Number of curves in the generalized Edwards form with minimal even cofactor of the curve order

Number of curves in the generalized Edwards form with minimal even cofactor of the curve order We analyze properties of points of orders 2, 4, and 8 of a curve in the generalized Edwards form. Arithmetic for group operations with singular points of these curves is introduced. We propose a classification of curves in the Edwards form into three disjoint classes. Formulas for the number of curves of order 4n of different classes are obtained. Works of other authors are critically analyzed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Number of curves in the generalized Edwards form with minimal even cofactor of the curve order

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946017010082
Publisher site
See Article on Publisher Site

Abstract

We analyze properties of points of orders 2, 4, and 8 of a curve in the generalized Edwards form. Arithmetic for group operations with singular points of these curves is introduced. We propose a classification of curves in the Edwards form into three disjoint classes. Formulas for the number of curves of order 4n of different classes are obtained. Works of other authors are critically analyzed.

Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 23, 2017

References

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