臺灣大學: 數學研究所陳君明江政融Jiang, Jeng-RungJeng-RungJiang2013-03-212018-06-282013-03-212018-06-282010http://ntur.lib.ntu.edu.tw//handle/246246/249841首先，本論文將介紹NTRU公鑰系統的基本運作，隨即以密碼分析的角度帶出lattice結構的一些相關知識，並且描述和證明LLL演算法，以說明現今攻擊NTRU系統的主要方法。最後將NTRU系統做更進一步的推廣，於參數上使用一些限制條件，賦予加密函數同態的特性。This thesis introduces how the NTRU cryptosystem works and an elementary cryptanalysis about lattice. After ntroducing NTRU, we briefly describe the lattice structure and LLL, the lattice reduction algorithm from a cryptanalytic point of view, and then express the relations between NTRU and the lattice structure. Finally, we extend the system by adjusting the key space, parameters and message space with appropriate restrictions to endow NTRU encryption with various properties of ring homomorphism.429582 bytesapplication/pdfen-US多項式環NTRUlatticeLLL演算法apprSVPhomomorphic encryptionPolynomial ringsLLL algorithmthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/249841/1/ntu-99-R97221001-1.pdf