Cryptology ePrint Archive: Report 2014/1014

Double-and-Add with Relative Jacobian Coordinates

Björn Fay

Abstract: One of the most efficient ways to implement a scalar multiplication on elliptic curves with precomputed points is to use mixed coordinates (affine and Jacobian). We show how to relax these preconditions by introducing relative Jacobian coordinates and give an algorithm to compute a scalar multiplication where the precomputed points can be given in Jacobian coordinates. We also show that this new approach is compatible with Meloni’s trick, which was already used in other papers to reduce the number of multiplications needed for a double-and-add step to 18 field multiplications.

Category / Keywords: implementation / elliptic curve, relative Jacobian coordinates, co-Z coordinates, scalar multiplication, double-and-add, precomputed points

Date: received 20 Dec 2014

Contact author: mail at bfay de

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Version: 20141226:231051 (All versions of this report)

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