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
이 문서의 목표는 유한 필드에 대한 대규모 대수 곡선 클래스의 야코비안 계산을 위한 실용적이고 효율적인 알고리즘을 설명하는 것입니다. 타원 및 초타원 곡선의 경우 야코비안 그룹 산술을 수행하는 알고리즘이 있습니다. O(g2) 기본 필드에서의 작업, 여기서 g 곡선의 종류입니다. 본 논문의 주요 문제는 보다 일반적인 곡선에서 연산을 수행할 수 있는 방법이 존재하는지 여부이다. Galbraith, Paulus 및 Smart는 산술 연산을 완성하는 알고리즘을 제안했습니다. O(g2) 소위 초타원 곡선에 대한 기본 필드에서의 작업입니다. 우리는 알고리즘을 다음 클래스로 일반화합니다. Cab 특수한 경우로 초타원 곡선을 포함하는 곡선. 게다가 다음의 경우 Cab 곡선을 통해 제안된 알고리즘이 단순히 일반적인 것이 아니라 매개변수로서 이전 알고리즘보다 더 효율적이라는 것을 보여줍니다. a in Cab 곡선이 커집니다.
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부
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
부
@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},}
부
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 -