The Quadratic Extension Extractor for (Hyper)Elliptic Curves in Odd Characteristic
نویسندگان
چکیده
We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve C, defined over Fq2 , where q is some power of an odd prime. Our extractor, for a given point P on C, outputs the first Fq-coefficient of the abscissa of the point P . We show that if a point P is chosen uniformly at random in C, the element extracted from the point P is indistinguishable from a uniformly random variable in Fq.
منابع مشابه
On Silverman's conjecture for a family of elliptic curves
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...
متن کاملA classification of elliptic curves with respect to the GHS attack in odd characteristic
The GHS attack is known to solve discrete logarithm problems (DLP) in the Jacobian of a curve C0 defined over the d degree extension field kd of k := Fq by mapping it to the DLP in the Jacobian of a covering curve C of C0 over k. Recently, classifications for all elliptic curves and hyperelliptic curves C0/kd of genus 2,3 which possess (2, ..., 2)-covering C/k of P were shown under an isogeny c...
متن کاملElliptic curves with weak coverings over cubic extensions of finite fields with odd characteristic
In this paper, we present a classification of elliptic curves defined over a cubic extension of a finite field with odd characteristic which have coverings over the finite field therefore subjected to the GHS attack. The densities of these weak curves, with hyperelliptic and non-hyperelliptic coverings, are then analyzed respectively. In particular, we show, for elliptic curves defined by Legen...
متن کاملFinding Large Selmer Rank via an Arithmetic Theory of Local Constants
We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields. Suppose K/k is a quadratic extension of number fields, E is an elliptic curve defined over k, and p is an odd prime. Let K− denote the maximal abelian p-extension of K that is unramified at all primes where E has bad reduction and that is Galois over k with dihedral Galois group (i.e., the gene...
متن کاملWeil Restriction of an Elliptic Curve over a Quadratic Extension
Let K be a finite field of characteristic not equal to 2, and L a quadratic extension of K. For a large class of elliptic curves E defined over L we construct hyperelliptic curves over K of genus 2 whose jacobian is isogenous to the Weil restriction ResK(E).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007