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The method for elliptic curve scalar multiplication is a method for fast, efficient multiplication of a point on an elliptic curve by a scalar. Two different parameters are used to assign separate projective coordinates to the x-coordinate and the y-coordinate. The x- and y-coordinates are projected by ZLx and ZLy, where Lx and Ly are exponential functions having a common base, i.e., Lx=gnx and Ly=gny, respectively. The use of projective coordinates reduces the number of inversions in scalar multiplication, thereby speeding processing time. Furthermore, since the parameters Lx and Ly are exponential functions, and since the base g is invariant, g−1 can be precomputed and stored. This practically eliminates any further inversions, since Lx−1=(g−1)nx and Ly−1=(g−1)ny so that inversions are simplified to exponentiation by substitution, further speeding processing time and reducing storage requirements.
