I am reading the source of
pbc_bce library which implements the Boneh Gentry Waters broadcast encryption scheme. In this paper the authors use for their construction a bilinear group $G$ and a bi-linear map $e$ but in the source of
pbc_bce I find the implementation of the bi-linear map. Which map is used for the pairing?
I ve read the paper a lot of times, but I am not sure that I have understood it. Their first construction begins with "Let $G$ be a bi-linear group..". The proof that $D(E(K)) = K$ make use of the properties of a bi-linear map, e.g.: $e(a \cdot x,b) = e(a,b) \cdot e(x,b)$. That's why expected them to expand on the maps. Yet, they didn't.
The paper merely states on page 1 and 2:
Our constructions use groups with an efficiently computable bilinear map. while section “2.2 Bilinear Maps” limits itself to (quote)
briefly review the necessary facts about bilinear maps and bilinear map groups.
Am I missing something? How is this not related to some specific maps?