On the number of elliptic curves with CM cover large algebraic fields
نویسندگان
چکیده
L’accès aux articles de la revue « Annales de l’institut Fourier » (http://aif.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://aif.cedram.org/legal/). Toute reproduction en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
منابع مشابه
A Summary of the Cm Theory of Elliptic Curves
The purpose of this expository paper is to describe some part of the intimate connection between this analytic function, the theory of elliptic curves with complex multiplication, and the algebraic number theory of imaginary quadratic fields. In terms of prerequisites, we will assume some familiarity with the j-function and its connection with the analytic geometry of elliptic curves, some basi...
متن کاملAn Efficient Threshold Verifiable Multi-Secret Sharing Scheme Using Generalized Jacobian of Elliptic Curves
In a (t,n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logar...
متن کاملElliptic Curves over Finite Fields
In this chapter, we study elliptic curves defined over finite fields. Our discussion will include the Weil conjectures for elliptic curves, criteria for supersingularity and a description of the possible groups arising as E(Fq). We shall use basic algebraic geometry of elliptic curves. Specifically, we shall need the notion and properties of isogenies of elliptic curves and of the Weil pairing....
متن کاملA descent method for explicit computations on curves
It is shown that the knowledge of a surjective morphism $Xto Y$ of complex curves can be effectively used to make explicit calculations. The method is demonstrated by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve with period lattice $(1,tau)$, the period matrix for the Jacobian of a family of genus-$2$ curves complementing the classi...
متن کاملStudy of Finite Field over Elliptic Curve: Arithmetic Means
Public key cryptography systems are based on sound mathematical foundations that are designed to make the problem hard for an intruder to break into the system. Number theory and algebraic geometry, namely the theory of elliptic curves defined over finite fields, has found applications in cryptology. The basic reason for this is that elliptic curves over finite fields provide an inexhaustible s...
متن کامل