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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 Higher-order differential cryptanalysis ： ウィキペディア英語版 Higher-order differential cryptanalysis In cryptography, higher-order differential cryptanalysis is a generalization of differential cryptanalysis, an attack used against block ciphers. While in standard differential cryptanalysis the difference between only two texts is used, higher-order differential cryptanalysis studies the propagation of a set of differences between a larger set of texts. Xuejia Lai, in 1994, laid the groundwork by showing that differentials are a special case of the more general case of higher order derivates. Lars Knudsen, in the same year, was able to show how the concept of higher order derivatives can be used to mount attacks on block ciphers. These attacks can be superior to standard differential cryptanalysis. Higher-order differential cryptanalysis has notably been used to break the KN-Cipher, a cipher which had previously been proved to be immune against standard differential cryptanalysis. ==Higher-order derivatives== A block cipher which maps $n$-bit strings to $n$-bit strings can, for a fixed key, be thought of as a function $f:\backslash mathbb^n\_2\backslash to\backslash mathbb^n\_2$. In standard differential cryptanalysis, one is interested in finding a pair of an input difference $\backslash alpha$ and an output difference $\backslash beta$ such that two input texts with difference $\backslash alpha$ are likely to result in output texts with a difference $\backslash beta$ i.e., that $f(m\backslash oplus\backslash alpha)\backslash oplus\; f(m)\; =\; \backslash beta$ is true for many $m\backslash in\backslash mathbb^n\_2$. Note that the difference used here is the XOR which is the usual case, though other definitions of difference are possible. This motivates defining the derivative of a function $f:\backslash mathbb^n\_2\backslash to\backslash mathbb^n\_2$ at a point $\backslash alpha$ as〔 $\backslash Delta\_\backslash alpha\; f(x)\; :=\; f(x\backslash oplus\backslash alpha)\backslash oplus\; f(x)$. Using this definition, the $i$-th derivative at $(\backslash alpha\_1,\backslash alpha\_2,\backslash dots,\backslash alpha\_i)$ can recursively be defined as〔 $\backslash Delta^\_\; f(x)\; :=\; \backslash Delta\_\backslash left(\backslash Delta^\_\_\; f(x)\; =\; f(x)\backslash oplus\; f(x\backslash oplus\backslash alpha\_1)\backslash oplus\; f(x\backslash oplus\backslash alpha\_2)\backslash oplus\; f(x\backslash oplus\backslash alpha\_1\backslash oplus\backslash alpha\_2)$. Higher order derivatives as defined here have many properties in common with ordinary derivative such as the sum rule and the product rule. Importantly also, taking the derivative reduces the algebraic degree of the function. 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「Higher-order differential cryptanalysis」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.