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

Authors:
Yasuyuki Nogami;Yoshitaka Morikawa
Affiliations:
Dept. of Communication Network Engineering, Okayama University, Okayama-shi, Japan;Dept. of Communication Network Engineering, Okayama University, Okayama-shi, Japan
Venue:
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Year:
2004

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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.