On the 2-adic valuation of the cardinality of elliptic curves over finite extensions of $$\mathbb {F}_{\varvec{q}} $$ F q

Autor: Jordi Pujolàs, Javier Valera, Josep M. Miret

Publikováno v: Archiv der Mathematik. 111:611-620

In this paper we study the difference between the 2-adic valuations of the cardinalities $$ \# E( \mathbb {F}_{q^k} ) $$ and $$ \# E( \mathbb {F}_q ) $$ of an elliptic curve E over $$ \mathbb {F}_q $$ . We also deduce information about the structure

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3d87690e6ff877213e6b1aaea2bd3e45
https://doi.org/10.1007/s00013-018-1245-2

Pairing-Based Cryptography on Elliptic Curves

Autor: Josep M. Miret, Juan G. Tena, Daniel Sadornil

Publikováno v: Mathematics in Computer Science. 12:309-318

We give a brief overview of a recent branch of Public Key Cryptography, the so called Pairing-based Cryptography or Identity-based Cryptography. We describe the Weil pairing and its applications to cryptosystems and cryptographic protocols based on p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::86e2c61ccf668ccd5bb4a8c8821a91e9
https://doi.org/10.1007/s11786-018-0347-3

Halving in some genus 2 curves over binary fields

Autor: Ricard Garra, Josep M. Miret, Jordi Pujolàs

Publikováno v: IEEE Latin America Transactions. 14:2885-2889

We give a method to compute the halving of a divisor in the Jacobian variety of a genus 2 curve in characteristic 2. We present explicit halving formulae for each possible divisor class for some curves (those with h(x)=x), detailing all the process t

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https://doi.org/10.1109/tla.2016.7555270

Digrafy s excesem 1

Autor: Josep M. Miret, Mirka Miller, Anita Abildgaard Sillasen

Publikováno v: Miller, M, Miret, J M & Sillasen, A A 2018, ' On digraphs of excess one ', Discrete Applied Mathematics, vol. 238, pp. 161-166 . https://doi.org/10.1016/j.dam.2017.06.016

Digraf, ve kterém pro každou dvojici (ne nutně různých) vrcholů u, v existuje nejvýše jeden sled délky nejvýše k z u do v se nazývá k-geodetický digraf. Počet vrcholů N(d,k) k-geodetického digrafu s minimálním výstupním stupněm

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6ab1fe4ee63021e62b384bef8db0599
https://vbn.aau.dk/da/publications/9ac18ed4-ed20-4f02-a674-2c6fea5b5176

Elliptic curves withj= 0,1728 and low embedding degree

Autor: Juan G. Tena, Daniel Sadornil, Josep M. Miret

Publikováno v: International Journal of Computer Mathematics, 2016, Vol. 93, No. 12, 2042?2053
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)

Elliptic curves over a finite field Fq with j-invariant 0 or 1728, both supersingular and ordinary, whose embedding degree k is low are studied. In the ordinary case we give conditions characterizing such elliptic curves with fixed embedding degree w

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::731585dc9d2b8f6b2921446013694398
https://doi.org/10.1080/00207160.2015.1083556