1,556 research outputs found
On the discrete logarithm problem in finite fields of fixed characteristic
For a prime power, the discrete logarithm problem (DLP) in
consists in finding, for any
and , an integer such that . We present
an algorithm for computing discrete logarithms with which we prove that for
each prime there exist infinitely many explicit extension fields
in which the DLP can be solved in expected quasi-polynomial
time. Furthermore, subject to a conjecture on the existence of irreducible
polynomials of a certain form, the algorithm solves the DLP in all extensions
in expected quasi-polynomial time.Comment: 15 pages, 2 figures. To appear in Transactions of the AM
On the complexity of computing Gr\"obner bases for weighted homogeneous systems
Solving polynomial systems arising from applications is frequently made
easier by the structure of the systems. Weighted homogeneity (or
quasi-homogeneity) is one example of such a structure: given a system of
weights , -homogeneous polynomials are polynomials
which are homogeneous w.r.t the weighted degree
. Gr\"obner bases for weighted homogeneous systems can be
computed by adapting existing algorithms for homogeneous systems to the
weighted homogeneous case. We show that in this case, the complexity estimate
for Algorithm~\F5 \left(\binom{n+\dmax-1}{\dmax}^{\omega}\right) can be
divided by a factor . For zero-dimensional
systems, the complexity of Algorithm~\FGLM (where is the
number of solutions of the system) can be divided by the same factor
. Under genericity assumptions, for
zero-dimensional weighted homogeneous systems of -degree
, these complexity estimates are polynomial in the
weighted B\'ezout bound .
Furthermore, the maximum degree reached in a run of Algorithm \F5 is bounded by
the weighted Macaulay bound , and this bound is
sharp if we can order the weights so that . For overdetermined
semi-regular systems, estimates from the homogeneous case can be adapted to the
weighted case. We provide some experimental results based on systems arising
from a cryptography problem and from polynomial inversion problems. They show
that taking advantage of the weighted homogeneous structure yields substantial
speed-ups, and allows us to solve systems which were otherwise out of reach
Pairing computation on hyperelliptic curves of genus 2
Bilinear pairings have been recently used to construct cryptographic schemes with new and novel properties, the most celebrated example being the Identity Based Encryption scheme of Boneh and Franklin. As pairing computation is generally the most computationally intensive part of any painng-based cryptosystem, it is essential to investigate new ways in which to compute pairings efficiently.
The vast majority of the literature on pairing computation focuscs solely on using elliptic curves. In this thesis we investigate pairing computation on supersingular hyperelliptic curves of genus 2 Our aim is to provide a practical alternative to using elliptic curves for pairing based cryptography. Specifically, we illustrate how to implement pairings efficiently using genus 2 curves, and how to attain performance comparable to using elliptic curves.
We show that pairing computation on genus 2 curves over F2m can outperform elliptic curves by using a new variant of the Tate pairing, called the r¡j pairing, to compute the fastest pairing implementation in the literature to date We also show for the first time how the final exponentiation required to compute the Tate pairing can be avoided for certain hyperelliptic curves.
We investigate pairing computation using genus 2 curves over large prime fields, and detail various techniques that lead to an efficient implementation, thus showing that these curves are a viable candidate for practical use
Exchange-Repairs: Managing Inconsistency in Data Exchange
In a data exchange setting with target constraints, it is often the case that
a given source instance has no solutions. In such cases, the semantics of
target queries trivialize. The aim of this paper is to introduce and explore a
new framework that gives meaningful semantics in such cases by using the notion
of exchange-repairs. Informally, an exchange-repair of a source instance is
another source instance that differs minimally from the first, but has a
solution. Exchange-repairs give rise to a natural notion of exchange-repair
certain answers (XR-certain answers) for target queries. We show that for
schema mappings specified by source-to-target GAV dependencies and target
equality-generating dependencies (egds), the XR-certain answers of a target
conjunctive query can be rewritten as the consistent answers (in the sense of
standard database repairs) of a union of conjunctive queries over the source
schema with respect to a set of egds over the source schema, making it possible
to use a consistent query-answering system to compute XR-certain answers in
data exchange. We then examine the general case of schema mappings specified by
source-to-target GLAV constraints, a weakly acyclic set of target tgds and a
set of target egds. The main result asserts that, for such settings, the
XR-certain answers of conjunctive queries can be rewritten as the certain
answers of a union of conjunctive queries with respect to the stable models of
a disjunctive logic program over a suitable expansion of the source schema.Comment: 29 pages, 13 figures, submitted to the Journal on Data Semantic
Improvements in the computation of ideal class groups of imaginary quadratic number fields
We investigate improvements to the algorithm for the computation of ideal
class groups described by Jacobson in the imaginary quadratic case. These
improvements rely on the large prime strategy and a new method for performing
the linear algebra phase. We achieve a significant speed-up and are able to
compute ideal class groups with discriminants of 110 decimal digits in less
than a week.Comment: 14 pages, 5 figure
An Opt + 1 algorithm for the cutting stock problem with a constant number of object lengths
In the cutting stock problem we are given a set of object types, where objects of type have integer length . Given a set of objects containing objects of type , for each , the problem is to pack into the minimum number of bins of capacity . In this paper we consider the version of the problem in which the number of different object types is constant and we present an algorithm that computes a solution using at most bins, where is the value of an optimum solution
pocl: A Performance-Portable OpenCL Implementation
OpenCL is a standard for parallel programming of heterogeneous systems. The
benefits of a common programming standard are clear; multiple vendors can
provide support for application descriptions written according to the standard,
thus reducing the program porting effort. While the standard brings the obvious
benefits of platform portability, the performance portability aspects are
largely left to the programmer. The situation is made worse due to multiple
proprietary vendor implementations with different characteristics, and, thus,
required optimization strategies.
In this paper, we propose an OpenCL implementation that is both portable and
performance portable. At its core is a kernel compiler that can be used to
exploit the data parallelism of OpenCL programs on multiple platforms with
different parallel hardware styles. The kernel compiler is modularized to
perform target-independent parallel region formation separately from the
target-specific parallel mapping of the regions to enable support for various
styles of fine-grained parallel resources such as subword SIMD extensions, SIMD
datapaths and static multi-issue. Unlike previous similar techniques that work
on the source level, the parallel region formation retains the information of
the data parallelism using the LLVM IR and its metadata infrastructure. This
data can be exploited by the later generic compiler passes for efficient
parallelization.
The proposed open source implementation of OpenCL is also platform portable,
enabling OpenCL on a wide range of architectures, both already commercialized
and on those that are still under research. The paper describes how the
portability of the implementation is achieved. Our results show that most of
the benchmarked applications when compiled using pocl were faster or close to
as fast as the best proprietary OpenCL implementation for the platform at hand.Comment: This article was published in 2015; it is now openly accessible via
arxi
Aerodynamic analysis of a horizontal axis wind turbine by use of helical vortex theory, volume 2: Computer program users manual
A description of a computer program entitled VORTEX that may be used to determine the aerodynamic performance of horizontal axis wind turbines is given. The computer code implements a vortex method from finite span wind theory and determines the induced velocity at the rotor disk by integrating the Biot-Savart law. It is assumed that the trailing helical vortex filaments form a wake of constant diameter (the rigid wake assumption) and travel downstream at the free stream velocity. The program can handle rotors having any number of blades which may be arbitrarily shaped and twisted. Many numerical details associated with the program are presented. A complete listing of the program is provided and all program variables are defined. An example problem illustrating input and output characteristics is solved
- …