### 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 y^{2} = x^{3} + a, a ∈ F_{p}. For the curve, an isomorphic substitution from G_{2} C E(F_{p}
^{12}) into G _{2} in subfield-twisted elliptic curve E(Fp2 ) speeds up scalar multiplications over G_{2} 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.

Original language | English |
---|---|

Pages (from-to) | 508-516 |

Number of pages | 9 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E92-A |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2009 |

### Fingerprint

### Keywords

- Ate pairing
- Fast computing
- Subfield arithmetic operation
- Twist

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
- Signal Processing

### Cite this

**Fast Ate pairing computation of embedding degree 12 using subfield-twisted elliptic curve.** / Akane, Masataka; Nogami, Yasuyuki; Morikawa, Yoshitaka.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E92-A, no. 2, pp. 508-516. https://doi.org/10.1587/transfun.E92.A.508

}

TY - JOUR

T1 - Fast Ate pairing computation of embedding degree 12 using subfield-twisted elliptic curve

AU - Akane, Masataka

AU - Nogami, Yasuyuki

AU - Morikawa, Yoshitaka

PY - 2009/2

Y1 - 2009/2

N2 - 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 C E(Fp 12) 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.

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 C E(Fp 12) 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.

KW - Ate pairing

KW - Fast computing

KW - Subfield arithmetic operation

KW - Twist

UR - http://www.scopus.com/inward/record.url?scp=70449513811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449513811&partnerID=8YFLogxK

U2 - 10.1587/transfun.E92.A.508

DO - 10.1587/transfun.E92.A.508

M3 - Article

AN - SCOPUS:70449513811

VL - E92-A

SP - 508

EP - 516

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 2

ER -