Fast algorithms for ell-adic towers over finite fields

نویسندگان

  • Luca De Feo
  • Javad Doliskani
  • Éric Schost
چکیده

Inspired by previous work of Shoup, Lenstra-De Smit and Couveignes-Lercier, we give fast algorithms to compute in (the first levels of) the l-adic closure of a finite field. In many cases, our algorithms have quasi-linear complexity.

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

Fast Algorithms for `-adic Towers over Finite Fields

Inspired by previous work of Shoup, Lenstra-De Smit and Couveignes-Lercier, we give fast algorithms to compute in (the first levels of) the `-adic closure of a finite field. In many cases, our algorithms have quasi-linear complexity.

متن کامل

Selmer groups and Mordell-Weil groups of elliptic curves over towers of function fields

In [12] and [13], Silverman discusses the problem of bounding the Mordell-Weil ranks of elliptic curves over towers of function fields. We first prove generalizations of the theorems of those two papers by a different method, allowing non-abelian Galois groups and removing the dependence on Tate’s conjectures. We then prove some theorems about the growth of Mordell-Weil ranks in towers of funct...

متن کامل

Fast arithmetic in unramified p-adic fields

Let p be prime and Zpn a degree n unramified extension of the ring of p-adic integers Zp. In this paper we give an overview of some very fast deterministic algorithms for common operations in Zpn modulo p . Combining existing methods with recent work of Kedlaya and Umans about modular composition of polynomials, we achieve quasi-linear time algorithms in the parameters n and N , and quasi-linea...

متن کامل

A p-adic Height Function Of Cryptanalytic Significance

It is noted that an efficient algorithm for calculating a p-adic height could have cryptanalytic applications. Elliptic curves and their generalizations are an active research topic with practical applications in cryptography [1], [2], [3]. If E is an elliptic curve defined over a finite field Fp, where p is prime, and if P and Q are points on the curve E such that Q = nP , then the elliptic cu...

متن کامل

Towers of Function Fields over Non-prime Finite Fields

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(`), for ` = p with p prime and n > 3 odd. A modular interpretation of the towers is given as well.

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:
  • CoRR

دوره abs/1301.6021  شماره 

صفحات  -

تاریخ انتشار 2013