Observability of permutations, and stream ciphers
Observability of permutations, and stream ciphers
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DOI：
10.1109/tit.2003.820032
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发表时间：
2003-12
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影响因子：
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通讯作者：
R. E. Byerly;L. Drager;Jeffrey M. Lee
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文献类型：
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作者：
R. E. Byerly;L. Drager;Jeffrey M. Lee
我们研究了由复杂值函数设置的有限函数上置换的可观察性。该分析是根据统计定义的函数的统一操作员的光谱理论进行的。任何功能f都可以独特地写作该操作员的特征函数的总和；我们将这些本征函数称为f的特征组件。结果表明，当且仅当其特征组件分开点时，并且仅当函数没有保留动力学的非平凡对称性时，才能观察到置换。讨论了更多的技术条件。讨论了对流密码的安全性的应用程序。
We study the observability of a permutation on a finite set by a complex-valued function. The analysis is done in terms of the spectral theory of the unitary operator on functions defined by the permutation. Any function f can be written uniquely as a sum of eigenfunctions of this operator; we call these eigenfunctions the eigencomponents of f. It is shown that a function observes the permutation if and only if its eigencomponents separate points and if and only if the function has no nontrivial symmetry that preserves the dynamics. Some more technical conditions are discussed. An application to the security of stream ciphers is discussed.