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Erschienen in:
01.12.2011
De Bruijn sequences and complexity of symmetric functions
Erschienen in: Cryptography and Communications | Ausgabe 4/2011
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Abstract
A multivalued function is a function from a set \(E_{q}^{n}\) to a set E
m
, where E
k
is a set which contains k elements. These functions are used in cryptography: cipher design, hash function design and in theoretical computer science. In this paper, we study the representation of these functions with Multivalued Decision Diagrams (MDD). This representation can be used both to measure complexity and to implement efficiently the functions in hardware. We are especially interested in symmetric functions. We show that symmetric functions MDDs have much lower size than classical functions MDDs. One major result is to determine exactly their MDD’s maximum size. Notably, we highlight the links between De Bruijn sequences and the most complex symmetric functions and new functions are exhibited in the case q = 2 and any m. Enumeration of these functions are supplied, they are shown to be sufficiently numerous to allow many applications.