes with novel functionality of signing right delegation are proposed.
Proxy signature scheme is widely discussed in early studies of signing right delegation, they allow a designated participant (proxy signer) to sign a message on behalf of the original signer. Unfortunately, a dishonest proxy signer is capable of signing arbitrary messages, this action might injure the original signer’s benefit; thus many researchers focus on the design of mechanisms to restrict the designated participant’s signing ability.
In recently studies of signing right delegation, proxy re-signature schemes allow an original signer (a.k.a., delegator) to delegate his signing right to a designated participant (a.k.a., delegatee) and a semi-trusted party known as the transformer. In brief, a delegator delegates his signing right to a delegatee, then the delegatee signs a message with his own private key, and the transformer translates the delegatee’s signature into the delegator’s signature.
But, in most proxy re-signature schemes in the literature, there are flaws in security, efficiency or privacy. For security flaw, a dishonest delegatee is still capable of signing a signature of an arbitrary message if the transformer translates naively. For efficiency flaw, in most existing schemes, a delegator must cooperate with the delegatee and the transformer to delegate his signing right by an interactive protocol; it is not efficient. As for privacy flaw, it is not safe for a delegate to sign a signature which can be verified by anyone, since he might have to sign a message he does not agree with. Therefore, new proxy re-signature schemes are proposed in this thesis to fix above-mentioned weakness. Additionally, a new scenario of signing right delegation, in which a delegator can delegate his signing right to multiple delegatees and single transformer, is also considered in the thesis.

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Our Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 A Proxy Re-signature Scheme with Privacy Protection . . . . 2
1.2.2 A Threshold Proxy Re-signature Scheme with Privacy Protection 3
2 Preliminaries 4
2.1 The Technique of (t; n) Threshold . . . . . . . . . . . . . . . . . . . . 4
2.2 The Elliptic Curve Discrete Logarithm Problem . . . . . . . . . . . . 5
2.3 Proxy Signature Schemes . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4 Proxy Re-signature Schemes . . . . . . . . . . . . . . . . . . . . . . . 6
2.5 Review of the Ateniese-Hohenberger Proxy Re-signature Scheme . . . 7
2.5.1 Properties of the Proxy Re-signature Scheme . . . . . . . . . . 7
2.5.2 De nition of the Proxy Re-signature Scheme . . . . . . . . . . 8
2.5.3 The Proxy Re-signature Scheme . . . . . . . . . . . . . . . . . 8
2.6 Review of the Libert-Vergnaud Proxy Re-signature Scheme . . . . . . 9
2.6.1 Properties of the Proxy Re-signature Scheme . . . . . . . . . . 9
2.6.2 De nition of the Proxy Re-signature Scheme . . . . . . . . . . 10
2.6.3 The Proxy Re-signature Scheme . . . . . . . . . . . . . . . . . 10
2.7 Threshold Proxy Re-signature schemes . . . . . . . . . . . . . . . . . 11
3 A Proxy Re-signature Scheme with Privacy Protection 12
3.1 Properties of the Proposed Scheme . . . . . . . . . . . . . . . . . . . 14
3.2 The Proposed Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 Eciency and Security Analyses . . . . . . . . . . . . . . . . . . . . . 17
3.3.1 Analysis from the Delegator's View. . . . . . . . . . . . . . . . 17
3.3.2 Analysis from the Delegatee's View . . . . . . . . . . . . . . . 19
3.3.3 Analysis from the Transformer's View . . . . . . . . . . . . . . 21
3.4 Extension System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.1 The Signature of the Delegator into a Designated Veri er Signature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4.2 Analyses of the Extension System . . . . . . . . . . . . . . . . 24
3.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6 Applications of the Proposed Scheme . . . . . . . . . . . . . . . . . . 27
4 A Threshold Proxy Re-signature Scheme with Privacy Protection 29
4.1 Properties of the Proposed Scheme . . . . . . . . . . . . . . . . . . . 31
4.2 The Proposed Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Eciency and Security Analyses . . . . . . . . . . . . . . . . . . . . . 35
4.3.1 Analysis from the Delegator's View: . . . . . . . . . . . . . . . 35
4.3.2 Analyses from a Delegatee's View . . . . . . . . . . . . . . . . 37
4.3.3 Analyses from the Transformer's View . . . . . . . . . . . . . 39
4.4 Extension System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.6 Applications of the Proposed Scheme . . . . . . . . . . . . . . . . . . 41
5 Conclusions 42
5.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Bibliography 46
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