An AGM-type elliptic curve point counting algorithm in characteristic three

نویسندگان

  • Trond Stølen Gustavsen
  • Kristian Ranestad
چکیده

Given an ordinary elliptic curve on Hesse form over a finite field of characteristic three, we give a sequence of elliptic curves which leads to an effective construction of the canonical lift, and obtain an algorithm for computing the number of points. Our methods are based on the study of an explicitly and naturally given 3-isogeny between elliptic curves on Hesse form.

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

The AGM-X0(N) Heegner Point Lifting Algorithm and Elliptic Curve Point Counting

We describe an algorithm, AGM-X0(N), for point counting on elliptic curves of small characteristic p using p-adic lifts of their invariants associated to modular curves X0(N). The algorithm generalizes the contruction of Satoh [10], SST [11], and Mestre [9]. We describe this method and give details of its implementation for characteristics 2, 3, 5, 7, and 13.

متن کامل

A General Framework for p–adic Point Counting and Application to Elliptic Curves on Legendre Form

In 2000 T. Satoh gave the first p–adic point counting algorithm for elliptic curves over finite fields. Satoh’s algorithm was followed by the SST algorithm and furthermore by the AGM and MSST algorithms for characteristic two only. All four algorithms are important to Elliptic Curve Cryptography. In this paper we present a general framework for p–adic point counting and we apply it to elliptic ...

متن کامل

Point Counting on Genus 3 Non Hyperelliptic Curves

We propose an algorithm to compute the Frobenius polynomial of an ordinary non hyperelliptic curve of genus 3 over F2N . The method is a generalization of Mestre’s AGM-algorithm for hyperelliptic curves and leads to a quasi quadratic time algorithm for point counting. The current methods for point counting on curves over finite fields of small characteristic rely essentially on a p-adic approac...

متن کامل

A Comparison and a Combination of SST and AGM Algorithms for Counting Points of Elliptic Curves in Characteristic 2

Since the first use of a p-adic method for counting points of elliptic curves, by Satoh in 1999, several variants of his algorithm have been proposed. In the current state, the AGM algorithm, proposed by Mestre is thought to be the fastest in practice, and the algorithm by Satoh–Skjernaa–Taguchi has the best asymptotic complexity but requires precomputations. We present an amelioration of the S...

متن کامل

Fast Elliptic Curve Point Counting Using Gaussian Normal Basis

In this paper we present an improved algorithm for counting points on elliptic curves over finite fields. It is mainly based on SatohSkjernaa-Taguchi algorithm [SST01], and uses a Gaussian Normal Basis (GNB) of small type t ≤ 4. In practice, about 42% (36% for prime N) of fields in cryptographic context (i.e., for p = 2 and 160 < N < 600) have such bases. They can be lifted from FpN to ZpN in a...

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:
  • IACR Cryptology ePrint Archive

دوره 2004  شماره 

صفحات  -

تاریخ انتشار 2004