The patent badge is an abbreviated version of the USPTO patent document. The patent badge does contain a link to the full patent document.
The patent badge is an abbreviated version of the USPTO patent document. The patent badge covers the following: Patent number, Date patent was issued, Date patent was filed, Title of the patent, Applicant, Inventor, Assignee, Attorney firm, Primary examiner, Assistant examiner, CPCs, and Abstract. The patent badge does contain a link to the full patent document (in Adobe Acrobat format, aka pdf). To download or print any patent click here.
Patent No.:
Date of Patent:
Feb. 12, 2013
Filed:
Nov. 30, 2009
Yasuyuki Nogami, Okayama, JP;
Yumi Sakemi, Okayama, JP;
Yoshitaka Morikawa, Okayama, JP;
National University Corporation Okayama University, Okayama-shi, JP;
Abstract
Provided are a scalar multiplier and a scalar multiplication program for performing a scalar multiplication at a high speed. In computing a scalar multiplication [s]P of a rational point P of an additive group E(F) including rational points on an elliptic curve where a characteristic p, an order r, and a trace t of a Frobenius endomorphism at an embedding degree k=12 using an integer variable χ are given by: p(χ)=36χ−36χ+24χ−6χ+1, r(χ)=36χ−36χ+18χ−6χ+1=p(χ)+1−t(χ), t(χ)=6χ+1, the scalar multiplication [s]P is computed as: [s]P=([A]φ'+[B])P, using a Frobenius map φ′given by: [p]P=φ′(P) assuming that a twist degree d is 6 and a positive integer e is 2 where k=d×e.