A Novel Elliptic Curve Scalar Multiplication Algorithm against Power Analysis

Algorithm 1

NAF of a positive integer 𝑘.

Input: Positive integer 𝑘,𝑘 = (𝑘_𝑙−1,𝑘_𝑙−2,…,𝑘₀)₂

Output: 𝑘_NAF, 𝑘_NAF = (𝑘_𝑙,𝑘_𝑙−1,𝑘_𝑙−2,…,𝑘₀)_NAF

(1) i = 0.

(2) While (k > 0) do

    (2.1) if (k is odd) then

     (2.2) 𝑘_𝑖= 2 − (k mod 4);

     (2.3) else

     (2.4) 𝑘_𝑖= 0;

     (2.5) k = (𝑘−𝑘_𝑖)/2;

     (2.6) 𝑖=𝑖+1;

(3)Return (k).