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some authors claimed that computational performance of a pairing-fee scheme (based on scalar multiplication over an elliptic curve group) is about 1000% more efficient than a pairing based one I would like to know: is there any advantage for a pairing-based scheme?

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You should link the paper. –  mikeazo Jul 13 at 17:08
    
To echo the comment by @mikeazo – can you please provide a link to the paper that contains that claim? (At least mention the title and authors so I can take a look at that paper you’re talking about…) –  e-sushi Jul 17 at 15:42

2 Answers 2

Pairings in cryptography is a very important tool, the introduction of which has developed a new field, that is pairing-based cryptography.

After the independent pioneering work by Joux and by Sakai et al.("Cryptosystems based on pairing"), many pairing-based crypto-systems emerged. In cryptography, pairings are often treated as "black-box", and then we build all kinds of cryptographic schemes making use of assumed properties of the pairings(e.g. bilinearity, non-degeneracy and computability). However, when it comes to the details of them, they can be very complex, especially the implementation and selection of them. Apparently it's undesirable. So, pairings have very excellent value in theory, but in practice, it's hard to implement them. That is why we need to consider the pairing-free cryptographic systems.

Sometimes, it's not a bad idea to treat pairings as "black-box". In this way, we can ignore the details of them and mainly focus on purely cryptographic aspects of the research. With pairings, we can construct many systems that we don't know how to do it previously, the most typical example is the well-known identity-based encryption by Boneh and Franklin.

In a word, parings just have very high theoretical value, but in the practice of application, we have to consider many details.

If you want to have a good knowledge of this aspect, I recommend you to read this paper "Pairings for Cryptographers"

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Thanks for your attention and response. however, i need to know what is the advantage of the output of a pairing map in compare with an output of a simple scalar multiplication of one of the members of elliptic curve based groups [e(aP,bQ) vs. (ab)P or ...] (such as the need to more computations to solve discrete logarithm problem or ...)? is there any advantage for pairings? please help me –  Mohsen Jul 13 at 13:08
    
@Mohsen Then you should make it clear in your question.. –  T.B Jul 13 at 13:16
    
ok. there are many pairing-based and pairing-free key agreement schemes. the authors of pairing-free ones claim that their scheme is much more efficient than pairing-based ones. therefore, what is the reason that some authors try to propose pairing-based key agreement schemes? is there any advantage for pairing-based ones? (or generally, is there any benefits of using pairings?) –  Mohsen Jul 13 at 13:41
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well, for identity-based key agreement schemes most of them are realized with pairings, because we can use the assumed properties of them as I said in my answer. (P.S. you should make your question understood by others and before you ask you should do some job on your own) –  T.B Jul 13 at 14:24
    
Thanks for your attention. actually my major is computer science and i usen –  Mohsen Jul 13 at 14:34

If you can use something more lightweight than pairings then you should skip pairings. There is a technical property of pairings than is not the case with other crypto primitives. And this is the evaluation of multiplications on the exponent that cannot be achieved in other cases. If you need some sort of summation then you encode in the exponent and then you multiply based on same base.

Check this answer also

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Thanks for your attention and response. however, i need to know what is the advantage of the output of a pairing map in compare with an output of a simple scalar multiplication of one of the members of elliptic curve based groups [e(aP,bQ) vs. (ab)P or ...] (such as the need to more computations to solve discrete logarithm problem or ...)? is there any advantage for pairings? please help me –  Mohsen Jul 13 at 13:08
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Well scalar multiplication does not have bilinearity, a pairing does. –  Maeher Jul 13 at 14:21
    
I read "Check this answer also", can you provide a reference for that? and for what you mentioned as my answer "There is a technical property of pairings than is not the case with other.............."? –  Mohsen Jul 14 at 5:37

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