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Pairings have now been used for constructive applications in cryptography for around eight years. In that time the range of applications has grown from a relatively narrow one of identity based encryption and signatures, through to more advanced protocols. In addition implementors have realised that pairing protocols once presented can often be greatly simplified or expanded using the mathematical structures of different types of pairings. This paper considers another advanced application of pairings, namely to the Direct Anonymous Attestation (DAA) schemes as found in the Trusted Computing Group standards. They show that a recent DAA proposal can be further optimized by transferring the underlying pairing groups from the symmetric to the asymmetric settings.
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