منابع مشابه
Estimating isogenies on elliptic curves
The object of this paper is to prove a new type of estimate for isogenies between elliptic curves. This has several diophantine applications (effective versions of Serre's Galois irreducibility theorem and Shafarevich's theorem, for example) which are presented in another paper [MW3]. Later articles will deal with the corresponding problems for abelian varieties of arbitrary dimension. Right at...
متن کاملIsogenies of Elliptic Curves: A Computational Approach
The study of elliptic curves has historically been a subject of almost purely mathematical interest. However, Koblitz and Miller independently showed that elliptic curves can be used to implement cryptographic primitives [13], [17]. This thrust elliptic curves from the abstract realm of pure mathematics to the preeminently applied world of communications security. Public key cryptography in gen...
متن کاملFast Point Multiplication on Elliptic Curves through Isogenies
Elliptic curve cryptosystems are usually implemented over fields of characteristic two or over (large) prime fields. For large prime fields, projective coordinates are more suitable as they reduce the computational workload in a point multiplication. In this case, choosing for parameter a the value −3 further reduces the workload. Over Fp, not all elliptic curves can be rescaled through isomorp...
متن کاملOn the Ranks of Elliptic Curves with Isogenies
In recent years, the question of whether the ranks of elliptic curves defined over Q are unbounded has garnered much attention. One can create refined versions of this question by restricting one’s attention to elliptic curves over Q with a certain algebraic structure, e.g., with a rational point of a given order. In an attempt to gather data about such questions, we look for examples of ellipt...
متن کاملClass number formulas via 2-isogenies of elliptic curves
A classical result of Dirichlet shows that certain elementary character sums compute class numbers of quadratic imaginary number fields. We obtain analogous relations between class numbers and a weighted character sum associated to a 2-isogeny of elliptic curves.
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 1990
ISSN: 0020-9910,1432-1297
DOI: 10.1007/bf01231178