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In this paper, the authors discuss identity-based encryption in multiple PKG environment. They formulate the security notions for multi-receiver multi-PKG Identity-Based Encryption (IBE) and present an efficient multi-receiver IBE scheme which is proven secure against a new hard problem called N-xDBDH in random oracle model. In order to simplify the key management in Public Key Infrastructure (PKI), Shamir in 1984 first formulated the concept of Identity-Based Cryptography, in which the user could choose an arbitrary string describing his/her identity as the public key, and the corresponding private key is extracted from a trusted "Private Key Generator" (PKG for short).
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