74 research outputs found
Achieving a log(n) Speed Up for Boolean Matrix Operations and Calculating the Complexity of the Dense Linear Algebra step of Algebraic Stream Cipher Attacks and of Integer Factorization Methods
The purpose of this paper is to calculate the running time of dense boolean matrix operations,
as used in stream cipher cryptanalysis and integer factorization. Several variations of Gaussian
Elimination, Strassen\u27s Algorithm and the Method of Four Russians are analyzed. In particular,
we demonstrate that Strassen\u27s Algorithm is actually slower than the Four Russians algorithm for
matrices of the sizes encountered in these problems. To accomplish this, we introduce a new model
for tabulating the running time, tracking matrix reads and writes rather than field operations, and
retaining the coefficients rather than dropping them. Furthermore, we introduce an algorithm known
heretofore only orally, a ``Modified Method of Four Russians\u27\u27, which has not appeared in the literature
before. This algorithm is times faster than Gaussian Elimination for dense boolean
matrices. Finally we list rough estimates for the running time of several recent stream cipher cryptanalysis
attacks
Statistics of Random Permutations and the Cryptanalysis Of Periodic Block Ciphers
A block cipher is intended to be computationally indistinguishable from a
random permutation of appropriate domain and range. But what are the properties
of a random permutation? By the aid of exponential and ordinary generating
functions, we derive a series of collolaries of interest to the cryptographic
community. These follow from the Strong Cycle Structure Theorem of
permutations, and are useful in rendering rigorous two attacks on Keeloq, a
block cipher in wide-spread use. These attacks formerly had heuristic
approximations of their probability of success. Moreover, we delineate an
attack against the (roughly) millionth-fold iteration of a random permutation.
In particular, we create a distinguishing attack, whereby the iteration of a
cipher a number of times equal to a particularly chosen highly-composite number
is breakable, but merely one fewer round is considerably more secure. We then
extend this to a key-recovery attack in a "Triple-DES" style construction, but
using AES-256 and iterating the middle cipher (roughly) a million-fold. It is
hoped that these results will showcase the utility of exponential and ordinary
generating functions and will encourage their use in cryptanalytic research.Comment: 20 page
Efficient Dense Gaussian Elimination over the Finite Field with Two Elements
In this work we describe an efficient implementation of a hierarchy of
algorithms for Gaussian elimination upon dense matrices over the field with two
elements. We discuss both well-known and new algorithms as well as our
implementations in the M4RI library, which has been adopted into Sage. The
focus of our discussion is a block iterative algorithm for PLE decomposition
which is inspired by the M4RI algorithm. The implementation presented in this
work provides considerable performance gains in practice when compared to the
previously fastest implementation. We provide performance figures on x86_64
CPUs to demonstrate the alacrity of our approach
Optimal strategies of radial velocity observations in planet search surveys
Applications of the theory of optimal design of experiments to radial
velocity planet search surveys are considered. Different optimality criteria
are discussed, basing on the Fisher, Shannon, and Kullback-Leibler
informations. Algorithms of optimal scheduling of RV observations for two
important practical problems are considered. The first problem is finding the
time for future observations to yield the maximum improvement of the precision
of exoplanetary orbital parameters and masses. The second problem is finding
the most favourable time for distinguishing alternative orbital fits (the
scheduling of discriminating observations).
These methods of optimal planning are demonstrated to be potentially
efficient for multi-planet extrasolar systems, in particular for resonant ones.
In these cases, the optimal dates of observations are often concentrated in
quite narrow time segments.Comment: 8 pages, 2 figures, no tables, Accepted to MNRA
Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications
We present a novel approach for solving systems of polynomial
equations via graph partitioning. The concept of a
variable-sharing graph of a system of polynomial equations is
defined. If such graph is disconnected, then the system of
equations is actually two separate systems that can be solved
individually. This can provide a significant speed-up in
computing the solution to the system, but is unlikely to occur
either randomly or in applications. However, by deleting a small
number of vertices on the graph, the variable-sharing graph
could be disconnected in a balanced fashion, and in turn the
system of polynomial equations are separated into smaller ones of
similar sizes. In graph theory terms, this process is equivalent to
finding balanced vertex partitions with minimum-weight vertex
separators.
The techniques of finding these vertex partitions are discussed,
and experiments are performed to evaluate its practicality for
general graphs and systems of polynomial equations. Applications
of this approach to the QUAD family of stream ciphers, algebraic
cryptanalysis of the stream cipher Trivium and its variants, as
well as some mathematical problems in game theory and
computational algebraic geometry are presented. In each of
these cases, the systems of polynomial equations involved are
well-suited to our graph partitioning method, and constructive
results are discussed
VAMP3/Syb and YKT6 are required for the fusion of constitutive secretory carriers with the plasma membrane
The cellular machinery required for the fusion of constitutive secretory vesicles with the plasma membrane in metazoans remains poorly defined. To address this problem we have developed a powerful, quantitative assay for measuring secretion and used it in combination with combinatorial gene depletion studies in Drosophila cells. This has allowed us to identify at least three SNARE complexes mediating Golgi to PM transport (STX1, SNAP24/29 and Syb; STX1, SNAP24/29 and YKT6; STX4, SNAP24 and Syb). RNAi mediated depletion of YKT6 and VAMP3 in mammalian cells also blocks constitutive secretion suggesting that YKT6 has an evolutionarily conserved role in this process. The unexpected role of YKT6 in plasma membrane fusion may in part explain why RNAi and gene disruption studies have failed to produce the expected phenotypes in higher eukaryotes
LSST: from Science Drivers to Reference Design and Anticipated Data Products
(Abridged) We describe here the most ambitious survey currently planned in
the optical, the Large Synoptic Survey Telescope (LSST). A vast array of
science will be enabled by a single wide-deep-fast sky survey, and LSST will
have unique survey capability in the faint time domain. The LSST design is
driven by four main science themes: probing dark energy and dark matter, taking
an inventory of the Solar System, exploring the transient optical sky, and
mapping the Milky Way. LSST will be a wide-field ground-based system sited at
Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m
effective) primary mirror, a 9.6 deg field of view, and a 3.2 Gigapixel
camera. The standard observing sequence will consist of pairs of 15-second
exposures in a given field, with two such visits in each pointing in a given
night. With these repeats, the LSST system is capable of imaging about 10,000
square degrees of sky in a single filter in three nights. The typical 5
point-source depth in a single visit in will be (AB). The
project is in the construction phase and will begin regular survey operations
by 2022. The survey area will be contained within 30,000 deg with
, and will be imaged multiple times in six bands, ,
covering the wavelength range 320--1050 nm. About 90\% of the observing time
will be devoted to a deep-wide-fast survey mode which will uniformly observe a
18,000 deg region about 800 times (summed over all six bands) during the
anticipated 10 years of operations, and yield a coadded map to . The
remaining 10\% of the observing time will be allocated to projects such as a
Very Deep and Fast time domain survey. The goal is to make LSST data products,
including a relational database of about 32 trillion observations of 40 billion
objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures
available from https://www.lsst.org/overvie
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