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I'm implementing a pairing-based signature scheme using Charm Crypto and PBC, and I'm struggling to understand the relationship between the curves proposed for use with pairings and the pairings themselves.

As I understand it, I can choose between various curves (e.g. I would like to use TypeD curves).

I know that there are different pairings such as the Weil, Tate, Eta and Ate pairing. I also read something about a classification in pairing types. So, MNT (TypeD) curves are useful for Type 3 pairings - or do they define Type 3 pairings? What is the relation to Tate / Ate / Eta pairings? And knowing that, how do I find which specific pairings are used with TypeD curves in Charm?

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