A note on the x-coordinate of points on an elliptic curve in characteristic two.N. P. Smart, A note on the x-coordinate of points on an elliptic curve in characteristic two.. CSTR-00-019, Department of Computer Science, University of Bristol. December 2000. PDF, 126 Kbytes.
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 both 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.