双完全非线性布尔置换
Doubly Perfect Nonlinear Boolean Permutations
摘要：
由于实现上的限制，异或运算被广泛地用于组合明文和密钥比特串。这种选择直接导致了经典版本的差分攻击使用XOR类差异。虽然非常自然，但XOR有许多替代方案。它们中的每一个都为相应的差分攻击引入了一种新的形式（使用适当的差分概念），因此分组密码需要使用抵抗这些非标准差分密码分析的S盒。在这方面的贡献，我们研究的功能，提供最好的抵抗差分攻击的基础上有限域乘法。我们还表明，在某些特定的情况下，有强大的排列，提供了最好的抵抗乘法和指数基差分攻击。我们称之为双完全非线性置换。
英文摘要：
Due to implementation constraints the XOR operation is widely used in order to combine plaintext and key bit-strings in secret-key block ciphers. This choice directly induces the classical version of the differential attack by the use of XOR-kind differences. While very natural, there are many alternatives to the XOR. Each of them inducing a new form for its corresponding differential attack (using the appropriate notion of difference) and therefore block-ciphers need to use S-boxes that are resistant against these nonstandard differential cryptanalysis. In this contribution we study the functions that offer the best resistance against a differential attack based on a finite field multiplication. We also show that in some particular cases, there are robust permutations which offers the best resistant against both multiplication and exponentiation base differential attacks. We call them doubly perfect nonlinear permutations.
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