355 research outputs found
Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography
The mathematical problems and their solutions of the Third International
Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider
mathematical problems related to the construction of algebraic immune vectorial
Boolean functions and big Fermat numbers, problems about secrete sharing
schemes and pseudorandom binary sequences, biometric cryptosystems and the
blockchain technology, etc. Two open problems in mathematical cryptography are
also discussed and a solution for one of them proposed by a participant during
the Olympiad is described. It was the first time in the Olympiad history
Cryptographic properties of a simple S-box construction based on a Boolean function and a permutation
We propose a simple method of constructing S-boxes using Boolean functions and permutations. Let n be an arbitrary permutation on n elements, f be a Boolean function in n variables. Define a vectorial Boolean function Fn : F^ F^ as Fn(x) = = (f (x), f (n(x)), f (n2(x)),..., f (nn-1(x))). We study cryptographic properties of Fn such as high nonlinearity, balancedness, low differential 5-uniformity in dependence on properties of f and n for small n
Metrical properties of the set of bent functions in view of duality
In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n + 2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n > 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered
UV graviton scattering and positivity bounds from IR dispersion relations
Scattering amplitudes mediated by graviton exchange display IR singularities
in the forward limit. This obstructs standard application of positivity bounds
based on twice subtracted dispersion relations. Such divergences can be
cancelled only if the UV limit of the scattering amplitude behaves in a
specific way, which implies a very non-trivial connection between the UV and IR
behaviors of the amplitude. We show that this relation can be expressed in
terms of an integral transform, obtaining analytic results when . Carefully applying this limit to dispersion relations,
we find that infinite arc integrals, which are usually taken to vanish, can
give a non-trivial contribution in the presence of gravity, unlike in the case
of finite negative . This implies that gravitational positivity bounds
cannot be trusted unless the size of this contribution is estimated in some
way, which implies assumptions on the UV completion of gravitational
interactions. We discuss the relevance of these findings in the particular case
of QED coupled to gravity.Comment: 20 pages, 2 figure
Relativistic Model of Detonation Transition from Neutron to Strange Matter
We study the conversion of neutron matter into strange matter as a detonation
wave. The detonation is assumed to originate from a central region in a
spherically symmetric background of neutrons with a varying radial density
distribution. We present self-similar solutions for the propagation of
detonation in static and collapsing backgrounds of neutron matter. The
solutions are obtained in the framework of general relativistic hydrodynamics,
and are relevant for the possible transition of neutron into strange stars.
Conditions for the formation of either bare or crusted strange stars are
discussed.Comment: 16 pages, 4 figures. Submitted to IJMP
On the number of unsuitable boolean functions in constructions of filter and combining models of stream ciphers
It is well known that every stream cipher is based on a good pseudorandom generator. For cryptographic purposes, we are interested in generation of pseudorandom sequences of the maximal possible period. A feedback register is one of the most known cryptographic primitives that is used in construction of stream generators. We analyze periodic properties of pseudorandom sequences produced by filter and combiner generators equipped with nonlinear Boolean functions. We determine which nonlinear functions in these schemes lead to pseudorandom sequences of not maximal possible period. We call such functions unsuitable and count the exact number of them for an arbitrary n
Post-inflationary GW production in generic higher (infinite) derivative gravity
Gravity can be embedded into a renormalizable theory by means of adding
quadratic in curvature terms. However, this at first leads to the presence of
the Weyl ghost. It is possible to get rid of this ghost if the locality
assumption is weakened and the propagator of the graviton is represented by an
entire function of the d'Alembertian operator without new poles and zeros.
Models of this type admit a cosmological solution describing the , or
Starobinsky, inflation. We study graviton production after inflation in this
model and show that it is negligible despite the presence of the higher
derivative operators which could potentially cause instabilities.Comment: We dedicate this paper to the memory of Valery Rubako
Monitoring-based analysis of agriculture in Iraq
The paper deals with change in area and structure of Iraq agricultural lands. It revealed the main reasons for the change: crisis (war, sanctions, etc.); economic (swamp and lake drainage, melioration, etc.); weather condition. Land-use intensification as a reason for reduction of agricultural land areas was not proved. The area of cultivated lands proved to correlate significantly with the level of precipitation, wheat productivity -with the average temperature in Iraq
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