48,609 research outputs found
A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes Fields of Even Degree
Functions with low differential uniformity can be used as the s-boxes of
symmetric cryptosystems as they have good resistance to differential attacks.
The AES (Advanced Encryption Standard) uses a differentially-4 uniform function
called the inverse function. Any function used in a symmetric cryptosystem
should be a permutation. Also, it is required that the function is highly
nonlinear so that it is resistant to Matsui's linear attack. In this article we
demonstrate that a highly nonlinear permutation discovered by Hans Dobbertin
has differential uniformity of four and hence, with respect to differential and
linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem
as the inverse function.Comment: 10 pages, submitted to Finite Fields and Their Application
On the Derivative Imbalance and Ambiguity of Functions
In 2007, Carlet and Ding introduced two parameters, denoted by and
, quantifying respectively the balancedness of general functions
between finite Abelian groups and the (global) balancedness of their
derivatives , (providing an
indicator of the nonlinearity of the functions). These authors studied the
properties and cryptographic significance of these two measures. They provided
for S-boxes inequalities relating the nonlinearity to ,
and obtained in particular an upper bound on the nonlinearity which unifies
Sidelnikov-Chabaud-Vaudenay's bound and the covering radius bound. At the
Workshop WCC 2009 and in its postproceedings in 2011, a further study of these
parameters was made; in particular, the first parameter was applied to the
functions where is affine, providing more nonlinearity parameters.
In 2010, motivated by the study of Costas arrays, two parameters called
ambiguity and deficiency were introduced by Panario \emph{et al.} for
permutations over finite Abelian groups to measure the injectivity and
surjectivity of the derivatives respectively. These authors also studied some
fundamental properties and cryptographic significance of these two measures.
Further studies followed without that the second pair of parameters be compared
to the first one.
In the present paper, we observe that ambiguity is the same parameter as
, up to additive and multiplicative constants (i.e. up to rescaling). We
make the necessary work of comparison and unification of the results on ,
respectively on ambiguity, which have been obtained in the five papers devoted
to these parameters. We generalize some known results to any Abelian groups and
we more importantly derive many new results on these parameters
On Equivalence of Known Families of APN Functions in Small Dimensions
In this extended abstract, we computationally check and list the
CCZ-inequivalent APN functions from infinite families on for n
from 6 to 11. These functions are selected with simplest coefficients from
CCZ-inequivalent classes. This work can simplify checking CCZ-equivalence
between any APN function and infinite APN families.Comment: This paper is already in "PROCEEDING OF THE 20TH CONFERENCE OF FRUCT
ASSOCIATION
Further Results of the Cryptographic Properties on the Butterfly Structures
Recently, a new structure called butterfly introduced by Perrin et at. is
attractive for that it has very good cryptographic properties: the differential
uniformity is at most equal to 4 and algebraic degree is also very high when
exponent . It is conjecture that the nonlinearity is also optimal for
every odd , which was proposed as a open problem. In this paper, we further
study the butterfly structures and show that these structure with exponent
have also very good cryptographic properties. More importantly, we
prove in theory the nonlinearity is optimal for every odd , which completely
solve the open problem. Finally, we study the butter structures with trivial
coefficient and show these butterflies have also optimal nonlinearity.
Furthermore, we show that the closed butterflies with trivial coefficient are
bijective as well, which also can be used to serve as a cryptographic
primitive.Comment: 20 page
High-frequency oscillations in low-dimensional conductors and semiconductor superlattices induced by current in stack direction
A narrow energy band of the electronic spectrum in some direction in
low-dimensional crystals may lead to a negative differential conductance and
N-shaped I-V curve that results in an instability of the uniform stationary
state. A well-known stable solution for such a system is a state with electric
field domain. We have found a uniform stable solution in the region of negative
differential conductance. This solution describes uniform high-frequency
voltage oscillations. Frequency of the oscillation is determined by antenna
properties of the system. The results are applicable also to semiconductor
superlattices.Comment: 8 pages, 3 figure
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