Number of Jacobi quartic curves over finite fields
نویسندگان
چکیده
In this paper the number of Fq-isomorphism classes of Jacobi quartic curves, i.e., the number of Jacobi quartic curves with distinct jinvariants, over finite field Fq is enumerated.
منابع مشابه
Ranks of Elliptic Curves with Prescribed Torsion over Number Fields
We study the structure of the Mordell–Weil group of elliptic curves over number fields of degree 2, 3, and 4. We show that if T is a group, then either the class of all elliptic curves over quadratic fields with torsion subgroup T is empty, or it contains curves of rank 0 as well as curves of positive rank. We prove a similar but slightly weaker result for cubic and quartic fields. On the other...
متن کاملExceptional elliptic curves over quartic fields
We study the number of elliptic curves, up to isomorphism, over a fixed quartic field K having a prescribed torsion group T as a subgroup. Let T = Z/mZ ⊕ Z/nZ, where m|n, be a torsion group such that the modular curve X1(m,n) is an elliptic curve. Let K be a number field such that there is a positive and finite number of elliptic curves E over K having T as a subgroup. We call such pairs (T,K) ...
متن کاملPairing Computation on Elliptic Curves of Jacobi Quartic Form
This paper proposes explicit formulae for the addition step and doubling step in Miller’s algorithm to compute Tate pairing on Jacobi quartic curves. We present a geometric interpretation of the group law on Jacobi quartic curves, which leads to formulae for Miller’s algorithm. The doubling step formula is competitive with that for Weierstrass curves and Edwards curves. Moreover, by carefully c...
متن کاملFamilies of elliptic curves over quartic number fields with prescribed torsion subgroups
We construct infinite families of elliptic curves with given torsion group structures over quartic number fields. In a 2006 paper, the first two authors and Park determined all of the group structures which occur infinitely often as the torsion of elliptic curves over quartic number fields. Our result presents explicit examples of their theoretical result. This paper also presents an efficient ...
متن کاملEfficient computation of pairings on Jacobi quartic elliptic curves
This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y 2 D dX C Z. We improve the doubling and addition steps in Miller’s algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific point representation to obtain the best res...
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:
- IACR Cryptology ePrint Archive
دوره 2010 شماره
صفحات -
تاریخ انتشار 2010