The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
O objetivo deste artigo é descrever um algoritmo prático e eficiente para calcular no Jacobiano uma grande classe de curvas algébricas sobre um corpo finito. Para curvas elípticas e hiperelípticas, existe um algoritmo para realizar aritmética de grupo Jacobiano em O(g2) operações no campo base, onde g é o gênero de uma curva. O principal problema neste artigo é se existe um método para realizar a aritmética em curvas mais gerais. Galbraith, Paulus e Smart propuseram um algoritmo para completar a aritmética em O(g2) operações no campo base para as chamadas curvas superelípticas. Generalizamos o algoritmo para a classe de Cab curvas, que inclui curvas superelípticas como um caso especial. Além disso, no caso de Cab curvas, mostramos que o algoritmo proposto não é apenas geral, mas mais eficiente que o algoritmo anterior como parâmetro a in Cab curvas fica grande.
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Ryuichi HARASAWA, Joe SUZUKI, "A Fast Jacobian Group Arithmetic Scheme for Algebraic Curve Cryptography" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 1, pp. 130-139, January 2001, doi: .
Abstract: The goal of this paper is to describe a practical and efficient algorithm for computing in the Jacobian of a large class of algebraic curves over a finite field. For elliptic and hyperelliptic curves, there exists an algorithm for performing Jacobian group arithmetic in O(g2) operations in the base field, where g is the genus of a curve. The main problem in this paper is whether there exists a method to perform the arithmetic in more general curves. Galbraith, Paulus, and Smart proposed an algorithm to complete the arithmetic in O(g2) operations in the base field for the so-called superelliptic curves. We generalize the algorithm to the class of Cab curves, which includes superelliptic curves as a special case. Furthermore, in the case of Cab curves, we show that the proposed algorithm is not just general but more efficient than the previous algorithm as a parameter a in Cab curves grows large.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_1_130/_p
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@ARTICLE{e84-a_1_130,
author={Ryuichi HARASAWA, Joe SUZUKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Fast Jacobian Group Arithmetic Scheme for Algebraic Curve Cryptography},
year={2001},
volume={E84-A},
number={1},
pages={130-139},
abstract={The goal of this paper is to describe a practical and efficient algorithm for computing in the Jacobian of a large class of algebraic curves over a finite field. For elliptic and hyperelliptic curves, there exists an algorithm for performing Jacobian group arithmetic in O(g2) operations in the base field, where g is the genus of a curve. The main problem in this paper is whether there exists a method to perform the arithmetic in more general curves. Galbraith, Paulus, and Smart proposed an algorithm to complete the arithmetic in O(g2) operations in the base field for the so-called superelliptic curves. We generalize the algorithm to the class of Cab curves, which includes superelliptic curves as a special case. Furthermore, in the case of Cab curves, we show that the proposed algorithm is not just general but more efficient than the previous algorithm as a parameter a in Cab curves grows large.},
keywords={},
doi={},
ISSN={},
month={January},}
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TY - JOUR
TI - A Fast Jacobian Group Arithmetic Scheme for Algebraic Curve Cryptography
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 130
EP - 139
AU - Ryuichi HARASAWA
AU - Joe SUZUKI
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2001
AB - The goal of this paper is to describe a practical and efficient algorithm for computing in the Jacobian of a large class of algebraic curves over a finite field. For elliptic and hyperelliptic curves, there exists an algorithm for performing Jacobian group arithmetic in O(g2) operations in the base field, where g is the genus of a curve. The main problem in this paper is whether there exists a method to perform the arithmetic in more general curves. Galbraith, Paulus, and Smart proposed an algorithm to complete the arithmetic in O(g2) operations in the base field for the so-called superelliptic curves. We generalize the algorithm to the class of Cab curves, which includes superelliptic curves as a special case. Furthermore, in the case of Cab curves, we show that the proposed algorithm is not just general but more efficient than the previous algorithm as a parameter a in Cab curves grows large.
ER -