A note on the x-coordinate of points on an elliptic curve in characteristic twoN. P. Smart, A note on the x-coordinate of points on an elliptic curve in characteristic two. Information Processing Letters, 80 (?). ISSN ?, pp. 261–263. October 2001. No electronic version available.
We consider how a linear condition on the bits representing an $x$-coordinate of a point on an elliptic curve over a field of characteristic two can lead to problems bot h in elliptic curve based Diffie-Hellman key agreement and the method of distinguished points for solving the elliptic curve discrete logarithm problem. Easy solutions are proposed which solve the problems in all cases.