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All these algorithms have [[Provable security|security proofs]].
== Advantages ==
One of the major advantages of any identity-based encryption scheme is that if there are only a finite number of users, after all users have been issued with keys the third party's secret can be destroyed. This can take place because this system assumes that, once issued, keys are always valid (as this basic system lacks a method of [[key revocation]]). The majority of derivatives of this system which have key revocation lose this advantage.
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