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Waters' variant of the Boneh-Boyen IBE scheme is attractive because of its efficiency, applications, and security attributes, but suffers from a relatively complex proof with poor concrete security. This is due in part to the proof's "Artificial abort" step, which has then been inherited by numerous derivative works. It has often been asked whether this step is necessary. The authors' show that it is not, providing a new proof that eliminates this step. The new proof is not only simpler than the original one but offers better concrete security for important ranges of the parameters. As a result, one can securely use smaller groups, resulting in significant efficiency improvements.
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