Results 41 to 50 of about 568 (60)

Balanced factorisations

, 2016
Any rational number can be factored into a product of several rationals whose sum vanishes. This simple but nontrivial fact was suggested as a problem on a maths olympiad for high-school students.
Klyachko, Anton A., Vassilyev, Anton N.
core   +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

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

On the Mahler measure of $1+X+1/X+Y+1/Y$

, 2011
We prove a conjectured formula relating the Mahler measure of the Laurent polynomial $1+X+X^{-1}+Y+Y^{-1}$, to the $L$-series of a conductor 15 elliptic curve.Comment: 18 pages, Fixed typos in Lemmas 3 and
Berndt, Bertin, Borwein, Borwein, Boyd, Boyd, Boyd, Brunault, Deninger, Guillera, Kurokawa, Köhler, Lalí, Martin, Mathew Rogers, Mellit, Pathakjee, Rodriguez-Villegas, Rogers, Rogers, Rolfsen, Smyth, Wadim Zudilin   +22 more
core   +3 more sources

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

A new family of elliptic curves with positive ranks arising from the Heron triangles [PDF]

, 2010
The aim of this paper is to introduce a new family of elliptic curves with positive ranks. These elliptic curves have been constructed with certain rational numbers, namely a, b, and c as sides of Heron triangles having rational areas $k$.
Izadi, F. A., Khoshnam, Foad, Nabardi, K.   +2 more
core  

Group structure of elliptic curves over ℤ/Nℤ

Journal of Mathematical Cryptology
We characterize the possible groups E(Z∕NZ)E\left({\mathbb{Z}}/N{\mathbb{Z}}) arising from elliptic curves over Z∕NZ{\mathbb{Z}}/N{\mathbb{Z}} in terms of the groups E(Fp)E\left({{\mathbb{F}}}_{p}), with pp varying among the prime divisors of NN.
Sala Massimiliano, Taufer Daniele
doaj   +1 more source

Isolated elliptic curves and the MOV attack

Journal of Mathematical Cryptology, 2017
We present a variation on the CM method that produces elliptic curves over prime fields with nearly prime order that do not admit many efficiently computable isogenies. Assuming the Bateman–Horn conjecture, we prove that elliptic curves produced this way
Scholl Travis
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  

Searchable encryption with randomized ciphertext and randomized keyword search

Journal of Mathematical Cryptology
The notion of public-key encryption with keyword search (PEKS) was introduced to search over encrypted data without performing any decryption. In this article, we propose a PEKS scheme in which both the encrypted keyword and the trapdoor are randomized ...
Calderini Marco, Longo Riccardo, Sala Massimiliano, Villa Irene   +3 more
doaj   +1 more source