岡山大学環境理工学部研究報告 ISSN 2187-6940
Published by Faculty of Environmental Science and Technology, Okayama University

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The order elliptic curves over finite fields of characteristic two using the Schoof algorithm

Imura Keigo
XiaoDong Wang
Abstract
The elliptic curve cryptosystem is a popular cryptosystem. Its safety depends on the difficulty of the elliptic curve discrete logarithm problem (ECDLP). From the viewpoint of ECDLP, it is very interesting to determine the order of elliptic curves. We tabulate the order of elliptic curves on the finite field of characteristic two using the Schoof algorithm, which is an efficient algorithm to decide orders. The Schoof algorithm is carried out by O(log(8)q). Because the calculation of y(q2) occupies most of the time used to execute the Schoof algorithm, it is necessary to reduce the amount of y(q2) calculations.
Keywords
elliptic curve
order
division polynomial
Schoof algorithm
finite field of characteristic two
ISSN
1341-9099
NCID
AN10529213