Point Compression on Jacobians of Hyperelliptic Curves over Fq

نویسنده

  • Colin Stahlke
چکیده

— Hyperelliptic curve cryptography recently received a lot of attention, especially for constrained environments. Since there space is critical, compression techniques are interesting. In this note we propose a new method which avoids factoring the first representing polynomial. In the case of genus two the cost for decompression is, essentially, computing two square roots in Fq, the cost for compression is much less.

برای دانلود رایگان 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

Fields 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 کامل

Constructing pairing-friendly hyperelliptic curves using Weil restriction

A pairing-friendly curve is a curve over a finite field whose Jacobian has small embedding degree with respect to a large prime-order subgroup. In this paper we construct pairing-friendly genus 2 curves over finite fields Fq whose Jacobians are ordinary and simple, but not absolutely simple. We show that constructing such curves is equivalent to constructing elliptic curves over Fq that become ...

متن کامل

Families 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 کامل

Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time

We provide a subexponential algorithm for solving the discrete logarithm problem in Jacobians of high-genus hyperelliptic curves over finite fields. Its expected running time for instances with genus g and underlying finite field Fq satisfying g ≥ θ log q for a positive constant θ is given by

متن کامل

Group Law Computations on Jacobians of Hyperelliptic Curves

We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring Fq[x], the algorithm we propose solves a linear...

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

عنوان ژورنال:
  • IACR Cryptology ePrint Archive

دوره 2004  شماره 

صفحات  -

تاریخ انتشار 2004