On the Analogue of the Division Polynomials for Hyperelliptic Curves

نویسندگان

  • Johannes Buchmann
  • Harald Niederreiter
  • Andrew M. Odlyzko
  • Horst G. Zimmer
  • Michael Laska
  • David G. Cantor
چکیده

On the Analogue of the Division Polynomials for Hyperelliptic Curves

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hyperelliptic curves, L-polynomials and random matrices

We analyze the distribution of unitarized L-polynomials L̄p(T ) (as p varies) obtained from a hyperelliptic curve of genus g ≤ 3 defined over Q. In the generic case, we find experimental agreement with a predicted correspondence (based on the Katz-Sarnak random matrix model) between the distributions of L̄p(T ) and of characteristic polynomials of random matrices in the compact Lie group USp(2g)....

متن کامل

Counting Points on Hyperelliptic Curves over Finite Fields

We describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm à la Schoof for genus 2 using Cantor’s division polynomials. These are combined with a birthday paradox algorithm to calculate the cardinality. Our methods ...

متن کامل

Computing the Characteristic Polynomials of a Class of Hyperelliptic Curves for Cryptographic Applications

Hyperelliptic curves have been widely studied for cryptographic applications, and some special hyperelliptic curves are often considered to be used in practical cryptosystems. Computing Jacobian group orders is an important operation in constructing hyperelliptic curve cryptosystems, and the most common method used for the computation of Jacobian group orders is by computing the zeta functions ...

متن کامل

Generating More Kawazoe-Takahashi Genus 2 Pairing-Friendly Hyperelliptic Curves

Constructing pairing-friendly hyperelliptic curves with small ρ-values is one of challenges for practicability of pairing-friendly hyperelliptic curves. In this paper, we describe a method that extends the Kawazoe-Takahashi method of generating families of genus 2 ordinary pairing-friendly hyperelliptic curves by parameterizing the parameters as polynomials. With this approach we construct genu...

متن کامل

Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2=x5ax

An explicit construction of pairing-friendly hyperelliptic curves with ordinary Jacobians was firstly given by D. Freeman. In this paper, we give other explicit constructions of pairing-friendly hyperelliptic curves with ordinary Jacobians based on the closed formulae for the order of the Jacobian of a hyperelliptic curve of type y = x + ax. We present two methods in this paper. One is an analo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012