## CryptoDB

### Naoki Kanayama

#### Publications

Year
Venue
Title
2010
EPRINT
In 2007, Stange proposed a novel method of computing the Tate pairing on an elliptic curve over a finite field. This method is based on elliptic nets, which are maps from $\mathbb{Z}^n$ to a ring that satisfy a certain recurrence relation. In this paper, we explicitly give formulae for computing some variants of the Tate pairing: Ate, Ate$_i$, R-Ate and Optimal pairings, based on elliptic nets. We also discuss their efficiency by using some experimental results.
2007
EPRINT
The Ate pairing and the twisted Ate pairing for ordinary elliptic curves which are generalizations of the $\eta_T$ pairing for supersingular curves have previously been proposed. It is not necessarily the case that both pairings are faster than the Tate pairing. In this paper we propose optimized versions of the Ate and twisted Ate pairings with the loop reduction method and show that both pairings are always at least as fast as the Tate pairing. We also provide suitable families of elliptic curves that our optimized Ate and optimized twisted Ate pairings can be computed with half the loop length compared to the Tate pairing.

#### Coauthors

Florian Hess (1)
Seiichi Matsuda (1)
Naoki Ogura (1)
Eiji Okamoto (2)
Shigenori Uchiyama (1)