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
본 논문에서는 임베딩 차수가 12인 빠른 Ate 페어링의 구현 기술을 제시합니다. 이 경우 소수차 페어링 친화적 곡선을 찾는 데 문제가 없습니다. E Barreto-Naehrig 곡선과 같은 y2=x3+a, a∈Fp. 곡선의 경우, G2 ⊂ E(Fp12 으로 G'2 in 서브필드 트위스트 타원 곡선 E'(Fp2) 스칼라 곱셈의 속도를 높입니다. G2 Miller의 알고리즘에서 분모 계산을 제거합니다. 본 논문에서는 적절한 하위 필드 산술 연산을 사용하여 Miller 알고리즘 계산의 약 30% 개선을 주로 제공합니다. 또한 BN 곡선의 효율적인 매개변수 설정도 제공합니다. 언제 p 은 254비트 소수, 임베딩 등급은 12, 프로세서는 Pentium4(3.6GHz)이므로 제안하는 알고리즘은 최종 지수화를 포함하여 13.3ms 만에 Ate pairing을 계산하는 것을 보여준다.
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Masataka AKANE, Yasuyuki NOGAMI, Yoshitaka MORIKAWA, "Fast Ate Pairing Computation of Embedding Degree 12 Using Subfield-Twisted Elliptic Curve" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 2, pp. 508-516, February 2009, doi: 10.1587/transfun.E92.A.508.
Abstract: This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y2=x3+a, a∈Fp. For the curve, an isomorphic substitution from G2 ⊂ E(Fp12 into G'2 in subfield-twisted elliptic curve E'(Fp2) speeds up scalar multiplications over G2 and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.508/_p
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@ARTICLE{e92-a_2_508,
author={Masataka AKANE, Yasuyuki NOGAMI, Yoshitaka MORIKAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Fast Ate Pairing Computation of Embedding Degree 12 Using Subfield-Twisted Elliptic Curve},
year={2009},
volume={E92-A},
number={2},
pages={508-516},
abstract={This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y2=x3+a, a∈Fp. For the curve, an isomorphic substitution from G2 ⊂ E(Fp12 into G'2 in subfield-twisted elliptic curve E'(Fp2) speeds up scalar multiplications over G2 and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.},
keywords={},
doi={10.1587/transfun.E92.A.508},
ISSN={1745-1337},
month={February},}
부
TY - JOUR
TI - Fast Ate Pairing Computation of Embedding Degree 12 Using Subfield-Twisted Elliptic Curve
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 508
EP - 516
AU - Masataka AKANE
AU - Yasuyuki NOGAMI
AU - Yoshitaka MORIKAWA
PY - 2009
DO - 10.1587/transfun.E92.A.508
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2009
AB - This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y2=x3+a, a∈Fp. For the curve, an isomorphic substitution from G2 ⊂ E(Fp12 into G'2 in subfield-twisted elliptic curve E'(Fp2) speeds up scalar multiplications over G2 and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.
ER -