2,802 research outputs found
A complete characterization of plateaued Boolean functions in terms of their Cayley graphs
In this paper we find a complete characterization of plateaued Boolean
functions in terms of the associated Cayley graphs. Precisely, we show that a
Boolean function is -plateaued (of weight ) if and only
if the associated Cayley graph is a complete bipartite graph between the
support of and its complement (hence the graph is strongly regular of
parameters ). Moreover, a Boolean function is
-plateaued (of weight ) if and only if the associated
Cayley graph is strongly -walk-regular (and also strongly
-walk-regular, for all odd ) with some explicitly given
parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201
Generalized bent Boolean functions and strongly regular Cayley graphs
In this paper we define the (edge-weighted) Cayley graph associated to a
generalized Boolean function, introduce a notion of strong regularity and give
several of its properties. We show some connections between this concept and
generalized bent functions (gbent), that is, functions with flat Walsh-Hadamard
spectrum. In particular, we find a complete characterization of quartic gbent
functions in terms of the strong regularity of their associated Cayley graph.Comment: 13 pages, 2 figure
Partially APN Boolean functions and classes of functions that are not APN infinitely often
In this paper we define a notion of partial APNness and find various
characterizations and constructions of classes of functions satisfying this
condition. We connect this notion to the known conjecture that APN functions
modified at a point cannot remain APN. In the second part of the paper, we find
conditions for some transformations not to be partially APN, and in the
process, we find classes of functions that are never APN for infinitely many
extensions of the prime field \F_2, extending some earlier results of Leander
and Rodier.Comment: 24 pages; to appear in Cryptography and Communication
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