Results 21 to 30 of about 59 (58)

Constructing elliptic curve isogenies in quantum subexponential time

Journal of Mathematical Cryptology, 2014
Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew, Jao David, Soukharev Vladimir   +2 more
doaj   +1 more source

Generating pairing-friendly elliptic curve parameters using sparse families

Journal of Mathematical Cryptology, 2018
The majority of methods for constructing pairing-friendly elliptic curves are based on representing the curve parameters as polynomial families. There are three such types, namely complete, complete with variable discriminant and sparse families. In this
Fotiadis Georgios, Konstantinou Elisavet
doaj   +1 more source

Complex Hyperbolic Surfaces of Abelian Type [PDF]

, 2004
2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ...
Holzapfel, R.
core  

The dihedral hidden subgroup problem

Journal of Mathematical Cryptology
The hidden subgroup problem (HSP) is a cornerstone problem in quantum computing, which captures many problems of interest and provides a standard framework algorithm for their study based on Fourier sampling, one class of techniques known to provide ...
Chen Imin, Sun David
doaj   +1 more source

A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves

Journal of Mathematical Cryptology, 2015
In this paper we present a new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves with small rho-values, and we improve on previously known best rho-values of families [J.
Yoon Kisoon
doaj   +1 more source

COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES

Forum of Mathematics, Sigma, 2016
Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
doaj   +1 more source

On characterizations of g n-helices with Euler angles

Open Mathematics
Curvature and torsion, in their most general forms, are defined in terms of Euler angle-based parametrization via the Cartan matrix, which leads to the Serret-Frenet equations.
Altinok Mesut, Kula Levent
doaj   +1 more source

On elliptic curves with a closed component passing through a hexagon

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
In general, there exists an ellipse passing through the vertices of a convex pentagon, but any ellipse passing through the vertices of a convex hexagon does not have to exist.
Kureš Miroslav
doaj   +1 more source

Application of Mordell–Weil lattices with large kissing numbers to acceleration of multiscalar multiplication on elliptic curves

Journal of Mathematical Cryptology
This article aims to speed up (the precomputation stage of) multiscalar multiplication (MSM) on ordinary elliptic curves of j-invariant 0 with respect to specific “independent” (also known as “basis”) points.
Koshelev Dmitrii
doaj   +1 more source

On the first fall degree of summation polynomials

Journal of Mathematical Cryptology, 2019
We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.
Kousidis Stavros, Wiemers Andreas
doaj   +1 more source