Improved CRT algorithm for class polynomials in genus 2
نویسندگان
چکیده
منابع مشابه
Improved CRT Algorithm for Class Polynomials in Genus 2
We present a generalization to genus 2 of the probabilistic algorithm in Sutherland [28] for computing Hilbert class polynomials. The improvement over the algorithm presented in [5] for the genus 2 case, is that we do not need to find a curve in the isogeny class with endomorphism ring which is the maximal order: rather we present a probabilistic algorithm for “going up” to a maximal curve (a c...
متن کاملImproved Crt Algorithm for Class Polynomials in Genus
We present a generalization to genus 2 of the probabilistic algorithm of Sutherland for computing Hilbert class polynomials. The improvement over the Bröker-Gruenewald-Lauter algorithm for the genus 2 case is that we do not need to find a curve in the isogeny class whose endomorphism ring is the maximal order; rather, we present a probabilistic algorithm for “going up” to a maximal curve (a cur...
متن کاملModular polynomials for genus 2
Modular polynomials are an important tool in many algorithms involving elliptic curves. In this article we generalize this concept to the genus 2 case. We give the theoretical framework describing the genus 2 modular polynomials and discuss how to explicitly compute them.
متن کاملA Crt Algorithm for Constructing Genus 2 Curves over Finite Fields
— We present a new method for constructing genus 2 curves over a finite field Fn with a given number of points on its Jacobian. This method has important applications in cryptography, where groups of prime order are used as the basis for discrete-log based cryptosystems. Our algorithm provides an alternative to the traditional CM method for constructing genus 2 curves. For a quartic CM field K ...
متن کاملFactoring Class Polynomials over the Genus Field
Aimed at computer scientists, this how to describes a method (with detailed algorithms) that allows to compute the factors of a class polynomial over the genus field. Though we only consider polynomials having real factors over the genus field, it is not difficult to adapt the method so that it works when these factors are complex.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Open Book Series
سال: 2013
ISSN: 2329-907X,2329-9061
DOI: 10.2140/obs.2013.1.437