1. A method performed by a system including a processor and memory, the method comprising: obtaining a point on an elliptic curve specified by n point coordinates for a first elliptic curve coordinate system, wherein n is greater than or equal to two; transforming, using the processor, the point from the first elliptic curve coordinate system to a transformed point in a second elliptic curve coordinate system, including performing a linear matrix transformation on the point coordinates using an n row by n column square linear matrix having n*n coefficients, where the linear matrix is invertible; and performing one or more modified field operations on the transformed point, wherein the modified field operations are modified from one or more initial field operations for the first elliptic curve coordinate system for use in the second elliptic curve coordinate system based on an inverse matrix of the linear matrix.