Cryptographically secure substitutions based on the approximation of mixing maps
Cryptographically secure substitutions based on the approximation of mixing maps
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DOI：
10.1109/tcsi.2004.841602
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发表时间：
2005-02
期刊：
影响因子：
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通讯作者：
J. Szczepański;J. Amigó;T. Michalek;L. Kocarev
中科院分区：
文献类型：
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作者：
J. Szczepański;J. Amigó;T. Michalek;L. Kocarev
在本文中，我们探讨，香农的建议，扩散应该是一个耐分组密码的成分，设计密码安全的替代（想想S盒，说）通过近似的混合映射的周期性变换的可行性。当然，这种方法背后的期望是，这种映射的良好扩散性质将被它们的近似所继承，至少如果收敛速度是适当的，并且相关的分区是足够精细的。我们的研究结果表明，这确实是这样的情况下，在原则上，块密码接近最佳免疫线性和差分密码分析（测量的线性和差分近似概率）可以设计沿着这些准则。我们还提供了实际的例子和数值证据，这种近似的哲学。
In this paper, we explore, following Shannon's suggestion that diffusion should be one of the ingredients of resistant block ciphers, the feasibility of designing cryptographically secure substitutions (think of S-boxes, say) via approximation of mixing maps by periodic transformations. The expectation behind this approach is, of course, that the nice diffusion properties of such maps will be inherited by their approximations, at least if the convergence rate is appropriate and the associated partitions are sufficiently fine. Our results show that this is indeed the case and that, in principle, block ciphers with close-to-optimal immunity to linear and differential cryptanalysis (as measured by the linear and differential approximation probabilities) can be designed along these guidelines. We provide also practical examples and numerical evidence for this approximation philosophy.