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I'm trying to get into pairing-based cryptography and I don't see why the group order of the group G in the pairing function

e:G*G-> G_t

has to be a prime number.

I don't find an argument why groups of order p^k for a prime number p and some entire number k cannot be used?

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marked as duplicate by otus, mikeazo Oct 2 '15 at 15:21

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  • $\begingroup$ Where did you read that it has to be prime? $\endgroup$ – mikeazo Oct 2 '15 at 12:01
  • $\begingroup$ en.wikipedia.org/wiki/Pairing-based_cryptography as well in the video right here youtube.com/watch?v=F4x2kQTKYFY in the beginning (+- 4th minute) $\endgroup$ – user28082 Oct 2 '15 at 12:05
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    $\begingroup$ Check out this question and the two answers with upvotes. Especially this answer as I think it answers your question. $\endgroup$ – mikeazo Oct 2 '15 at 12:17
  • $\begingroup$ @mikeazo Thank you very much! So from a mathematical (theoretical) point of view it doesnt matter if it is a primer order or a power of a prime order. the main reason to use prime numbers is to speed up calculations. Furthermore we can most of the time pass from a prime-power order to a prime order groups. $\endgroup$ – user28082 Oct 2 '15 at 12:32

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