Enumerating nondegenerate permutations

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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 fi that describes the output ci is nondegenerate, for 1 ≤ i ≤ n. Let Nn, n be the set of nondegenerate permutations. We will derive an exact expression for |Nn,n|, and show that (Formula presented.).

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O’Connor, L. (1991). Enumerating nondegenerate permutations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 547 LNCS, pp. 368–377). Springer Verlag. https://doi.org/10.1007/3-540-46416-6_31

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