Counting curves over finite fields
نویسنده
چکیده
Article history: Received 25 August 2014 Received in revised form 10 September 2014 Accepted 18 September 2014 Available online 4 November 2014 Communicated by H. Stichtenoth MSC: 11G20 10D20 14G15 14H10
منابع مشابه
Generators of Finite Fields with Powers of Trace Zero and Cyclotomic Function Fields
Using the relation between the problem of counting irreducible polynomials over finite fields with some prescribed coefficients to the problem of counting rational points on curves over finite fields whose function fields are subfields of cyclotomic function fields, we count the number of generators of finite fields with powers of trace zero up to some point, answering a question of Z. Reichste...
متن کاملCounting Points for Hyperelliptic Curves of Type y2= x5 + ax over Finite Prime Fields
Counting rational points on Jacobian varieties of hyperelliptic curves over finite fields is very important for constructing hyperelliptic curve cryptosystems (HCC), but known algorithms for general curves over given large prime fields need very long running times. In this article, we propose an extremely fast point counting algorithm for hyperelliptic curves of type y = x + ax over given large...
متن کاملFields of definition of torsion points on the Jacobians of genus 2 hyperelliptic curves over finite fields
This paper deals with fields of definition of the l-torsion points on the Jacobians of genus 2 hyperelliptic curves over finite fields in order to speed Gaudry and Schost’s point counting algorithm for genus 2 hyperelliptic curves up. A result in this paper shows that the extension degrees of the fields of difinition of the l-torsion points can be in O(l) instead of O(l). The effects of the res...
متن کاملCounting the Number of Points on Elliptic Curves over Finite Fields: Strategies and Performance
Cryptographic schemes using elliptic curves over finite fields require the computation of the cardinality of the curves. Dramatic progress have been achieved recently in that field. The aim of this article is to highlight part of these improvements and to describe an efficient implementation of them in the particular case of the field GF (2n), for n ≤ 500.
متن کاملFibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients
For any positive integers n ≥ 3, r ≥ 1 we present formulae for the number of irreducible polynomials of degree n over the finite field F2r where the coefficients of xn−1, xn−2 and xn−3 are zero. Our proofs involve counting the number of points on certain algebraic curves over finite fields, a technique which arose from Fourier-analysing the known formulae for the F2 base field cases, reverse-en...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Finite Fields and Their Applications
دوره 32 شماره
صفحات -
تاریخ انتشار 2015