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I am trying to find a method of implementing identity based cryptography to generate key pairs without the use of a trusted PKG that holds the private keys. Has there been any solutions to overcoming this challenge?

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It's not possible to completely get rid of the PKG, but one can limit the amount of trust on a (single) PKG through distributed key generation --- see BF01,§6. On the other hand, one could hold the PKG accountable in case it behaves malicously --- see Goy07.

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