on pg. 378 section 2 (Overview) it says "We let G be a multiplicative group of prime order p , and g be a generator of G. We let e : G x G –> $G_T$" be a bilinear map.
If somebody could please break each piece of this into smaller parts I would really appreciate it. Here is my attempt:
G is a multiplicative group in order p. Since G is cyclic this means any member of G multiplied by any integer mod p yields identity (1).
g being the generator, means that you always start with g. So you can raise g to a power or you can multiply g by a random integer. But you always have to get 1 mod p for it to be a member of G.
Before looking at binlinear map, I thought I should first read what a linear map is. According to wikipedia, a linear map always yields the same subspace of the input subspaces. So bilinear I think you can end up with something that is not linear (like an elliptic curve?).
My understanding of all this is quite fuzzy and I would appreciate it if someone could explain these to me in simple English or easy-to-understand drawings.
Best Answer
$G$ is not the group of integers mod $p$.