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I have recently read a paper about pairings, which only implemented asymmetric bilinear pairings and it mentiond that $\eta_{T}$ pairing is the most efficient algorithm for symmetric pairings. I wonder is there any software implementation on elliptic curves could achieve both asymmetric and symmetrci pairings e.g. $e(g,g), e(g,h), g\in G_{1}, h\in G_{2}$

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Take a look to MAGMA. To evaluate MAGMA scripts, in their website go to the tab Calculator. Craige Costello has a free tutorial titled Pairings for Beginners with examples of the Weil and Tate pairings in MAGMA.

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  • $\begingroup$ I have found a solution for my project, but I am still grateful for your material. It's good for me to learn more about pairings under ECC. $\endgroup$ – Mkotori Mar 19 at 3:12

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