Simultaneous multiple expansion

Question

I am working on algorithm called as Simultaneous multiple exponentiation, I need to understand the mathematical meaning, like from $j=0$ to $k-1$, how, we calculate the value for $G_i$? What does the mathematical expression mean?

$For\space\ i\space\ = 1 \space\ to\space\ (2^k-1):G_i\leftarrow\prod_{j=0}^{k-1}g_j^{i_j}\space \text{where} \space i=(i_{k-1}\cdots i_0)_2$

Thanks in advance.

Answer 1

This simply means the value of i inside the 'j' loop will be either 0 or 1. And since, i varies from 0 to k, we represent the g_j in the binary values from 0 to 7. For example: if k =3, therefore, i will vary from i = 0 to 7, and another for loop for j will vary from 0 to 2. Therefore, for i=0 to 7, inside j loop we represent i as below:

2 1 0
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

By this, we will get the value for G_i from i =0 to 7.