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Enumerating Nondegenerate Permutations

  • Luke O’Connor
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)

Abstract

Every cryptosystem with an n-bit block length may be modeled as a system of n-bit boolean equations. The cipher is said to be nondegenerate if the equation f i that describes the output c i is nondegenerate, for 1 ≤ in. Let N n,n be the set of nondegenerate permutations. We will derive an exact expression for |N n,n|, and show that
$$ \frac{{\left| {\mathcal{N}^{n,n} } \right|}} {{2^n !}} = 1 + o\left( {\frac{{\sqrt {2^n } }} {{2^{2^{n - 1} + n} }}} \right). $$
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Luke O’Connor
    • 1
  1. 1.Department of Computer ScienceUniversity of WaterlooOntarioCanada

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