A Novel Elliptic Curve Scalar Multiplication Algorithm against Power Analysis

Algorithm 5

Zhang, Chen, Xiao's algorithm.

Input: 𝑃,𝑘 = (𝑘_𝑙−1,𝑘_𝑙−2,…,𝑘₀)₂

Output: 𝑄=[𝑘]𝑃

(1) Select a random 𝑟;

    𝑟=(𝑟_𝑙−1,𝑟_𝑙−2,…,𝑟₀)₂;

    𝑘^′=𝑘−𝑟;

(2) HBF(𝑟,𝑙);

(3) For 𝑖 from 0 downto 𝑙−1

    If 𝑟+𝑘^′_𝑖=0

    (𝑘^′_𝑙−1,…,𝑘^′_𝑖+1) +𝑘^′_𝑖,𝑘^′_𝑖 = −𝑘^′_𝑖

(4) Construct a pre-computation table 𝑇

    𝑇=𝑂;𝑇[1]=𝑃;𝑇[−1]=−𝑃;

    𝑇[2] = 2𝑃; 𝑇[−2] = −2𝑃;

(5) For 𝑖 from 𝑙−1 downto 0 do

     (5.1) 𝑇=2𝑇;

     (5.2) 𝑇=𝑇+𝑇[𝑟+𝑘^′_𝑖];

(6) Return (𝑇).