A Novel Elliptic Curve Scalar Multiplication Algorithm against Power Analysis

Algorithm 2

Binary NAF method for scalar multiplication.

Input: Positive integer 𝑘, 𝑃∈𝐸

Output: 𝑄=𝑘𝑃

(1) Use Algorithm 1 to compute 𝑘_NAF.

(2) 𝑄=𝑂.

(3) For 𝑖 from 𝑙−1 downto 0 do

   (3.1) Q = 2Q.

    (3.2) If 𝑘_𝑖 = 1 then 𝑄=𝑄+𝑃;

    (3.3) If 𝑘_𝑖= −1 then 𝑄=𝑄−𝑃;

(4) Return (Q).