在2010年, Fan 等人最早提出基於身份之多接收者匿名加密機制 (Anonymous Mutli-Receiver Identity-Based Encryption, AMRIBE)的概念, 他們使用了Fujisaki-Okamoto 轉換 (Fujisaki-Okamoto transformation) 作為輔助來進行安全性證明。在此研究發表後，許多與此主題相關的論文也相繼發表，許多的研究者同樣使用了 Fujisaki-Okamoto 轉換來協助達到基於身份多接收者機密不可區分選擇密文攻擊安全等級。然而，我們發現這些使用了 Fujisaki-Okamoto 轉換的機制無法達到針對內部攻擊的匿名性。在這篇論文中，我們使用遊戲序列的方式來證明使用 Fujisaki-Okamoto 轉換的基於身份之多接收者匿名加密機制機制將會無法達到選擇明文攻擊以及選擇密文攻擊之匿名性。

In 2010, Fan extit{et al.} first introduced the concept of anonymous multi-receiver identity-based encryption (AMRIBE). They used the concept of Fujisaki-Okamoto transformation (F.O. transformation) to support their proof in random oracle models. Recently, many works on this topic have been proposed. Most of them adopted Fujisaki-Okamoto transformation to achieve the indistinguishability of encryptions under multi-ID, chosen-ciphertext attacks (IND-MID-CCA) security. However, we find out that these schemes do not gain anonymity against insider attacks. In this thesis, we use a sequence of games to prove that any AMRIBE scheme will fail to gain anonymity under chosen-ciphertext attacks and chosen-plaintext attacks if the IND-MID-CCA security is proven using Fujisaki-Okamoto transformation.

論文審定書i
Acknowledgments iii
摘要iv
Abstract v
Chapter 1 Introduction 1
Chapter 2 Preliminaries 3
2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 AMRIBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 3 Related Works 6
3.1 Fan et al.’s AMRIBE Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1.1 Cryptanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Wang et al.’s AMRIBE Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2.1 Cryptanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Zhang et al.’s AMRIBE Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3.1 Cryptanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4 K. He et al.’s IBBE Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4.1 Cryptanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter 4 Generic AMRIBE Based on Fujisaki-Okamoto Transformation 16
Chapter 5 Security Notations 18
5.1 Security Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.2 One-Way(OW) AMRIBE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.3 One-Time(OT) Secure Symmetric Encryption . . . . . . . . . . . . . . . . . . . 21
5.4 Well-Spread Encryption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Chapter 6 Impossibility of Anonymity for AMRIBE Using Fujisaki-Okamoto Transformation 23
6.1 Proof for IND-MID-CCA of Generic Construction . . . . . . . . . . . . . . . . 23
6.2 Impossibility on Anonymity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 7 Conclusions 32
Bibliography 33

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