Memoirs of the Faculty of Engineering, Okayama University 40巻 1号
2006-01 発行
Morikawa, Yoshitaka
The Graduate School of Natural Science and Technology Okayama University
This paper particularly deals with elliptic curves in the form of E(x, y) = y(2) − x(3) −b = 0, b ∈ F(* q) , where 3 divides q−1. In this paper, we refer to the well-known twist technique as x-twist and propose y-twist. By combining x-twist and y-twist, we can consider six elliptic curves and this paper proposes a method to obtain the orders of these six curves by counting only one order among the six curves.
elliptic curve
twist
third power residue/non-residue