[Resource Topic] 2006/220: Multi-Dimensional Montgomery Ladders for Elliptic Curves

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Multi-Dimensional Montgomery Ladders for Elliptic Curves

Authors: Daniel R. L. Brown


Montgomery’s ladder algorithm for elliptic curve scalar multiplication uses only the x-coordinates of points. Avoiding calculation of the y-coordinates saves time for certain curves. Montgomery introduced his method to accelerate Lenstra’s elliptic curve method for integer factoring. Bernstein extended Montgomery’s ladder algorithm by computing integer combinations of two points, thus accelerating signature verification over certain curves. This paper modifies and extends Bernstein’s algorithm to integer combinations of two or more points.

ePrint: https://eprint.iacr.org/2006/220

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