A Novel Elliptic Curve Scalar Multiplication Algorithm against Power Analysis

Algorithm 4

Lee's algorithm.

Input: 𝑃,𝑘 =(𝑘_𝑙−1,𝑘_𝑙−2,…,𝑘₀)₂ ,𝑆,𝑚=(𝑚_𝑙−1,𝑚_𝑙−2,…,𝑚₀)₂

Output: 𝑄=[𝑘]𝑃+[𝑚]𝑆

(1) (𝑘,𝑚) is transformed to (𝑘^′,𝑚^′) as Table 1 rule;

(2) Pre-computation

    𝑇[0,1]=𝑆;𝑇[1,0]=𝑃;𝑇[1,1]=𝑃+𝑆;

    𝑇[0,2]=2𝑆;𝑇[0,−2]=−2𝑆;

(3) 𝑅=𝑇[𝑘^′_𝑙−1,𝑚^′_𝑙−1];

(4) For 𝑖 from 𝑙−2 downto 0 do

   (4.1) 𝑅=2𝑅;

    (4.2) 𝑅=𝑅+𝑇[𝑘^′_𝑖,𝑚^′_𝑖];

(5 ) Return (𝑅).