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Secure Identity Based Encryption without random oracles

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TLDR
Boneh and Franklin this paper presented a fully secure identity based encryption scheme whose proof of security does not rely on the random oracle heuristic. Security is based on the Decision Bilinear Diffie-Hellman assumption.
Abstract
We present a fully secure Identity Based Encryption scheme whose proof of security does not rely on the random oracle heuristic. Security is based on the Decision Bilinear Diffie-Hellman assumption. This solves an open problem posed by Boneh and Franklin in 2001.

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