700 research outputs found
On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees
In the literature, few constructions of -variable rotation symmetric bent
functions have been presented, which either have restriction on or have
algebraic degree no more than . In this paper, for any even integer
, a first systemic construction of -variable rotation symmetric
bent functions, with any possible algebraic degrees ranging from to , is
proposed
Systematic Constructions of Bent-Negabent Functions, 2-Rotation Symmetric Bent-Negabent Functions and Their Duals
Bent-negabent functions have many important properties for their application
in cryptography since they have the flat absolute spectrum under the both
Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present
four new systematic constructions of bent-negabent functions on
and variables, respectively, by modifying the truth tables of two
classes of quadratic bent-negabent functions with simple form. The algebraic
normal forms and duals of these constructed functions are also determined. We
further identify necessary and sufficient conditions for those bent-negabent
functions which have the maximum algebraic degree. At last, by modifying the
truth tables of a class of quadratic 2-rotation symmetric bent-negabent
functions, we present a construction of 2-rotation symmetric bent-negabent
functions with any possible algebraic degrees. Considering that there are
probably no bent-negabent functions in the rotation symmetric class, it is the
first significant attempt to construct bent-negabent functions in the
generalized rotation symmetric class
Algebraic normal form of a bent function: properties and restrictions
Maximally nonlinear Boolean functions in variables, where n is
even, are called bent functions. There are several ways to represent
Boolean functions. One of the most useful is via algebraic normal
form (ANF). What can we say about ANF of a bent function? We try to
collect all known and new facts related to ANF of a bent function. A
new problem in bent functions is stated and studied: is it true that
a linear, quadratic, cubic, etc. part of ANF of a bent function can
be arbitrary? The case of linear part is well studied before. In
this paper we prove that a quadratic part of a bent function can be
arbitrary too
Construction of cubic homogeneous boolean bent functions
We prove that cubic homogeneous bent functions f : V2n → GF(2) exist for all n ≥ 3 except for n = 4
Nonsupersymmetric Brane/Antibrane Configurations in Type IIA and M Theory
We study metastable nonsupersymmetric configurations in type IIA string
theory, obtained by suspending D4-branes and anti-D4-branes between
holomorphically curved NS5's, which are related to those of hep-th/0610249 by
T-duality. When the numbers of branes and antibranes are the same, we are able
to obtain an exact M theory lift which can be used to reliably describe the
vacuum configuration as a curved NS5 with dissolved RR flux for g_s<<1 and as a
curved M5 for g_s>>1. When our weakly coupled description is reliable, it is
related by T-duality to the deformed IIB geometry with flux of hep-th/0610249
with moduli exactly minimizing the potential derived therein using special
geometry. Moreover, we can use a direct analysis of the action to argue that
this agreement must also hold for the more general brane/antibrane
configurations of hep-th/0610249. On the other hand, when our strongly coupled
description is reliable, the M5 wraps a nonholomorphic minimal area curve that
can exhibit quite different properties, suggesting that the residual structure
remaining after spontaneous breaking of supersymmetry at tree level can be
further broken by the effects of string interactions. Finally, we discuss the
boundary condition issues raised in hep-th/0608157 for nonsupersymmetric IIA
configurations, their implications for our setup, and their realization on the
type IIB side.Comment: 84 pages (57 pages + 4 appendices), 18 figure
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