Cryptology ePrint Archive: Report 2009/586

A mean value formula for elliptic curves

Rongquan Feng and Hongfeng Wu

Abstract: It is proved in this paper that for any point on an elliptic curve, the mean value of $x$-coordinates of its $n$-division points is the same as its $x$-coordinate and the mean value of $y$-coordinates of its $n$-division points is the $n$ times of its $y$-coordinate.

Category / Keywords: foundations / elliptic curves, point multiplication, division polynomial

Date: received 1 Dec 2009, last revised 15 Jul 2010

Contact author: whfmath at gmail com

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Version: 20100716:052455 (All versions of this report)

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