13,363 research outputs found
Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation
A permutation P on {1,..,N} is a_fast_forward_permutation_ if for each m the
computational complexity of evaluating P^m(x)$ is small independently of m and
x. Naor and Reingold constructed fast forward pseudorandom cycluses and
involutions. By studying the evolution of permutation graphs, we prove that the
number of queries needed to distinguish a random cyclus from a random
permutation on {1,..,N} is Theta(N) if one does not use queries of the form
P^m(x), but is only Theta(1) if one is allowed to make such queries.
We construct fast forward permutations which are indistinguishable from
random permutations even when queries of the form P^m(x) are allowed. This is
done by introducing an efficient method to sample the cycle structure of a
random permutation, which in turn solves an open problem of Naor and Reingold.Comment: Corrected a small erro
A Distinguisher on PRESENT-Like Permutations with Application to SPONGENT
At Crypto 2015, Blondeau et al. showed a known-key analysis on the full PRESENT lightweight block cipher. Based on some of the best differential distinguishers, they introduced a meet in the middle (MitM) layer to pre-add the differential distinguisher, which extends the number of attacked rounds on PRESENT from 26 rounds to full rounds without reducing differential probability.
In this paper, we generalize their method and present a distinguisher on a kind of permutations called PRESENT-like permutations. This generic distinguisher is divided into two phases. The first phase is a truncated differential distinguisher with strong bias, which describes the unbalancedness of the output collision on some fixed bits, given the fixed input in some bits, and we take advantage of the strong relation between truncated differential probability and capacity of multidimensional linear approximation to derive the best differential distinguishers. The second phase is the meet-in-the-middle layer, which is pre-added to the truncated differential to propagate the differential properties as far as possible. Different with Blondeau et al.\u27s work, we extend the MitM layers on a 64-bit internal state to states with any size, and we also give a concrete bound to estimate the attacked rounds of the MitM layer.
As an illustration, we apply our technique to all versions of SPONGENT permutations. In the truncated differential phase, as a result we reach one, two or three rounds more than the results shown by the designers. In the meet-in-the-middle phase, we get up to 11 rounds to pre-add to the differential distinguishers. Totally, we improve the previous distinguishers on all versions of SPONGENT permutations by up to 13 rounds
Testing Universality in Critical Exponents: the Case of Rainfall
One of the key clues to consider rainfall as a self-organized critical
phenomenon is the existence of power-law distributions for rain-event sizes. We
have studied the problem of universality in the exponents of these
distributions by means of a suitable statistic whose distribution is inferred
by several variations of a permutational test. In contrast to more common
approaches, our procedure does not suffer from the difficulties of multiple
testing and does not require the precise knowledge of the uncertainties
associated to the power-law exponents. When applied to seven sites monitored by
the Atmospheric Radiation Measurement Program the test lead to the rejection of
the universality hypothesis, despite the fact that the exponents are rather
close to each other
The order of large random permutations with cycle weights
The order of a permutation of objects is the
smallest integer such that the -th iterate of gives the
identity. A remarkable result about the order of a uniformly chosen permutation
is due to Erd\"os and Tur\'an who proved in 1965 that satisfies a
central limit theorem. We extend this result to the so-called
\textit{generalized Ewens measure} in a previous paper. In this paper, we
establish a local limit theorem as well as, under some extra moment condition,
a precise large deviations estimate. These properties are new even for the
uniform measure. Furthermore, we provide precise large deviations estimates for
random permutations with polynomial cycle weights.Comment: 41 pages, 5 figure
Three-Body Forces Produced by a Similarity Renormalization Group Transformation in a Simple Model
A simple class of unitary renormalization group transformations that force
hamiltonians towards a band-diagonal form produce few-body interactions in
which low- and high-energy states are decoupled, which can greatly simplify
many-body calculations. One such transformation has been applied to
phenomenological and effective field theory nucleon-nucleon interactions with
success, but further progress requires consistent treatment of at least the
three-nucleon interaction. In this paper we demonstrate in an extremely simple
model how these renormalization group transformations consistently evolve two-
and three-body interactions towards band-diagonal form, and introduce a
diagrammatic approach that generalizes to the realistic nuclear problem.Comment: 25 pages, 18 figures, minor typos corrected and references update
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