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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 陳君明 | zh_TW |
dc.contributor.advisor | Jiun-Ming Chen | en |
dc.contributor.author | 胡政賢 | zh_TW |
dc.contributor.author | Cheng-Hsien Hu | en |
dc.date.accessioned | 2024-02-22T16:20:04Z | - |
dc.date.available | 2024-02-23 | - |
dc.date.copyright | 2024-02-22 | - |
dc.date.issued | 2024 | - |
dc.date.submitted | 2024-02-04 | - |
dc.identifier.citation | [Ajt96] Miklós Ajtai. Generating hard instances of lattice problems. Electron. Colloquium Comput. Complex., TR96, 1996.
[ALS20] Thomas Attema, Vadim Lyubashevsky, and Gregor Seiler. Practical product proofs for lattice commitments. In Daniele Micciancio and Thomas Ristenpart, editors, Advances in Cryptology – CRYPTO 2020, pages 470–499, Cham, 2020. Springer International Publishing. [Ban93] W. Banaszczyk. New bounds in some transference theorems in the geometry of numbers. Mathematische Annalen, 296(1):625–635, Dec 1993. [BDL+18] Carsten Baum, Ivan Damgård, Vadim Lyubashevsky, Sabine Oechsner, and Chris Peikert. More efficient commitments from structured lattice assumptions. In Dario Catalano and Roberto De Prisco, editors, Security and Cryptography for Networks, pages 368–385, Cham, 2018. Springer International Publishing. [BLS19] Jonathan Bootle, Vadim Lyubashevsky, and Gregor Seiler. Algebraic techniques for short(er) exact lattice-based zero-knowledge proofs. In Alexandra Boldyreva and Daniele Micciancio, editors, Advances in Cryptology – CRYPTO 2019, pages 176–202, Cham, 2019. Springer International Publishing. [ENS20] Muhammed F. Esgin, Ngoc Khanh Nguyen, and Gregor Seiler. Practical exact proofs from lattices: New techniques to exploit fully-splitting rings. In Shiho Moriai and Huaxiong Wang, editors, Advances in Cryptology – ASIACRYPT 2020, pages 259–288, Cham, 2020. Springer International Publishing. [ESLL19] Muhammed F. Esgin, Ron Steinfeld, Joseph K. Liu, and Dongxi Liu. Lattice-based zero-knowledge proofs: New techniques for shorter andfaster constructions and applications. In Alexandra Boldyreva and Daniele Micciancio, editors, Advances in Cryptology – CRYPTO 2019,pages 115–146, Cham, 2019. Springer International Publishing. [LNP22] Vadim Lyubashevsky, Ngoc Khanh Nguyen, and Maxime Plancon. Lattice-based zero-knowledge proofs and applications: Shorter, simpler, and more general. Cryptology ePrint Archive, Paper 2022/284, 2022. https://eprint.iacr.org/2022/284. [LNS20] Vadim Lyubashevsky, Ngoc Khanh Nguyen, and Gregor Seiler. Practical lattice-based zero-knowledge proofs for integer relations. Cryptology ePrint Archive, Paper 2020/1183, 2020. https://eprint.iacr.org/2020/1183. [LNS21] Vadim Lyubashevsky, Ngoc Khanh Nguyen, and Gregor Seiler. Shorter lattice-based zero-knowledge proofs via one-time commitments. In Juan A. Garay, editor, Public-Key Cryptography – PKC 2021, pages 215–241, Cham, 2021. Springer International Publishing. [LNSW13] San Ling, Khoa Nguyen, Damien Stehlé, and Huaxiong Wang. Improved zero-knowledge proofs of knowledge for the isis problem, and applications. In Kaoru Kurosawa and Goichiro Hanaoka, editors, Public-Key Cryptography – PKC 2013, pages 107–124, Berlin, Heidelberg, 2013. Springer Berlin Heidelberg. [Lyu12] Vadim Lyubashevsky. Lattice signatures without trapdoors. In David Pointcheval and Thomas Johansson, editors, Advances in Cryptology – EUROCRYPT 2012, pages 738–755, Berlin, Heidelberg, 2012. Springer Berlin Heidelberg. [Ste94] Jacques Stern. A new identification scheme based on syndrome decoding. In Douglas R. Stinson, editor, Advances in Cryptology — CRYPTO’ 93, pages 13–21, Berlin, Heidelberg, 1994. Springer Berlin Heidelberg. | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91706 | - |
dc.description.abstract | 在[LNS20]中,作者設計兩個整數關係的晶格基底零知識證明協定,分別是證明第三個秘密整數是另外兩個秘密整數的和,而另一個則是其乘法版本的,然而這兩個協定都要求底層的環擁有多個CRT slots,這導致了無法忽視的可靠度誤差。
依據[LNP22]的基礎,我們建構了兩個零知識協定,用於證明先前所提及的整數問題,而無需對底層的環進行先前的限制。此外,我們將加法版本協定推廣到證明k個整數之和,其中k取決於秘密整數的二進位表示。 關鍵字: 整數關係的晶格基底零知識證明協定、ABDLOP承諾計畫、承諾與證明協定、MSIS問題、Extended-MLWE問題 | zh_TW |
dc.description.abstract | In [LNS20], the authors designed two zero-knowledge protocols for integer relations. The underlying rings of the two lattice-based protocols possess many CRT slots, which has a negative effect on soundness error. One is for proving that the third secret integer is the sum of two other secret integers, while the other is the multiplicative version. Based on the foundation laid by [LNP22], we construct two zero-knowledge protocols dealing with the original problem without the previous requirement for the underlying ring. Moreover, we generalize the addition protocol from sum of two integers to sum of k integers, dependent of bits representing our secret ones.
Keywords: Lattice-based zero-knowledge protocol for integer relations, ABDLOP commitment scheme, Commit-and-prove protocol, MSIS, Extended-MLWE | en |
dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-02-22T16:20:03Z No. of bitstreams: 0 | en |
dc.description.provenance | Made available in DSpace on 2024-02-22T16:20:04Z (GMT). No. of bitstreams: 0 | en |
dc.description.tableofcontents | Contents
Acknowledgements i 摘要 ii Abstract iii 1 Introduction 1 2 Preliminaries 3 2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Cyclotomic Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Discrete Gaussian Distributions . . . . . . . . . . . . . . . . . . . . . 5 2.4 Module-SIS and Module-LWE Problems . . . . . . . . . . . . . . . . 5 2.5 Rejection Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.6 Challenge Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Proofs for Quadratic Relations 10 3.1 Commit-and-prove Protocol . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Main Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4 Applications to Integer Relation 20 4.1 Integer Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.2 Integer Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . 28 References 30 | - |
dc.language.iso | en | - |
dc.title | 格基底整數關係的承諾與證明 | zh_TW |
dc.title | Lattice-Based Commit-and-Prove Proofs for Integer Relations | en |
dc.type | Thesis | - |
dc.date.schoolyear | 112-1 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 楊柏因;陳君朋;陳榮傑;謝致仁 | zh_TW |
dc.contributor.oralexamcommittee | Bo-Yin Yang;Jiun-Peng Chen;Rong-Jaye Chen;Jyh-Ren Shieh | en |
dc.subject.keyword | 整數關係的晶格基底零知識證明協定,ABDLOP承諾計畫,承諾與證明協定,MSIS問題,Extended-MLWE問題, | zh_TW |
dc.subject.keyword | Lattice-based zero-knowledge protocol for integer relations,ABDLOP commitment scheme,Commit-and-prove protocol,MSIS,Extended-MLWE, | en |
dc.relation.page | 32 | - |
dc.identifier.doi | 10.6342/NTU202400442 | - |
dc.rights.note | 同意授權(全球公開) | - |
dc.date.accepted | 2024-02-06 | - |
dc.contributor.author-college | 理學院 | - |
dc.contributor.author-dept | 數學系 | - |
顯示於系所單位: | 數學系 |
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