Name
Title | ||
|---|---|---|
Scalar Multiplication Using Frobenius Expansion Over Twisted Elliptic Curve For Ate Pairing Based Cryptography |
Abstract | ||
|---|---|---|
For ID-based cryptography, not only pairing but also scalar multiplication must be efficiently computable. In this paper, we propose a scalar multiplication method on the circumstances that we work at Ate pairing with Barreto-Naehrig (BN) curve. Note that the parameters of BN curve are given by a certain integer, namely mother parameter. Adhering the authors' previous policy that we execute scalar multiplication on subfield-twisted curve (E) over tilde (F-p2) instead of doing on the original curve E(F-p12), we at first show sextic twisted subfield Frobenius mapping (ST-SFM) in E(Fp2). On BN curves, note (phi) over tilde is identified with the scalar multiplication by p. However a scalar is always smaller than the order r of BN curve for Ate pairing, so ST-SFM does not directly applicable to the above circumstances. We then exploit the expressions of the curve order r and the characteristic p by the mother parameter to derive some radices such that they are expressed as a polynomial of p. Thus, a scalar multiplication [s] can be written by the series of ST-SFMs (phi) over tilde. In combination with the binary method or multi-exponentiation technique, this paper shows that the proposed method runs about twice or more faster than plain binary method. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1587/transfun.E92.A.182 | IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES |
Keywords | Field | DocType |
Ate pairing, BN curve, scalar multiplication, Frobenius mapping, twisted subfield computation | Integer,Discrete mathematics,Scalar multiplication,Polynomial,Pairing-based cryptography,Scalar (physics),Pairing,Mathematics,Elliptic curve,Binary number | Journal |
Volume | Issue | ISSN |
E92A | 1 | 0916-8508 |
Citations | PageRank | References |
8 | 0.63 | 7 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yasuyuki Nogami | 1 | 146 | 52.44 |
| Yumi Sakemi | 2 | 48 | 7.49 |
| Takumi Okimoto | 3 | 8 | 0.63 |
| Kenta Nekado | 4 | 44 | 4.07 |
| Masataka Akane | 5 | 32 | 2.51 |
| Yoshitaka Morikawa | 6 | 100 | 14.92 |