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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 Damgård–Jurik cryptosystem ： ウィキペディア英語版 Damgård–Jurik cryptosystem The Damgård–Jurik cryptosystem〔Ivan Damgård, Mads Jurik: (A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System ). Public Key Cryptography 2001: 119-136〕 is a generalization of the Paillier cryptosystem. It uses computations modulo $n^$ where $n$ is an RSA modulus and $s$ a (positive) natural number. Paillier's scheme is the special case with $s=1$. The order $\backslash varphi(n^)$ (Euler's totient function) of $Z^$ *_} can be written as the direct product of $G\; \backslash times\; H$. $G$ is cyclic and of order $n^s$, while $H$ is isomorphic to $Z^$ *_n. For encryption, the message is transformed into the corresponding coset of the factor group $G/H$ and the security of the scheme relies on the difficulty of distinguishing random elements in different cosets of $H$. It is semantically secure if it is hard to decide if two given elements are in the same coset. Like Paillier, the security of Damgård–Jurik can be proven under the decisional composite residuosity assumption. == Key generation == #Choose two large prime numbers ''p'' and ''q'' randomly and independently of each other. #Compute $n=pq$ and $\backslash lambda=\backslash operatorname(p-1,q-1)$. #Choose an element $g\; \backslash in\; \backslash mathbb^$ *_ for a known $j$ relative prime to $n$ and $x\; \backslash in\; H$. #Using the Chinese Remainder Theorem, choose $d$ such that $d\; \backslash mod\; n\; \backslash in\; \backslash mathbb^$ *_n and $d=\; 0\; \backslash mod\; \backslash lambda$. For instance $d$ could be $\backslash lambda$ as in Paillier's original scheme. *The public (encryption) key is $(n,\; g)$. *The private (decryption) key is $d$. 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「Damgård–Jurik cryptosystem」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.