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i don't know whether it is correct e(c1,d1) = e(g^s, mk.(y^id.h)^r) =e(g^s,mk).e(g^s, (y^id.h)^r) = e(g^s , g1^α ) . e(g^r , (y^id.h)^s) = e(y , g1^α ) . e(g^r , (y^id.h)^s) e(c2,d2) = e((Y^id.h)^s , g^r) = e((Y^id.h)^s , g^r) therefore e(c1,d1)/e(c2,d2) = e(y , g1^α )


The Extract phase is performed by the Private Key Generator (PKG). Note that in IBE it is not necessary a Public Key Generator, since public keys are just arbitrary bit strings or "identities". So, to sum up: Setup, executed by the PKG. This algorithm creates, among other things, a master key for the PKG. Extract, executed by the PKG. This algorithm ...

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