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 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.
| 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 |
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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.
In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E92-A, No. 2, 02.2009, p. 508-516.Research output: Contribution to journal › Article
}
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
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 -