With the Brickell, Gordon, McCurley and Wilson (BGMW) method [1] we can setup fast exponentiation using pre-computed values. With this we have the form of \(g^n\) and where we store the precomuted values of \(g^{x_0}\), \(g^{x_1}\) ... \(g^{x_{m-1}}\), we find the decomposition of:
\(n=\sum_{i=0}^{m=1} a_i x_i \)
The core application of this is where we have a fixed value of \(g\), and can thus build up pre-computed values (\(g^{x_0}\), \(g^{x_1}\) ... \(g^{x_{m-1}}\)) in order to compute \(g^n\).