A method for distinguishing the two candidate elliptic curves in the complex multiplication method

Yasuyuki Nogami, Mayumi Obara, Yoshitaka Morikawa

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we particularly deal with no Fp-rational two-torsion elliptic curves, where Fp is the prime field of the characteristic p. First we introduce a shift product-based polynomial transform. Then, we show that the parities of (#E - 1)/2 and (#E′ - 1)/2 are reciprocal to each other, where #E and #E′ are the orders of the two candidate curves obtained at the last step of complex multiplication (CM)-based algorithm. Based on this property, we propose a method to check the parity by using the shift product-based polynomial transform. For a 160 bits prime number as the characteristic, the proposed method carries out the parity check 25 or more times faster than the conventional checking method when 4 divides the characteristic minus 1. Finally, this paper shows that the proposed method can make CM-based algorithm that looks up a table of precomputed class polynomials more than 10 percent faster.

Original languageEnglish
Pages (from-to)745-760
Number of pages16
JournalETRI Journal
Volume28
Issue number6
Publication statusPublished - Dec 2006

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Polynomials
Torsional stress

Keywords

  • CM method
  • Irreducible cubic polynomial
  • Quadratic power residue/non-residue

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Networks and Communications

Cite this

A method for distinguishing the two candidate elliptic curves in the complex multiplication method. / Nogami, Yasuyuki; Obara, Mayumi; Morikawa, Yoshitaka.

In: ETRI Journal, Vol. 28, No. 6, 12.2006, p. 745-760.

Research output: Contribution to journalArticle

Nogami, Yasuyuki ; Obara, Mayumi ; Morikawa, Yoshitaka. / A method for distinguishing the two candidate elliptic curves in the complex multiplication method. In: ETRI Journal. 2006 ; Vol. 28, No. 6. pp. 745-760.
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