Embedding Degree of Hyperelliptic Curves with Complex Multiplication
نویسنده
چکیده
Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect to l is one.
منابع مشابه
Pairing - friendly Hyperelliptic Curves of Type y 2 = x 5 + ax
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. Our methods are based on the closed formulae for the order of the Jacobian of a hyperelliptic curve of type y = x + ax over a finite prime field Fp which are given by E. Furukawa, ...
متن کاملSpeeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms
As Koblitz curves were generalized to hyperelliptic Koblitz curves for faster point multiplication by Günter,et al [10], we extend the recent work of Gallant,et al [8] to hyperelliptic curves. So the extended method for speeding point multiplication applies to a much larger family of hyperelliptic curves over finite fields that have efficiently-computable endomorphisms. For this special family ...
متن کاملFamilies of genus 2 curves with small embedding degree
Hyperelliptic curves of small genus have the advantage of providing a group of comparable size as that of elliptic curves, while working over a field of smaller size. Pairing-friendly hyperelliptic curves are those whose order of the Jacobian is divisible by a large prime, whose embedding degree is small enough for computations to be feasible, and whose minimal embedding field is large enough f...
متن کاملFast Scalar Multiplications on Hyperelliptic Curve Cryptosystems
Scalar multiplication is the key operation in hyperelliptic curve cryptosystem. By making use of Euclidean lengths of algebraic integral numbers in a related algebraic integer ring, we discuss the Frobenius expansions of algebraic numbers, theoretically and experimentally show that the multiplier in a scalar multiplication can be reduced and converted into a Frobenius expansion of length approx...
متن کاملOn near prime-order elliptic curves with small embedding degrees (Full version)
In this paper, we extend the method of Scott and Barreto and present an explicit and simple algorithm to generate families of generalized MNT elliptic curves. Our algorithm allows us to obtain all families of generalized MNT curves with any given cofactor. Then, we analyze the complex multiplication equations of these families of curves and transform them into generalized Pell equation. As an e...
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 2007 شماره
صفحات -
تاریخ انتشار 2007