2,257 research outputs found
An Equivalent Condition on the Switching Construction of Differentially -uniform Permutations on \gf_{2^{2k}} from the Inverse Function
Differentially -uniform permutations on \gf_{2^{2k}} with high nonlinearity are often chosen as substitution boxes in block ciphers.
Recently, Qu et al. used the powerful switching method to construct permutations with low differential uniformity from the inverse function \cite{QTTL, QTLG} and proposed a sufficient but not necessary condition for these permutations to be differentially -uniform.
In this paper, a sufficient and necessary condition is presented.
We also give a compact estimation for the number of constructed differentially -uniform permutations.
Comparing with those constructions in \cite{QTTL, QTLG}, the number of functions constructed here is much bigger.
As an application, a new class of differentially -uniform permutations is constructed.
The obtained functions in this paper may provide more choices for the design of substitution boxes
A New Class of Differentially 4-uniform Permutations from the Inverse Function
Differentially 4-uniform permutations on with high nonlinearity and algebraic degree are often used in block ciphers and some stream ciphers as Substitution boxes. Recently,Chen et al.(An equivalent
condition on the switching construction of differentially 4-uniform permutations on from the inverse function, International Journal of Computer Mathematics, DOI:10.1080/00207160.2016.1167884) presented a n equivalent condition on the switching construction. More precisely,they presented a sufficient and necessary condition on differentially 4-uniform permutations on of the form , where is a Boolean function. However, the number of the satisfied functions is so enormous that it is difficult to find all the functions. In this paper,a new class of such functions are constructed. These functions may provide more options for the design of Substitute boxes
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
Wave-Shaped Round Functions and Primitive Groups
Round functions used as building blocks for iterated block ciphers, both in
the case of Substitution-Permutation Networks and Feistel Networks, are often
obtained as the composition of different layers which provide confusion and
diffusion, and key additions. The bijectivity of any encryption function,
crucial in order to make the decryption possible, is guaranteed by the use of
invertible layers or by the Feistel structure. In this work a new family of
ciphers, called wave ciphers, is introduced. In wave ciphers, round functions
feature wave functions, which are vectorial Boolean functions obtained as the
composition of non-invertible layers, where the confusion layer enlarges the
message which returns to its original size after the diffusion layer is
applied. This is motivated by the fact that relaxing the requirement that all
the layers are invertible allows to consider more functions which are optimal
with regard to non-linearity. In particular it allows to consider injective APN
S-boxes. In order to guarantee efficient decryption we propose to use wave
functions in Feistel Networks. With regard to security, the immunity from some
group-theoretical attacks is investigated. In particular, it is shown how to
avoid that the group generated by the round functions acts imprimitively, which
represent a serious flaw for the cipher
New Results about the Boomerang Uniformity of Permutation Polynomials
In EUROCRYPT 2018, Cid et al. \cite{BCT2018} introduced a new concept on the
cryptographic property of S-boxes: Boomerang Connectivity Table (BCT for short)
for evaluating the subtleties of boomerang-style attacks. Very recently, BCT
and the boomerang uniformity, the maximum value in BCT, were further studied by
Boura and Canteaut \cite{BC2018}. Aiming at providing new insights, we show
some new results about BCT and the boomerang uniformity of permutations in
terms of theory and experiment in this paper. Firstly, we present an equivalent
technique to compute BCT and the boomerang uniformity, which seems to be much
simpler than the original definition from \cite{BCT2018}. Secondly, thanks to
Carlet's idea \cite{Carlet2018}, we give a characterization of functions
from to itself with boomerang uniformity by
means of the Walsh transform. Thirdly, by our method, we consider boomerang
uniformities of some specific permutations, mainly the ones with low
differential uniformity. Finally, we obtain another class of -uniform BCT
permutation polynomials over , which is the first binomial.Comment: 25 page
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