在現代社會中，我們越發依賴雲端伺服器來提供存儲空間和服務。 但是在增進生活的便利性的同時，我們可能會因為使用了雲端服務而喪失了隱私。 最自然的解決方法就是將存儲在雲端的個人資訊進行加密，但由於加密過後的資訊難以搜索，因此也會妨礙數據的處理。 謂詞加密是可搜索加密的一個子集，它提供了一種通過利用與某些屬性關聯的密鑰來搜索加密數據的方法。 然而，這並不能保證我們的網路活動還是能保持匿名性，因為資訊仍然可能通過搜尋或搬動數據而洩露。 在本論文中，我們首先建立了如何通過匿名路由和不可鏈接操作來確保網路隱私。 然後我們提出一個使用謂詞加密並支援匿名分享的存取控制系統。 我們同時也證明了此系統屬性隱藏功能的安全性證明並提出其可能的應用。

In modern society we rely greatly on cloud servers to provide storage and service. However, through our usage of cloud services, privacy may come as a cost to our convenience. Encrypting contents stored in the cloud is a natural solution to protect our personal information, but it also hinders the handling of data since it is difficult to search over encrypted information. Predicate encryption, a sub-set of searchable encryption, offers a way to search encrypted data through utilizing a secret key associated with a certain set predicate. However this does not guarantee online anonymity since information could still be leaked through the handling of data. In this thesis we first establish the steps to ensure online privacy through anonymous routing and unlinkable operations. We then propose an access control system that supports anonymous sharing using predicate encryption. We give security proof on the attribute hiding features and possible applications of our scheme.

論文審定書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
論文授權書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Privacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Anonymous Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Unlinkable Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3 Total Anonymity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Pairings and Complexity Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 The Non-Trivial Factoring of N Problem . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Predicate Encryption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Security Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 3 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1 Boneh et al.’s PKE with Keyword Search . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Katz et al.’s Inner Product Predicate Encryption . . . . . . . . . . . . . . . . . . . . 11
3.3 Okamoto et al.’s HPE for Inner-Products . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4 Li et al.’s APKS over Encrypted Data . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.5 Oblivious Transfer/Private Information Retrieval . . . . . . . . . . . . . . . . . . . . . 14
3.6 Ring Signature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter 4 Our Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2 The Proposed Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.2 Encryption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.3 Generating Token . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.4 Query . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2.5 Rerandomizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3 Correctness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 5 Applications of Our Construction . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.1 Access Rights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.1.1 Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.1.2 Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.1.3 Editing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.1.4 Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 Our System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2.1 Initializing the Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2.2 Retrieving Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2.3 Preparing Files and Tokens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2.4 Adding to the Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2.5 Sharing Access Rights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.6 A Simple Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Chapter 6 Security Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.1 Threat Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.1.1 Security of Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.1.2 Security of Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.1.3 Security of Rerandomized Tokens . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 7 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Chapter 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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