Výsledky vyhledávání - "Fabien Pazuki"

Autor: Fabien Pazuki, Andrea Basso

Publikováno v: Basso, A & Pazuki, F 2022, ' On the supersingular GPST attack ', Journal of Mathematical Cryptology, vol. 16, no. 1, pp. 14-19 . https://doi.org/10.1515/jmc-2021-0020
Journal of Mathematical Cryptology, Vol 16, Iss 1, Pp 14-19 (2021)

The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange. In this pap

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https://curis.ku.dk/ws/files/284298954/On_the_supersingular_GPST_attack.pdf

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The regulator dominates the rank

Autor: Fabien Pazuki

Publikováno v: Pazuki, F 2022 ' The regulator dominates the rank ' arXiv preprint .
University of Copenhagen

After noticing that the regulator of a number field dominates the rank of its group of units, we bound from below the regulator of the Mordell-Weil group of elliptic curves over global function fields of characteristic p ≥ 5 p\geq 5 . The lower bou

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https://curis.ku.dk/portal/da/publications/the-regulator-dominates-the-rank(ddeaa499-ed59-4bd2-915c-85339630d39b).html

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Bertini and Northcott

Autor: Martin Widmer, Fabien Pazuki

Publikováno v: Research in Number Theory. 7

We prove a new Bertini-type Theorem with explicit control of the genus, degree, height, and the field of definition of the constructed curve. As a consequence we provide a general strategy to reduce certain height and rank estimates on abelian variet

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https://doi.org/10.1007/s40993-021-00236-2

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Isogenies of elliptic curves over function fields

Autor: Fabien Pazuki, Richard Griffon

We prove two theorems concerning isogenies of elliptic curves over function fields. The first one describes the variation of the height of the $j$-invariant in an isogeny class. The second one is an "isogeny estimate", providing an explicit bound on

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http://arxiv.org/abs/2005.02920

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Bad reduction of genus curves with CM jacobian varieties

Autor: Philipp Habegger, Fabien Pazuki

Publikováno v: Compositio Mathematica. 153:2534-2576

We show that a genus $2$ curve over a number field whose jacobian has complex multiplication will usually have stable bad reduction at some prime. We prove this by computing the Faltings height of the jacobian in two different ways. First, we use a k

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https://doi.org/10.1112/s0010437x17007424

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Heights and isogenies of Drinfeld modules

Autor: Florian Breuer, Fabien Pazuki, Mahefason Heriniaina Razafinjatovo

We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular polynomials

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http://arxiv.org/abs/1908.03485

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Regulators of elliptic curves

Autor: Fabien Pazuki, Pascal Autissier, Marc Hindry

Publikováno v: International Mathematics Research Notices
International Mathematics Research Notices, Oxford University Press (OUP), 2018, ⟨10.1093/imrn/rny285⟩
Autissier, P, Hindry, M & Pazuki, F 2021, ' Regulators of Elliptic Curves ', International Mathematics Research Notices, vol. 2021, no. 7, pp. 4976–4993 . https://doi.org/10.1093/imrn/rny285

We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic $p>0$. We prove a new Northcott property for the regulator of elliptic curves of rank

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http://arxiv.org/abs/1805.03484

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Modular invariants and isogenies

Autor: Fabien Pazuki

Publikováno v: Pazuki, F 2019, ' Modular invariants and isogenies ', International Journal of Number Theory, vol. 15, no. 3, pp. 569-584 . https://doi.org/10.1142/S1793042119500295

We provide explicit bounds on the difference of heights of the [Formula: see text]-invariants of isogenous elliptic curves defined over [Formula: see text]. The first one is reminiscent of a classical estimate for the Faltings height of isogenous abe

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http://arxiv.org/abs/1611.01094

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Remarques sur une conjecture de Lang

Autor: Fabien Pazuki

Publikováno v: Journal de Théorie des Nombres de Bordeaux
Journal de Théorie des Nombres de Bordeaux, Société Arithmétique de Bordeaux, 2010, 22 (1), pp.161-179

Le but de cet article est d'etudier une conjecture de Lang enoncee sur les courbes elliptiques dans un livre de Serge Lang, puis generalisee aux varietes abeliennes de dimension superieure dans un article de Joseph Silverman. On donne un resultat asy

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https://doi.org/10.5802/jtnb.709

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