A Novel Elliptic Curve Scalar Multiplication Algorithm against Power Analysis

Algorithm 3

Ciet and Joye's algorithm.

Input: 𝑃,𝑘 = 𝑘_𝑙−1,𝑘_𝑙−2,…,𝑘₀₂, 𝑆,

  𝑑 = (𝑑_𝑙−1,𝑑_𝑙−2,…,𝑑₀)₂

Output: 𝑄=[𝑘]𝑃+[𝑑]𝑆

(1) 𝑅₁ =𝑃;𝑅₂=𝑆;𝑅₃=𝑃+𝑆;

(2) 𝑗=2𝑑_𝑙−1+𝑘_𝑙−1;𝑅₀=𝑅_𝑗

(3) For 𝑖 from 𝑙−2 downto 0 do

   (3.1) 𝑅₀=2𝑅₀,𝑅₁=𝑃;

   (3.2) c = !(𝑘_𝑖||𝑑_𝑖), 𝑗=2𝑑_𝑖+𝑘_𝑖;

   (3.3) 𝑅_𝑐=𝑅_𝑐+𝑅_𝑗;

(4) Return (𝑅₀).