The Orders of Elliptic Curves y(2) = x(3) + b, b ∈ F(* q)

• Nogami Yasuyuki

• Morikawa Yoshitaka

抄録

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.

収録刊行物

• Memoirs of the Faculty of Engineering, Okayama University

  Memoirs of the Faculty of Engineering, Okayama University 40 (1), 83-94, 2006-01

  Faculty of Engineering, Okayama University

キーワード

• elliptic curve
• twist
• third power residue/non-residue

詳細情報

• CRID: 1390853649525360384
• NII論文ID: 120002308548
• NII書誌ID: AA10699856
• ISSN: 04750071
• DOI: 10.18926/14126
• Web Site: https://ousar.lib.okayama-u.ac.jp/14126
• 本文言語コード: en
• データソース種別:
  • JaLC
  • IRDB
  • CiNii Articles