Exploració per tema "Elliptic curves"
Ara es mostren els items 1-17 de 17
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A survey on the group of points arising from Elliptic Curves with a Weierstrass model over a ring
(American Mathematical Society (AMS), 2023-06)
Ressenya
Accés obertReview of " A survey on the group of points arising from Elliptic Curves with a Weierstrass model over a ring, Massimiliano Sala and Daniele Taufer, International Journal of Group Theory, 12 (3), (2023),177-196. " -
Bhargava cubes and elliptic curves
(Universitat Politècnica de Catalunya, 2021-02-22)
Treball Final de Grau
Accés obertEn les seves cèlebres Disquisitiones Arithmeticae, Gauss va descobrir una llei de composició que confereix una estructura de grup al conjunt de classes de formes quadràtiques binàries amb discriminant fixat. Dos segles més ... -
Bielliptic modular curves X-0*(N)
(2020-10-01)
Article
Accés obertLet N = 1 be a integer such that the modular curve X* 0 (N) has genus = 2. We prove that X* 0 (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X* 0 (N) is bielliptic over the base field for all ... -
Birch and Swinertonn-Dyer conjecture
(Universitat Politècnica de Catalunya, 2016-01)
Treball Final de Grau
Accés obertEsta tesis tiene diversos objetivos: el primero de ellos es introducir temas básicos de teoría de números, empezando por la teoría algebraica (cuerpos de clases, teorema de Dirichlet...) y continuando por una exposición ... -
CM elliptic curves and the Coates-Wiles Theorem
(Universitat Politècnica de Catalunya, 2019-02-19)
Treball Final de Grau
Accés obert
Realitzat a/amb: Princeton UniversityThis project will take place in the field of elliptic curves and more precisely it will focus on the study of a particular instance of a known case of the Birch and Swinnerton-Dyer Conjecture (BSD Conjecture). This case ... -
Crypto-test-lab for security validation of ECC co-processor test infrastructure
(Institute of Electrical and Electronics Engineers (IEEE), 2018)
Text en actes de congrés
Accés obertElliptic Curve Cryptography (ECC) is a technology for public-key cryptography that is becoming increasingly popular because it provides greater speed and implementation compactness than other public-key technologies. ... -
Design of a Modular Exponentiation Module for an RSA Cryptographic Coprocessor with Power Analysis Countermeasures
(Universitat Politècnica de Catalunya, 2018-06-21)
Treball Final de Grau
Accés obertRivest-Shamir-Adleman (RSA) is a widely used public key cryptographic method. The main operation performed in this method, for encryption and decryption, is modular exponentiation. The way modular exponentiation is computed ... -
Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions
(2017-07-01)
Article
Accés obertThis article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic rank 0, for elliptic curves over $ \mathbb{Q}$ viewed over the fields cut out by certain self-dual Artin representations of dimension ... -
Factorization and Malleability of RSA Moduli, and Counting Points on Elliptic Curves Modulo N
(Multidisciplinary Digital Publishing Institute (MDPI), 2020-11-27)
Article
Accés obertIn this paper we address two different problems related with the factorization of an RSA (Rivest–Shamir–Adleman cryptosystem) modulus N. First we show that factoring is equivalent, in deterministic polynomial time, to ... -
Greenberg’s methods on the Iwasawa theory for Elliptic Curves
(Universitat Politècnica de Catalunya, 2023-05-30)
Treball Final de Grau
Accés obert
Realitzat a/amb: University of California, Santa BarbaraAquesta tesi pretén descriure alguns dels mètodes introduïts per Ralph Greenberg per a l'estudi de la teoria d'Iwasawa per a Corbes El·líptiques. Aquests mètodes s'inspiren en idees presentades per Kenkichi Iwasawa en el ... -
Isogeny-Based Post-Quantum Cryptography
(Universitat Politècnica de Catalunya, 2019-10)
Projecte Final de Màster Oficial
Accés restringit per decisió de l'autorThe present thesis focus on one of the post-quantum cryptosystems, in particular, the isogenybased cryptography. Because of its certain properties like the hard problem of computing isogenies between two elliptic curves, ... -
On elliptic Galois representations and genus-zero modular units
(2006-07-03)
Article
Accés obertGiven an odd prime \,$p$\, and a representation $\varrho$\, of the absolute Galois group of a number field $k$ onto $\mathrm{PGL}_2(\mathbb{F}_p)$ with cyclotomic determinant, the moduli space of elliptic curves defined ... -
On periodic solutions of 2-periodic Lyness difference equations
(2012-01-04)
Altres
Accés obertWe study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known ... -
Periodic orbits of planar integrable birational maps
(2014-02-14)
Report de recerca
Accés obertA birational planar map F possessing a rational first integral preserves a foliation of the plane given by algebraic curves which, if F is not globally periodic, is given by a foliation of curves that have generically ... -
Rational points on twists of X0(63)
(2006-02-07)
Article
Accés obertLet $\varrho\colon G_\mathbb{Q}\longrightarrow PGL_2(\mathbb{F}_p)$ be a Galois representation with cyclotomic determinant, and let $N>1$ be an integer that is square mod $p$. There exist two twisted modular curves ... -
Stark points and the Hida-Rankin p-adic L-function
(2018-02)
Article
Accés obertThis article is devoted to the elliptic Stark conjecture formulated by Darmon (Forum Math Pi 3:e8, 2015), which proposes a formula for the transcendental part of a p-adic avatar of the leading term at s=1 of the Hasse–Weil–Artin ... -
Tècniques geomètriques en monogeneïcitat
(Universitat Politècnica de Catalunya, 2023-10-17)
Projecte Final de Màster Oficial
Accés obertBy the primitive element theorem, any number field K of degree n can be written as Q(α) for some α in K. However, the analogous affirmation is not always true in the case of the ring of integers. When the ring of integers ...
