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論文名稱 Title |
植基於多線性映射且具動態條件生成之金鑰聚合代理重加
密機制 Key-Aggregate Proxy Re-Encryption with Dynamic Condition Generation Using Multilinear Maps |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
55 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2018-06-25 |
繳交日期 Date of Submission |
2018-08-10 |
關鍵字 Keywords |
資訊安全、代理重加密、CCA 安全、標準模型、密碼學、多重線性映射 Information Security, CCA Security, The Standard Model, Cryptography, Multilinear Maps, Proxy Re-Encryption |
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統計 Statistics |
本論文已被瀏覽 5650 次,被下載 0 次 The thesis/dissertation has been browsed 5650 times, has been downloaded 0 times. |
中文摘要 |
在現今科技發達的時代下,許多人會將檔案上傳於雲儲存空間,但為了顧及安全及隱私性,大部分的使用者都會將資料加密後再上傳於雲儲存空間,其中有些使用者希望直接在雲儲存空間分享資料給其他使用者。這時我們可以透過代理者加密技術,在符合使用者所設定的條件下,轉加密給另一位使用者。然而Chen等人發現使用者的轉加密金鑰(或條件金鑰)會伴隨著條件的增加而增長,於是提出了金鑰聚合轉加密機制解決轉加密金鑰線性增長的問題。但我們發現到Chen等人的機制中一旦固定了條件後便不能任意的改變條件,唯一改變的方法就是重新產生公開參數,這樣會使得此機制變得非常不靈活且耗時。於是我們導入了多重線性映射使得條件數量可以擴展成指數數量。如此一來,便可解決了Chen等人機制的問題。此外,我們也證明了我們的機制於標準模型中可具有CCA安全等級。 |
Abstract |
With the growing accessibility of the internet, many people store files in the cloud storage. In consideration of privacy preserving, users tent to encrypt their files before uploading them to the cloud. Under certain conditions, a file owner may want to share the encrypted files directly on the cloud. In such cases, the file owner will delegate the re-encryption ability to a proxy with re-encryption keys. However, Chen et al. found that the size of the re-encryption key (or condition key) would increase with the number of the conditions, which motivated them in proposing the concept of key-aggregate proxy re-encryption. Unfortunately, we found that the conditions cannot be changed arbitrarily once we set the conditions at the beginning. To solve the problem, we apply the multilinear maps to the key-aggregate proxy re-encryption to extend the number of conditions to be exponentially large, while keeping the size of public parameters small and practical. Furthermore, the proposed scheme is proven to be CCA secure without random oracles. |
目次 Table of Contents |
Contents 論文審定書 i Acknowledgments iii 摘要 iv Abstract v List of Figures viii List of Tables ix Chapter 1 Introduction 1 Chapter 2 Preliminaries 4 2.1 Multilinear Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 -Graded Encoding System . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Efficient Procedures for Multilinear Map . . . . . . . . . . . . . . . . . 5 2.2 The Model and Security Notions of Unidirectional Key-Aggregate PRE . . . . 6 2.2.1 Unidirectional Key-Aggregate PRE . . . . . . . . . . . . . . . . . . . . . 6 2.3 The Chosen-Ciphertext Security . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 The Security of Second Level Ciphertext . . . . . . . . . . . . . . . . . . . . . . 8 2.5 The Security of First Level Ciphertext . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Master Secret Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.7 3-weak Decisional Multilinear Diffie-Hellman Inversion (3-wDMDHI) Assumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Chapter 3 Related Works 13 3.1 Weng et al.’s C-PRE Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Chu et al.’s CPBRE Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Liang et al.’s IBCPRE Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.4 Chen et al.’s KAPRE Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Chapter 4 Our Construction 23 4.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 The Proposed Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2.1 Setup() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2.2 KeyGen(i) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2.3 ReKeyGen(S; ski; pkj) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2.4 Enc2(pki;m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2.5 Enc1(pkj ;m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2.6 ReEnc(S,rki→j,C) 4.2.7 Dec2(ski;C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2.8 Dec1(skj ;C') . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3 Correctness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Chapter 5 Security Proof 30 5.1 The IND-2PRE-CCA Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.2 The IND-1PRE-CCA Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.3 Master Secret Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Chapter 6 Comparisons 39 Chapter 7 Conclusion 42 Bibliography 43 |
參考文獻 References |
[1] Giuseppe Ateniese, Karyn Benson, and Susan Hohenberger. Key-private proxy re-encryption. In Cryptographers’ Track at the RSA Conference, pages 279–294. Springer, 2009. [2] Matt Blaze, Gerrit Bleumer, and Martin Strauss. Divertible protocols and atomic proxy cryptography. In International Conference on the Theory and Applications of Cryptographic Techniques, pages 127–144. Springer, 1998. [3] Dan Boneh, Xavier Boyen, and Eu-Jin Goh. Hierarchical identity based encryption with constant size ciphertext. In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 440–456. Springer, 2005. [4] Dan Boneh and Alice Silverberg. Applications of multilinear forms to cryptography. Contemporary Mathematics, 324(1):71–90, 2003. [5] Ran Canetti and Susan Hohenberger. Chosen-ciphertext secure proxy re-encryption. In Proceedings of the 14th ACM conference on Computer and communications security, pages 185–194. ACM, 2007. [6] Wei-Hao Chen. Efficient key-aggregate proxy re-encryption for secure data sharing in clouds. Master thesis, National Sun Yet-sen University, 2017. [7] Cheng-Kang Chu, Jian Weng, Sherman SM Chow, Jianying Zhou, and Robert H Deng. Conditional proxy broadcast re-encryption. In Australasian Conference on Information Security and Privacy, pages 327–342. Springer, 2009. [8] Jean-Sébastien Coron. On the exact security of full domain hash. In Annual International Cryptology Conference, pages 229–235. Springer, 2000. [9] Jean-Sébastien Coron, Tancrede Lepoint, and Mehdi Tibouchi. Practical multilinear maps over the integers. In Advances in Cryptology–CRYPTO 2013, pages 476–493. Springer, 2013. [10] Sanjam Garg, Craig Gentry, and Shai Halevi. Candidate multilinear maps from ideal lattices. In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 1–17. Springer, 2013. [11] Aurore Guillevic. Comparing the pairing efficiency over composite-order and primeorder elliptic curves. In International Conference on Applied Cryptography and Network Security, pages 357–372. Springer, 2013. [12] Kaitai Liang, Zhen Liu, Xiao Tan, Duncan S Wong, and Chunming Tang. A cca-secure identity-based conditional proxy re-encryption without random oracles. In International Conference on Information Security and Cryptology, pages 231–246. Springer, 2012. [13] Benoît Libert and Damien Vergnaud. Unidirectional chosen-ciphertext secure proxy reencryption. In International Workshop on Public Key Cryptography, pages 360–379. Springer, 2008. [14] Jian Weng, Robert H Deng, Xuhua Ding, Cheng-Kang Chu, and Junzuo Lai. Conditional proxy re-encryption secure against chosen-ciphertext attack. In Proceedings of the 4th International Symposium on Information, Computer, and Communications Security, pages 322–332. ACM, 2009. |
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