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研究生:吳俊輝
研究生(外文):Jun-Hui Wu
論文名稱:一種安全的門檻式Paillier代理簽章機制
論文名稱(外文):A Secure Threshold Paillier Proxy Signature Scheme
指導教授:丁培毅丁培毅引用關係
指導教授(外文):Pei-Yih Ting
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:資訊工程學系
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:2008
畢業學年度:96
語文別:英文
論文頁數:63
中文關鍵詞:門檻式代理簽章
外文關鍵詞:threshold proxy signature
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本論文提出一種門檻式 Paillier 代理簽章機制。Paillier 密碼系統的加法同形性質,加上代理簽章機制以及門檻信任模型,使得在設計電子投票系統或電子投標系統時,它比其他密碼系統還要方便。 在隨機智者模型下,證明本文中所提出的方法能抵抗選擇明文攻擊者的攻擊,並具有:不可偽造性、保護代理簽章者、不可否認性、祕密性以及可分辨代理簽章者等安全性質。本機制所用的假設和 Paillier 密碼系統相同,都是基於計算合成數模數 n 次方根問題的困難性。
In this thesis, a threshold Paillier proxy signature scheme is proposed. The additive homomorphism of the Paillier cryptosystem, together with the proxy mechanism and the threshold trust make it more convenient than other probabilistic cryptosystems in designing electronic voting systems or electronic auction systems. In this thesis, this scheme is proven to be unforgeabile, proxy-protected, undeniabile, secret and signer-identi?able against chosen message attackers in the random oracle model. These security properties of this scheme are based on the computational composite residuosity assumption.
1 Introduction 1
2 Basic tools 6
2.1 Public Key Cryptosystem . . . . . . . . . . . . . . . . . . . . 6
2.2 Paillier Cryptosystem . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Encryption and Decryption . . . . . . . . . . . . . . . 8
2.2.3 Digital Signature and Veri?cation . . . . . . . . . . . . 8
2.2.4 Some Important Properties . . . . . . . . . . . . . . . 9
2.3 Modi?ed Setting in QRn2 . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.2 Encryption and Decryption . . . . . . . . . . . . . . . 11
2.3.3 Some Properties of the Modi?ed Setting . . . . . . . . 12
2.4 Paillier Proxy Signature . . . . . . . . . . . . . . . . . . . . . 18
2.4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.2 Proxy Delegation Protocol . . . . . . . . . . . . . . . . 18
2.4.3 Proxy Signature Signing Protocol . . . . . . . . . . . . 19
2.4.4 Proxy Signature Veri?cation Protocol . . . . . . . . . . 19
3 The Security Model 20
3.1 Intractability Assumption . . . . . . . . . . . . . . . . . . . . 20
3.2 Security De?nitions of a Threshold Proxy Signature . . . . . . 21
4 A Paillier (d, `)-threshold Proxy Signature Scheme 27
4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Proxy Delegation Protocol . . . . . . . . . . . . . . . . . . . . 28
4.3 Proxy Key Veri?cation Protocol . . . . . . . . . . . . . . . . . 29
4.4 Proxy Signature Signing Protocol . . . . . . . . . . . . . . . . 30
4.5 Proxy Signature Share Veri?cation Protocol . . . . . . . . . . 31
4.6 Proxy Signature Combination Protocol . . . . . . . . . . . . . 31
4.7 Proxy Signature Veri?cation Protocol . . . . . . . . . . . . . . 33
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Security Analysis 34
6 Conclusions 48
Appendices 49
A The Schnorr Signature 50
B GQ Signature 52
C Decryption with the modi?ed setting 54
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
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