Titlebook: Arithmetic of Finite Fields; 6th International Wo Sylvain Duquesne,Svetla Petkova-Nikova Conference proceedings 2016 Springer International

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A Brief History of PairingsPairings are a relatively new tool in cryptography. Recent progress on the attack algorithms have changed the security estimations. We make a list of pairing families and explain their advantages but also their weaknesses.

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Adequate Elliptic Curves for Computing the Product of , Pairingsspecially when . as mentioned in [.], KSS16 curves are recommended for computing product of . pairings. Furthermore, we prove that the curve presented by Zhang et . [.] is not resistant against small subgroup attacks. We provide an example of KSS16 curve protected against such attacks.

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