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  1. I have seen authors taking $G_1=G_2=G_T=G$ to be the same group of prime order $q$.

  2. What I know is that for pairing of type $$e:G_1\times G_2\rightarrow G_T,$$ size of the element in the target group is $kn$ where $n$ is the size of an element in $G_1$ and $k$ is the embedding degree.

Source: A New Family of Pairing-Friendly elliptic curves by Michael Scott and Aurore Guillevic. and this question

I am confused as it looks like these two points are contradicting each other.

Shweta Aggrawal
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