Boneh 在 2004 年提出的具有關鍵字搜索之公開金鑰加密是一個能在公開金鑰加密機制中對加密資料進行搜尋的突破性方法。在這個架構中，資料發送方可以從文檔中提取特定關鍵字來生成可搜索的密文並上傳到伺服器中；而資料接收者可以使用持有的私鑰生成對應的陷門在存放著加密文檔的伺服器當中根據關鍵字進行搜索。

近期，Jiang 基於具有關鍵字搜索之公開金鑰加密機制提出了一種改進的方案，稱為具有授權關鍵字搜索之公鑰加密機制，在他們的機制中允許獲得授權的使用者為特定的關鍵字集合製作陷門，即便這些使用者沒有辦法取得私鑰。然而，在此機制中有關授權的執行不夠靈活，只能仰賴系統當中唯一一個權威機構替所有使用者執行，這個權威機構無法將自己授權的權力委託給已獲得授權的使用者代為執行授權的處理。考量到實際的企業場景中並不適合具有這種限制的機制。

為了解決上述問題，本論文提出了一種新的密碼機制，稱為具有階層式授權關鍵字搜索之公鑰加密機制，與Jiang提出的機制相比，此論文提出的機制中允許獲得授權的使用者能夠進一步階層式地委派授權工作的執行，替未經授權的使用者製作陷門。

此論文根據提出的密碼機制定義了能夠支援一次多個關鍵字搜尋的系統模型，並根據實際情況會面臨到攻擊訂定安全需求。最後，我們採用對偶向量空間技術實際建構了一個可證明安全性的架構，來表明此論文所提出的密碼機制能夠安全地適用在有階層式授權需求的場景中順利運作而不被破解。

Public key encryption with keyword search , which was introduced by Boneh et al. at Eurocrypt'04, is a breakthrough approach to searching encrypted data under a public key setting. Recently, Jiang et al. proposed an improved PEKS scheme called public key encryption with authorized keyword search , which allows authorized users to generate trapdoors for specific sets of keywords even if they do not have access to the private key. Unfortunately, authorized users cannot delegate their own power to other unauthorized users because the authorization in PEAKS is not flexible enough; therefore, this scheme is not suitable for enterprise scenarios in general. In this work, we introduce a novel cryptographic primitive called public key encryption with hierarchical authorized keyword search to solve the above problem. Compared with PEAKS, the proposed primitive allows authorized users to further hierarchically delegate their power to generate trapdoors for unauthorized users. We formally define the system model of PEHAKS under a multi-keyword setting and design the desired security requirements to withstand attacks in a real scenario. Furthermore, we propose a provably secure scheme using the dual pairing vector spaces technique, and show that the scheme is secure under the hardness of the 𝑛-extended decisional Diffie-Hellman assumption. Therefore, the proposed scheme can work securely in scenarios that require hierarchical authorization. To the best of the authors' knowledge, no PEKS variant schemes have discussed for this property.

致謝 ... iii
摘要 ... v
Abstract ... vii
Contents ... ix
List of Definitions ... xv
List of Theorems ... xvii
1 Introduction ... 1
1.1 Contribution ... 2
1.2 Technical Overview ... 3
1.3 Related works ... 4
1.4 Organization ... 5
2 Problem Formulation ... 7
2.1 System Description ... 7
2.2 Algorithm Definitions ... 7
2.3 Security Model ... 9
3 Preliminaries ... 11
3.1 Dual Pairing Vector Spaces (DPVS) ... 11
3.2 Complexity Assumptions ... 12
4 Public Key Encryption with Hierarchical Authorized Keyword
Search ... 15
5 Security Proof ... 19
6 Comparison ... 29
6.1 Comparison ... 29
6.2 Experimental Result ... 30
7 Conclusion ... 33
Bibliography ... 35

[ADP12] M. Abdalla, A. De Caro, and D. H. Phan, “Generalized key delegation for wildcarded identity-based
and inner-product encryption,” IEEE Transactions on Information Forensics and security, vol. 7,
no. 6, pp. 1695–1706, 2012 (cit. p. 3).

[APW10] H. Abu-Libdeh, L. Princehouse, and H. Weatherspoon, “RACS: A case for cloud storage diversity,”
in ACM Symposium on Cloud Computing, 2010 (cit. p. 1).

[BCO+04] D. Boneh, G. D. Crescenzo, R. Ostrovsky, and G. Persiano, “Public key encryption with keyword
search,” in EUROCRYPT, 2004 (cit. p. 1).

[CMY+16] R. Chen, Y. Mu, G. Yang, et al., “Server-aided public key encryption with keyword search,” IEEE
Transactions on Information Forensics and Security, vol. 11, no. 12, pp. 2833–2842, 2016 (cit. p. 1).

[Con85] J. H. Conway, Atlas of finite groups: maximal subgroups and ordinary characters for simple groups.
Oxford University Press, 1985 (cit. p. 12).

[CDL+17] H. Cui, R. H. Deng, J. K. Liu, and Y. Li, “Attribute-based encryption with expressive and authorized
keyword search,” in Australasian Conference on Information Security and Privacy, Springer, 2017,
pp. 106–126 (cit. p. 4).

[Hay08] B. Hayes, Cloud computing, 2008 (cit. p. 1).

[JMG+16] P. Jiang, Y. Mu, F. Guo, and Q. Wen, “Public key encryption with authorized keyword search,” in
ACISP, 2016 (cit. pp. 1, 2, 4, 5, 9, 10, 29–32).

[LOS+10] A. Lewko, T. Okamoto, A. Sahai, K. Takashima, and B. Waters, “Fully secure functional encryption:
Attribute-based encryption and (hierarchical) inner product encryption,” in EUROCRYPT, 2010 (cit.
pp. 12, 13).

[LTT+21] Z.-Y. Liu, Y.-F. Tseng, R. Tso, Y.-C. Chen, and M. Mambo, “Identity-certifying authority-aided
identity-based searchable encryption framework in cloud systems,” IEEE Systems Journal, 2021
(cit. p. 1).

[OT09] T. Okamoto and K. Takashima, “Hierarchical predicate encryption for inner-products,” in
EUROCRYPT, 2009 (cit. pp. 2, 11).

[OT10] ——, “Fully secure functional encryption with general relations from the decisional linear
assumption,” in CRYPTO, 2010 (cit. p. 13).

[QLD+09] L. Qian, Z. Luo, Y. Du, and L. Guo, “Cloud
computing: An overview,” in IEEE International
Conference on Cloud Computing, 2009 (cit. p. 1).

[QCH+20] B. Qin, Y. Chen, Q. Huang, X. Liu, and D. Zheng, “Public-key authenticated encryption with keyword
search revisited: Security model and constructions,” Information Sciences, vol. 516, pp. 515–528,
2020 (cit. p. 1).

[SYL+14] W. Sun, S. Yu, W. Lou, Y. T. Hou, and H. Li, “Protecting your right: Attribute-based keyword search
with fine-grained owner-enforced search authorization in the cloud,” in IEEE INFOCOM 2014-IEEE
conference on computer communications, IEEE, 2014, pp. 226–234 (cit. p. 5).

[WC22] J. Wang and S. S. Chow, “Omnes pro uno: Practical multi-writer encrypted database,” in USENIX
Security, 2022 (cit. p. 1).

[WCX+22] P. Wang, B. Chen, T. Xiang, and Z. Wang, “Lattice-based public key searchable encryption with
fine-grained access control for edge computing,” Future Generation Computer Systems, vol. 127,
pp. 373–383, 2022 (cit. p. 1).

[WQS+21] T. Wang, Y. Quan, X. S. Shen, et al., “A privacy-enhanced retrieval technology for the cloud-assisted
internet of things,” IEEE Transactions on Industrial Informatics, 2021 (cit. p. 1).

[Wat09] B. Waters, “Dual system encryption: Realizing fully secure ibe and hibe under simple assumptions,”
in Annual International Cryptology Conference, Springer, 2009, pp. 619–636 (cit. p. 19).

[WZC+14] L. Wei, H. Zhu, Z. Cao, et al., “Security and privacy for storage and computation in cloud computing,”
Information Sciences, vol. 258, pp. 371–386, 2014 (cit. p. 1).

[XLZ+19] L. Xu, W. Li, F. Zhang, R. Cheng, and S. Tang, “Authorized keyword searches on public key
encrypted data with time controlled keyword privacy,” IEEE Transactions on Information Forensics
and Security, vol. 15, pp. 2096–2109, 2019 (cit. pp. 4, 5).