Results 1 to 10 of about 45 (45)

Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves

Journal of Mathematical Cryptology, 2021
Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve E defined over 𝔽p2, if an imaginary quadratic order O can be embedded in End(E) and a ...
Xiao Guanju, Luo Lixia, Deng Yingpu
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A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves

Transactions of the London Mathematical Society, 2021
Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
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Elliptic curve and k-Fibonacci-like sequence

Scientific African, 2023
In this paper, we will introduce a modified k-Fibonacci-like sequence defined on an elliptic curve and prove Binet’s formula for this sequence. Moreover, we give a new encryption scheme using this sequence.
Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib   +2 more
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Orienting supersingular isogeny graphs

Journal of Mathematical Cryptology, 2020
We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
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Different approach on elliptic curves mathematical models study and their applications

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
In a research project in which a group of mathematical researchers is involved, it was necessary to create a system of nonlinear equations defined over a particular nonsupersingular elliptic space.
Alsaedi Ramzi, Dhifli Abdelwahab, Ghanmi Abdeljabbar   +2 more
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Torsion subgroups of rational Mordell curves over some families of number fields

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
Mordell curves over a number field K are elliptic curves of the form y2 = x3 + c, where c ∈ K \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}.
Gužvić Tomislav, Roy Bidisha
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GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS

Forum of Mathematics, Sigma, 2019
Given an elliptic curve $E$ over $\mathbb{Q}$, a celebrated conjecture of Goldfeld asserts that a positive proportion of its quadratic twists should have analytic rank 0 (respectively 1).
DANIEL KRIZ, CHAO LI
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STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE

Forum of Mathematics, Pi, 2015
Let $E$ be an elliptic curve over $\mathbb{Q}$, and let ${\it\varrho}_{\flat }$ and ${\it\varrho}_{\sharp }$ be odd two-dimensional Artin representations for which ${\it\varrho}_{\flat }\otimes {\it\varrho}_{\sharp }$ is self-dual.
HENRI DARMON, ALAN LAUDER, VICTOR ROTGER
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Nonlinearities on particular elliptic curves subspaces and applications

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
Researching on mathematical models for cryptography means to, primary, define the optimal spaces and rules for which we can archive the maximum time to find the involved parameters of the keys and, in the same time, to optimise the time for key ...
Alsaedi Ramzi, Dhifli Abdelwahab, Ghanmi Abdeljabbar   +2 more
doaj   +1 more source

Growth of torsion groups of elliptic curves upon base change

, 2020
We study how the torsion of elliptic curves over number fields grows upon base change, and in particular prove various necessary conditions for torsion growth.
Najman, Filip, González Jiménez, Enrique   +1 more
core   +1 more source