Power signature attack resistant cryptography

摘要

This invention provides a method of computing a multiple k of a point P on an elliptic curve defined over a field, the method including the steps of representing the number k as binary vector k₁, forming an ordered pair of point P₁ and P₂, wherein the points P₁ and P₂ differ at most by P, and selecting each of the bits k_i in sequence, and for each of the k_i, upon k_i being a 0, computing a new set of points P₁′, P₂′ by doubling the first point P₁ to generate the point P₁′ and adding the points P₁ and P₂ to generate the point P₂′ or upon k_i being a 1, computing a new set of points P₁′, P₂′ by doubling the second point P₂ to generate the point P₂′ and adding the points P₁ and P₂ to produce the point P₁′, whereby the doubles or adds are always performed in the same order for each of the bits b_i, thereby minimizing a timing attack on the method. An embodiment of the invention applies to both multiplicative and additive groups.