Based on what mentioned in the paper "Pairings For Cryptographers" http://www.sciencedirect.com/science/article/pii/S0166218X08000449 the two inputs of a pairing map are two members of two additive groups on elliptic curves, while the output is an element of a multiplicative group on a finite field. I would like to know is there any mathematical or technical advantages for a multiplicative finite filed group (in compare with an additive elliptic curve group)? or is there any mathematical or technical disadvantages for an additive elliptic curve group (in compare with multiplicative finite filed group)? The following image shows this question more accurate. Please help me
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