THE INCLUSION-EXCLUSION PRINCIPLE AND ITS APPLICATIONS TO CRYPTOGRAPHY

The inclusion-exclusion principle is a combinatorial method for determining the cardinality of a set where each element X∈U satisfies a list of properties . In this paper we will display the usefulness of the inclusion-exclusion principle by solving 8 problems of interest to cryptography. These prob...

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Vydáno v:Cryptologia Ročník 17; číslo 1; s. 63 - 79
Hlavní autor: O'Connor, Luke
Médium: Journal Article
Jazyk:angličtina
Vydáno: Rose-Hulman Institute of Technology 01.01.1993
Témata:
boolean functions
enumeration
inclusion-exclusion principle
permutations
Probability
ISSN:0161-1194, 1558-1586
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Shrnutí:The inclusion-exclusion principle is a combinatorial method for determining the cardinality of a set where each element X∈U satisfies a list of properties . In this paper we will display the usefulness of the inclusion-exclusion principle by solving 8 problems of interest to cryptography. These problems will concentrate on the enumeration of boolean functions and permutations that have properties which are considered to be necessary for a cryptographic mapping to be secure. In particular we will be concerned with the properties of nonlinearity and nondegeneracy as these properties correspond to Shannon's notions of confusion and diffusion, respectively.
ISSN:0161-1194
1558-1586
DOI:10.1080/0161-119391867773