請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8350完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳君明(Jiun-Ming Chen) | |
| dc.contributor.author | Yi-Lin Hung | en |
| dc.contributor.author | 洪逸霖 | zh_TW |
| dc.date.accessioned | 2021-05-20T00:52:33Z | - |
| dc.date.available | 2020-08-25 | |
| dc.date.available | 2021-05-20T00:52:33Z | - |
| dc.date.copyright | 2020-08-25 | |
| dc.date.issued | 2020 | |
| dc.date.submitted | 2020-08-03 | |
| dc.identifier.citation | [1]C. P. Abhishek Banerjee and A. Rosen. Pseudorandom functions and lattices. 26,2011. [2]E. T. Adriana Lopez-Alt and V. Vaikuntanathan. On-the-fly multiparty computationon the cloud via multikey fully homomorphic encryption. 70, 2013. [3]G. T. D. K. G. Christopher Carr, Anamaria Costache and M. Strand. Zero-knowledgeproof of decryption for fhe ciphertexts. 16:16, 2018. [4]C. Gentry. Fully homomorphic encryption using ideal lattices. 28:169–178, 2009. [5]T. L. Jean-Sebastien Coron and M. Tibouchi. Batch fully homomorphic encryptionover the integers. 27, 2013. [6]D. N. Jean-S ́ebastien Coron and M. Tibouchi. Public key compression and modulusswitching for fully homomorphic encryption over the integers. 27, 2011. [7]K. P. Joel Alwen, Stephan Krenn and D. Wichs. Learning with rounding, revisited.AnnualCryptologyConference, 18:57–74, 2013. [8]Z. Z. Long Chen and Z. Zhang. On the hardness of the computational ring-lwr prob-lem and its applications. 33, 2018. [9]D. S. Miruna Rosca, Amin Sakzad and R. Steinfeld. Middle-product learning witherrors. 17, 2017. [10]D. D. A. R.-L. W. W. Shi Bai, Katharina Boudgoust and Z. Zhang. Middle-productlearning with rounding problem and its applications. 32, 2019. [11]C. G. Zvika Brakerski and V. Vaikuntanathan. Fully homomorphic encryption with-out bootstrapping. 26, 2011. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8350 | - |
| dc.description.abstract | 我們改良了Zvika Brakerski 研發的全同態加密系統，改成使用難題假設LWR以及RLWR而不是原先使用的LWE以及RLWE難題假設。並且我們用類似的方法使得可以在MPLWR難題假設上使用同態加密。在過去，Rosca證明了難題假設MPLWE的安全性，我們同樣使用相似於的方法做成全同態加密。 | zh_TW |
| dc.description.abstract | We modified the fully homomorphic encryption (FHE) scheme produced by Zvika Brakerski with the hardness assumption learning with rounding (LWR) and ring learning with rounded (RLWR) instead of the hardness assumption learning with error (LWE) and ring learning with rounding (RLWE). And we use the similar methods on the hardness assumption middle product learning with rounding (MPLWR), i.e. making it into FHE. In present, Rosca proves the hardness assumption middle product learning with error (MPLWE). We also use 'similar' Brakerski ideas to make it into FHE. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T00:52:33Z (GMT). No. of bitstreams: 1 U0001-3107202009490700.pdf: 341460 bytes, checksum: 99f0ac1022cb0f2d1f1edf4a480c689c (MD5) Previous issue date: 2020 | en |
| dc.description.tableofcontents | Chapter 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.1 Our result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Modular Switching. . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 FHE Scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Compare to LWE (RLWE). . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 2 Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . .5 Chapter 3 Our Construction. . . . . . . . . . . . . . . . . . . . .9 3.1 Basic LWR (RLWR) encryption scheme. . . . . . . . . . . . . . . . 9 3.2 Basic MPLWE encryption scheme. . . . . . . . . . . . . . . . . . . 10 3.3 Basic MPLWR encryption scheme. . . . . . . . . . . . . . . . . . . 10 3.4 Key Switching for MPLWE and MPLWR based. . . . . . . . . . . . 11 3.5 Key Switching for LWR(RLWR) based. . . . . . . . . . . . . . . . 13 3.6 FHE scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Chapter 4 Correctness. . . . . . . . . . . . . . . . . . . . . . . . . .17 4.1 Correctness of LWR (RLWR) scheme. . . . . . . . . . . . . . . . . 17 4.2 Correctness of MPLWE(MPLWR) scheme. . . . . . . . . . . . . . 18 Chapter 5 Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.1 Bootstrapping and Batching. . . . . . . . . . . . . . . . . . . . . . 21 5.2 Public Key Compression for LWR. . . . . . . . . . . . . . . . . . . 21 Chapter 6 Zero knowledge proof. . . . . . . . . . . . . . . . . . 23 Chapter 7 Application. . . . . . . . . . . . . . . . . . .25 Chapter 8 Summary. . . . . . . . . . . . . . . . . . .27 Chapter 9 Future Work. . . . . . . . . . . . . . . . . . .29 References. . . . . . . . . . . . . . . . . . .31 | |
| dc.language.iso | en | |
| dc.title | "LWR, MPLWE 和 MPLWR 上的全同態加密" | zh_TW |
| dc.title | Fully Homomorphic Encryption on LWR, MPLWE and MPLWR | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳君朋(Jiun-Peng Chen),楊柏因(Bo-Yin Yang),謝致仁(Jyh-Ren Shieh),陳榮傑(Rong-Jaye Chen) | |
| dc.subject.keyword | LWR同態加密,環LWR同態加密,中間積LWE同態加密,中間積LWR同態加密, | zh_TW |
| dc.subject.keyword | Learning with rounding FHE,Ring learning with rounding FHE,Middle product learning with error FHE,Middle product learning with rounding FHE, | en |
| dc.relation.page | 32 | |
| dc.identifier.doi | 10.6342/NTU202002146 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2020-08-03 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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|---|---|---|---|
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