Exponentiating in Pairing Groups

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Provided by: Microsoft Research
Topic: Security
Format: PDF
At the turn of the century it was shown that elliptic curves can be used to build powerful cryptographic primitives: bilinear pairings. Pairings are used in a large variety of protocols, and even when considering the recent breakthrough paper which shows how to instantiate multi-linear maps using ideal lattices, pairings remain the preferred choice for a bilinear map due to their superior performance. Algorithms to compute cryptographic pairings involve computations on elements in all three pairing groups, G1, G2 and GT, but protocols usually require many additional standalone exponentiations in any of these three groups.
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