A method for distinguishing the two candidate elliptic curves in CM method

Yasuyuki Nogami, Yoshitaka Morikawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

In this paper, we first introduce a shift product-based polynomial transformation. 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 CM method algorithm. Based on this property, we propose a method to check the parity by using the shift product-based polynomial transformation. For a 160-bits prime number as the characteristic, the proposed method carries out the parity check about 20 times faster than the conventional method when 4 divides the characteristic minus 1.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science
EditorsC. Park, S. Chee
Pages249-260
Number of pages12
Volume3506
Publication statusPublished - 2005
Event7th International Conference on Information Security and Cryptology - ICISC 2004 - Seoul, Korea, Republic of
Duration: Dec 2 2004Dec 3 2004

Other

Other7th International Conference on Information Security and Cryptology - ICISC 2004
CountryKorea, Republic of
CitySeoul
Period12/2/0412/3/04

Fingerprint

Polynomials

Keywords

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

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

Cite this

Nogami, Y., & Morikawa, Y. (2005). A method for distinguishing the two candidate elliptic curves in CM method. In C. Park, & S. Chee (Eds.), Lecture Notes in Computer Science (Vol. 3506, pp. 249-260)

A method for distinguishing the two candidate elliptic curves in CM method. / Nogami, Yasuyuki; Morikawa, Yoshitaka.

Lecture Notes in Computer Science. ed. / C. Park; S. Chee. Vol. 3506 2005. p. 249-260.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nogami, Y & Morikawa, Y 2005, A method for distinguishing the two candidate elliptic curves in CM method. in C Park & S Chee (eds), Lecture Notes in Computer Science. vol. 3506, pp. 249-260, 7th International Conference on Information Security and Cryptology - ICISC 2004, Seoul, Korea, Republic of, 12/2/04.
Nogami Y, Morikawa Y. A method for distinguishing the two candidate elliptic curves in CM method. In Park C, Chee S, editors, Lecture Notes in Computer Science. Vol. 3506. 2005. p. 249-260
Nogami, Yasuyuki ; Morikawa, Yoshitaka. / A method for distinguishing the two candidate elliptic curves in CM method. Lecture Notes in Computer Science. editor / C. Park ; S. Chee. Vol. 3506 2005. pp. 249-260
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