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it the following example for page 56 of the book http://www.craigcostello.com.au/pairings/PairingsForBeginners.pdf I could not understand how the author found the Weil pairing of two points p and Q. I attached the picture of the example. Can you help me to this? Thanks. enter image description here

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They used Miller's algorithm, which is explained in the next chapter.

(To be concrete, they used a implementation in Magma which is available in the author's website)

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  • $\begingroup$ Sorry, I do not know how to work with Magma. I should to understand ABE and try to understand pairing for that. So, I do not know that if I would need to Magma or not? What is your idea? $\endgroup$
    – tesoke
    Commented Mar 2, 2018 at 2:19
  • $\begingroup$ @tesoke you don't need to know Magma to understand the book. But it certainly helps if you want a more concrete understanding. If you don't have access to Magma, you could rewrite the scripts in Sage - it would be a good exercise. $\endgroup$
    – Conrado
    Commented Mar 2, 2018 at 12:30

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