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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 Affine cipher ： ウィキペディア英語版 Affine cipher The affine cipher is a type of monoalphabetic substitution cipher, wherein each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and converted back to a letter. The formula used means that each letter encrypts to one other letter, and back again, meaning the cipher is essentially a standard substitution cipher with a rule governing which letter goes to which. As such, it has the weaknesses of all substitution ciphers. Each letter is enciphered with the function $(ax+b)\backslash mod(26)$, where $b$ is the magnitude of the shift. ==Description== In the affine cipher the letters of an alphabet of size $m$ are first mapped to the integers in the range $0\; ..\; m-1$. It then uses modular arithmetic to transform the integer that each plaintext letter corresponds to into another integer that correspond to a ciphertext letter. The encryption function for a single letter is :$\backslash mbox(x)=(ax+b)\backslash mod,$ where modulus $m$ is the size of the alphabet and $a$ and $b$ are the key of the cipher. The value $a$ must be chosen such that $a$ and $m$ are coprime. The decryption function is :$\backslash mbox(x)=a^(x-b)\backslash mod,$ where $a^$ is the modular multiplicative inverse of $a$ modulo $m$. I.e., it satisfies the equation :$1\; =\; a\; a^\backslash mod.$ The multiplicative inverse of $a$ only exists if $a$ and $m$ are coprime. Hence without the restriction on $a$ decryption might not be possible. It can be shown as follows that decryption function is the inverse of the encryption function, :$$ \begin \mbox(\mbox(x)) &= a^(\mbox(x)-b)\mod\\ &= a^(((ax+b)\mod)-b)\mod \\ &= a^(ax+b-b)\mod \\ &= a^ax \mod\\ &= x\mod. \end 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「Affine cipher」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.