Representation of Torsion Points on Pairing Curves of Embedding Degree 1 [in Japanese]
Access this Article
Search this Article
Recent efficient pairings such as Ate pairing use two efficient rational point subgroups such thatπ(P) = P and π(Q) = [p]Q, where π, p, P, and Q are the Frobenius map for rational point, thecharacteristic of definition field, and torsion points for pairing, respectively. This relation accelerates notonly pairing but also pairing–related operations such as scalar multiplications. It holds in the case thatthe embedding degree k divides r − 1, where r is the order of torsion rational points. Thus, such a casehas been well studied. Alternatively, this paper focuses on the case that the degree divides r + 1 butdoes not divide r − 1. Then, this paper shows a multiplicative representation for r–torsion points basedon the fact that the characteristic polynomial f(π) becomes irreducible over Fr for which π also plays arole of variable.
- Memoirs of the Faculty of Engineering, Okayama University
Memoirs of the Faculty of Engineering, Okayama University 47, 19-24, 2013-01
Faculty of Engineering, Okayama University