4.2 The left-to-right binary method

With the same parameters E, P, n, and v which are used in the RLB method, the computation of vP using the LRB method can be done easily. A scalar v can be written in a binary representation string (et � 1, …, e1, e0)2. Let us start with a point Q in E(Fp), where Q = ∞. With the i index which takes the values t � 1,…, 1, 0, then the computation of 2Q can be done and plugged into Q. After then, the value Q = Q þ P is computed. The processing continues until the last value 0. Therefore, the last computed value of a point Q is the scalar multiplication point vP. The LRB method can be summarized in Algorithm (4.2) [1].
