I have a question about implementation. How is an operation like this implemented?
With all $g$, $k$, and $\alpha$ being large numbers. The thing that I find tricky is that the $k$ is large and in that operation I can't use the modular exponentiation apparently. Once this number is calculated, I can imagine the modular exponentiation with $\alpha$ and $p$ being feasible, but $$g^k$$ can easily explode. What's the right way to implement something like this?