Abstract
It is said that the lower bound of the number of iterations of Miller's algorithm for pairing calculation is log2 r/φ(k), where φ(·) is the Euler's function, r is the group order, and k is the embedding degree. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from ⌊log2 r⌋ to ⌊log2(t-1)⌋, where t is the Frobenius trace. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ." For such a curve, this paper gives integer variable χ-based Ate (Xate) pairing that achieves the lower bound. In the case of the well-known Barreto-Naehrig pairing-friendly curve, it reduces the number of loops to ⌊log 2χ⌋. Then, this paper optimizes Xate pairing for Barreto-Naehrig curve and shows its efficiency based on some simulation results.
| Original language | English |
|---|---|
| Pages (from-to) | 1859-1867 |
| Number of pages | 9 |
| Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
| Volume | E92-A |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Aug 2009 |
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Keywords
- Ate pairing
- Miller's algorithm
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
- Signal Processing
Cite this
Integer variable χ-based cross twisted Ate pairing and its optimization for Barreto-Naehrig curve. / Nogami, Yasuyuki; Sakemi, Yumi; Kato, Hidehiro; Akane, Masataka; Morikawa, Yoshitaka.
In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E92-A, No. 8, 08.2009, p. 1859-1867.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Integer variable χ-based cross twisted Ate pairing and its optimization for Barreto-Naehrig curve
AU - Nogami, Yasuyuki
AU - Sakemi, Yumi
AU - Kato, Hidehiro
AU - Akane, Masataka
AU - Morikawa, Yoshitaka
PY - 2009/8
Y1 - 2009/8
N2 - It is said that the lower bound of the number of iterations of Miller's algorithm for pairing calculation is log2 r/φ(k), where φ(·) is the Euler's function, r is the group order, and k is the embedding degree. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from ⌊log2 r⌋ to ⌊log2(t-1)⌋, where t is the Frobenius trace. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ." For such a curve, this paper gives integer variable χ-based Ate (Xate) pairing that achieves the lower bound. In the case of the well-known Barreto-Naehrig pairing-friendly curve, it reduces the number of loops to ⌊log 2χ⌋. Then, this paper optimizes Xate pairing for Barreto-Naehrig curve and shows its efficiency based on some simulation results.
AB - It is said that the lower bound of the number of iterations of Miller's algorithm for pairing calculation is log2 r/φ(k), where φ(·) is the Euler's function, r is the group order, and k is the embedding degree. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from ⌊log2 r⌋ to ⌊log2(t-1)⌋, where t is the Frobenius trace. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ." For such a curve, this paper gives integer variable χ-based Ate (Xate) pairing that achieves the lower bound. In the case of the well-known Barreto-Naehrig pairing-friendly curve, it reduces the number of loops to ⌊log 2χ⌋. Then, this paper optimizes Xate pairing for Barreto-Naehrig curve and shows its efficiency based on some simulation results.
KW - Ate pairing
KW - Miller's algorithm
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UR - http://www.scopus.com/inward/citedby.url?scp=84881008209&partnerID=8YFLogxK
U2 - 10.1587/transfun.E92.A.1859
DO - 10.1587/transfun.E92.A.1859
M3 - Article
AN - SCOPUS:84881008209
VL - E92-A
SP - 1859
EP - 1867
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 - 8
ER -