منابع مشابه
Genus 2 point counting over prime fields
For counting points of jacobians of genus 2 curves over a large prime field, the best known approach is essentially an extension of Schoof’s genus 1 algorithm. We propose various practical improvements to this method and illustrate them with a large scale computation: we counted hundreds of curves, until one was found that is suitable for cryptographic use, with a state-ofthe-art security level...
متن کاملA Comparison of Point Counting methods for Hyperelliptic Curves over Prime Fields and Fields of Characteristic 2
Computing the order of the Jacobian of a hyperelliptic curve remains a hard problem. It is usually essential to calculate the order of the Jacobian to prevent certain sub-exponential attacks on the cryptosystem. This paper reports on the viability of implementations of various point-counting techniques. We also report on the scalability of the algorithms as the fields grow larger.
متن کاملKummer for Genus One over Prime Order Fields
This work considers the problem of fast and secure scalar multiplication using curves of genus one defined over a field of prime order. Previous work by Gaudry and Lubicz in 2009 had suggested the use of the associated Kummer line to speed up scalar multiplication. In this work, we explore this idea in detail. The first task is to obtain an elliptic curve in Legendre form which satisfies necess...
متن کاملFixed-point-free Representations over Fields of Prime Characteristic
The irreducible representations over prime fields of characteristic p for those solvable groups which occur as groups of fixed-point-free automorphisms on finite groups are determined.
متن کاملConstructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians
We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. Our algorithm works for arbitrary embedding degrees k and prime subgroup orders r. The resulting abelian surfaces are defined over prime fields Fq with q ≈ r. We also provide an algorithm for constructing genus 2 curves ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2012
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2011.09.003