I am trying to implement a PoC of some variant of monero.
Currently for start, I want to generate the expression G*a*i^2 given all the scalars (a,i,2).
I've lost my way while looking at Monero libraries since the structs and the names of the functions and their inputs/outputs are not clear and well documented.
Assuming G is the base point and i is a scalar (the convention is to write points in capital letters and scalars in lowercase letters):
rct::key tmp;
sc_mul(i.bytes, i.bytes, i.bytes); // i = i^2
sc_mul(tmp.bytes, a.bytes, i.bytes); // tmp = a * i^2
rct::scalarmultBase(tmp, tmp); // tmp = a * i^2 * G
The rct API is easier to use than the fe/ge API, but it has a single type for points and scalars, which make it more error prone. sc_mul (scalar multiplication) is the fe API, and scalarmultBase is the rct API.
i^30 ; is there an efficient way to do it? (the naive way of doing it in an iterative manner seems really inefficient).
i is of type key, while also temp. Though, temp is a point on the curve and i is a scalar. How is it possible?