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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 Wiener's attack ： ウィキペディア英語版 Wiener's attack The Wiener's attack, named after cryptologist Michael J. Wiener, is a type of cryptographic attack against RSA. The attack uses the continued fraction method to expose the private key ''d'' when ''d'' is small. == Background on RSA == Before we discuss how Wiener's attack works, we will first briefly explain how RSA works. For more details see the main entry on the RSA cryptosystem. Let Alice and Bob be two people who want to communicate securely. More specifically, Alice wants to send a message to Bob which only Bob can read. First Bob chooses two primes ''p'' and ''q''. Then he calculates the RSA modulus ''N'' = ''pq''. This RSA modulus is made public together with the encryption exponent ''e''. ''N'' and ''e'' form the public key pair ''(e,N)''. By making this information public, anyone can encrypt messages to Bob. The decryption exponent ''d'' satisfies $ed=1\; \backslash bmod\; \backslash varphi\; (N)$, where $\backslash varphi\; (N)=\; (p-1)(q-1)$, is Euler’s phi function (note: this is the order of the multiplicative group $\backslash mathbb\_N^$ *). The encryption exponent ''e'' and $\backslash varphi\; (N)$ also must be relatively prime so that there is a modular inverse. The factorization of ''N'' and the private key ''d'' are kept secret, so that only Bob can decrypt the message. We denote the private key pair as ''(d, N)''. The encryption of the message ''M'' is given by $C\backslash equiv\; M^e\backslash bmod\; \backslash varphi\; (N)$ and the decryption of cipher text $C$ is given by $C^d\backslash equiv\; (M^e)^d\backslash equiv\; M^\backslash equiv\; M\; \backslash bmod\; \backslash varphi\; (N)$ (using Fermat's little theorem). Using the Euclidean algorithm, one can efficiently recover the secret key ''d'' if one knows the factorization of ''N.'' By having the secret key ''d'', one can efficiently factor the modulus of ''N''.〔(L. Render, Elaine (2007). Wiener's Attack on Short Secret Exponents. )〕 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「Wiener's attack」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.