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2014 (3)
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English (6)
6 documents, page 1 of 1

An algorithm for the principal ideal problem in indefinite quaternion algebras

Page, Aurel (2014)
Projects: EC | ANTICS (278537)
International audience; Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory. For indefinite quaternion algebras, the decision problem reduces to that in the underlying number field. Finding a generator is hard, and we present a heuristically subexponential algorithm.

Efficient implementation of elementary functions in the medium-precision range

Johansson, Fredrik (2014)
Projects: EC | ANTICS (278537)
International audience; We describe a new implementation of the elementary transcendental functions exp, sin, cos, log and atan for variable precision up to approximately 4096 bits. Compared to the MPFR library, we achieve a maximum speedup ranging from a factor 3 for cos to 30 for atan. Our implementation uses table-based argument reduction together with rectangular splitting to evaluate Taylor series. We collect denominators to reduce the number of divisions in the Taylor series, and avoid ...

Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language

Fieker , Claus; Hart , William; Hofmann , Tommy; Johansson , Fredrik (2017)
Projects: EC | ANTICS (278537)
International audience; We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algorithms can be implemented in Julia, without the need to resort to a low-level C implementation. For specialised algorithms, we use Julia's efficient native C interface to wrap existing C/C++ libraries such as Flint, Arb, Antic and Singular. We give examples of how to use Hecke and Nemo and disc...

Haberland's formula and numerical computation of Petersson scalar products

Cohen , Henri (2012)
Projects: EC | ANTICS (278537)
International audience; We study several methods for the numerical computation of Petersson scalar products, and in particular we prove a generalization of Haberland's formula to any subgroup of finite index G of Gamma = PSL_2 (Z), which gives a fast method to compute these scalar products when a Hecke eigenbasis is not necessarily available.

Improved CRT Algorithm for Class Polynomials in Genus $2$

Lauter , Kristin; Robert , Damien (2012)
Projects: EC | ANTICS (278537)
International audience; We present a generalization to genus~2 of the probabilistic algorithm of Sutherland for computing Hilbert class polynomials. The improvement over the Br{ö}ker-Gruenewald-Lauter algorithm for the genus~2 case is that we do not need to find a curve in the isogeny class whose endomorphism ring is the maximal order; rather, we present a probabilistic algorithm for ''going up'' to a maximal curve (a curve with maximal endomorphism ring), once we find any curve in the right ...

Implementing cryptographic pairings at standard security levels

Enge , Andreas; Milan , Jérôme (2014)
Projects: EC | ANTICS (278537)
International audience; This study reports on an implementation of cryptographic pairings in a general purpose computer algebra system. For security levels equivalent to the different AES flavours, we exhibit suitable curves in parametric families and show that optimal ate and twisted ate pairings exist and can be efficiently evaluated. We provide a correct description of Miller's algorithm for signed binary expansions such as the NAF and extend a recent variant due to Boxall et al. to additi...
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