IEICE TRANSACTIONS on Fundamentals
Fast Ate Pairing Computation of Embedding Degree 12 Using Subfield-Twisted Elliptic Curve
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.2 pp.508-516
- Publication Date
- 2009/02/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E92.A.508
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
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
Copy
@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},}
Copy
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 -
English
