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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Ideal lattice cryptography ： ウィキペディア英語版 Ideal lattice cryptography Ideal lattices are a special class of lattices and a generalization of cyclic lattices.〔 Vadim Lyubashevsky. (Lattice-Based Identification Schemes Secure Under Active Attacks ). In ''Proceedings of the Practice and theory in public key cryptography , 11th international conference on Public key cryptography'', 2008.〕 Ideal lattices naturally occur in many parts of number theory, but also in other areas. In particular, they have a significant place in cryptography. Micciancio defined a generalization of cyclic lattices as ideal lattices. They can be used in cryptosystems to decrease by a square root the number of parameters necessary to describe a lattice, making them more efficient. Ideal lattices are a new concept, but similar lattice classes have been used for a long time. For example cyclic lattices, a special case of ideal lattices, are used in NTRUEncrypt and NTRUSign. Ideal lattices also form the basis for quantum computer attack resistant cryptography based on the Ring Learning with Errors. These cryptosystems are provably secure under the assumption that the Shortest Vector Problem (SVP) is hard in these ideal lattices. ==Introduction== In general terms, ideal lattices are lattices corresponding to ideals in rings of the form $\backslash mathbb()/\backslash langle\; f\; \backslash rangle$ for some irreducible polynomial $f$ of degree $n$.〔 All of the definitions of ''ideal lattices'' from prior work are instances of the following general notion: let $R$ be a ring whose additive group is isomorphic to $\backslash mathbb^n$ (i.e., it is a free $\backslash mathbb$-module of rank $n$), and let $\backslash sigma$ be an additive isomorphism mapping $R$ to some lattice $\backslash sigma(R)$ in an $n$-dimensional real vector space (e.g., $\backslash mathbb^n$). The family of ''ideal lattices'' for the ring $R$ under the embedding $\backslash sigma$ is the set of all lattices $\backslash sigma(I)$, where $I$ is an ideal in $R.$〔Vadim Lyubashevsky, Chris Peikert and Oded Regev. ( On Ideal Lattices and Learning with Errors over Rings ). In Eurocrypt 2010, ''Lecture Notes in Computer Science'', 2010.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ideal lattice cryptography」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.