Enumerating nondegenerate permutations

Authors:
Luke O'Connor
Affiliations:
Department of Computer Science, University of Waterloo, Ontario, Canada
Venue:
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Year:
1991

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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 Nn,n|/2n! = 1+o(√2n/22n-1+n).